Machine Learning (Theory)

6/26/2009

Netflix nearly done

A $1M qualifying result was achieved on the public Netflix test set by a 3-way ensemble team. This is just in time for Yehuda’s presentation at KDD, which I’m sure will be one of the best attended ever.

This isn’t quite over—there are a few days for another super-conglomerate team to come together and there is some small chance that the performance is nonrepresentative of the final test set, but I expect not.

Regardless of the final outcome, the biggest lesson for ML from the Netflix contest has been the formidable performance edge of ensemble methods.

6/24/2009

Interesting papers at UAICMOLT 2009

Tags: Conferences, Machine Learning, Papers jl@ 2:36 am

Here’s a list of papers that I found interesting at ICML/COLT/UAI in 2009.

  1. Elad Hazan and Comandur Seshadhri Efficient learning algorithms for changing environments at ICML. This paper shows how to adapt learning algorithms that compete with fixed predictors to compete with changing policies. The definition of regret they deal with seems particularly useful in many situation.
  2. Hal Daume, Unsupervised Search-based Structured Prediction at ICML. This paper shows a technique for reducing unsupervised learning to supervised learning which (a) make a fast unsupervised learning algorithm and (b) makes semisupervised learning both easy and highly effective.
  3. There were two papers with similar results on active learning in the KWIK framework for linear regression, both reducing the sample complexity to . One was Nicolo Cesa-Bianchi, Claudio Gentile, and Francesco Orabona Robust Bounds for Classification via Selective Sampling at ICML and the other was Thomas Walsh, Istvan Szita, Carlos Diuk, Michael Littman Exploring compact reinforcement-learning representations with linear regression at UAI. The UAI paper covers application to RL as well.
  4. Ping Li, Improving Compressed Counting at UAI. This paper talks about how to keep track of the moments in a datastream with very little space and computation. I’m not sure I have a use for it yet, but it seems like a cool piece of basic technology.
  5. Mark Reid and Bob Williamson Surrogate Regret Bounds for Proper Losses at ICML. This paper points out that via the integral characterization of proper losses, proper scoring rules can be reduced to binary classification. The results unify and generalize the Probing and Quanting reductions we worked on previously. This paper is also related to Nicolas Lambert’s work, which is quite thought provoking in terms of specifying what is learnable.
  6. Daniel Hsu, Sham M. Kakade and Tong Zhang. A Spectral Algorithm for Learning Hidden Markov Models COLT. This paper shows that a subset of HMMs can be learned using an SVD-based algorithm.
  7. Samory Kpotufe, Escaping the curse of dimensionality with a tree-based regressor at COLT. This paper shows how to directly applying regression in high dimensional vector spaces and have it succeed anyways because the data is naturally low-dimensional.
  8. Shai Ben-David, David Pal and Shai Shalev-Shwartz. Agnostic Online Learning at COLT. This paper characterizes the ability to learn when an adversary is choosing features in the online setting as the “Littlestone dimension”.

6/15/2009

In Active Learning, the question changes

Tags: Active, Questions jl@ 10:54 am

A little over 4 years ago, Sanjoy made a post saying roughly “we should study active learning theoretically, because not much is understood”.

At the time, we did not understand basic things such as whether or not it was possible to PAC-learn with an active algorithm without making strong assumptions about the noise rate. In other words, the fundamental question was “can we do it?”

The nature of the question has fundamentally changed in my mind. The answer is to the previous question is “yes”, both information theoretically and computationally, most places where supervised learning could be applied.

In many situation, the question has now changed to: “is it worth it?” Is the programming and computational overhead low enough to make the label cost savings of active learning worthwhile? Currently, there are situations where this question could go either way. Much of the challenge for the future is in figuring out how to make active learning easier or more worthwhile.

At the active learning tutorial, I stated a set of somewhat more precise research questions that I don’t yet have answer to, and which I believe are worth answering. Here is a bit of an expansion on those questions for those interested.

  1. Is active learning possible in a fully adversarial setting? By fully adversarial, I mean when an adversary controls all the algorithms observations. Some work by Claudio and Nicolo has moved in this direction, but there is not yet a solid answer.
  2. Is there an efficient and effective reduction of active learning to supervised learning? The bootstrap IWAL approach is efficient but not effective in some situations where other approaches can succeed. The algorithm here is a reduction to a special kind of supervised learning where you can specify both examples and constraints. For many supervised learning algorithms, adding constraints seems problematic.
  3. Can active learning succeed with alternate labeling oracles? The ones I see people trying to use in practice often differ because they can provide answers of varying specificity and cost, or because some oracles are good for some questions, but not good for others.
  4. At this point, there have been several successful applications of active learning, but that’s not the same thing as succeeding with more robust algorithms. Can we succeed empirically with more robust algorithms? And is the empirical cost of additional robustness worth the empirical peace-of-mind that your learning algorithm won’t go astray where other more aggressive approaches may do so?

6/3/2009

Functionally defined Nonlinear Dynamic Models

Suppose we have a set of observations over time x1,x2,…,xt and want to predict some future event yt+1. An inevitable problem arises, because learning a predictor h(x1,…,xt) of yt+1 is generically intractable due to the size of the input. To make this problem tractable, what’s necessary is a method for summarizing the relevant information in past observations for the purpose of prediction in the future. In other words, state is required.

Existing approaches for deriving state have some limitations.

  1. Hidden Markov models learned with EM suffer from local minima, use tabular learning approaches which provide dubious generalization ability, and often require substantial a.priori specification of the observations.
  2. Kalman Filters and Particle Filters are very parametric in the sense that substantial information must be specified up front.
  3. Dynamic Bayesian Networks (graphical models through time) require substantial a.priori specification and often require the solution of difficult computational problems to use. Some of these difficulties are representational rather than computational.
  4. The Subspace-ID approach from control theory uses a linear representation, with the basic claim that it works well when all transformations are linear, but not so well when things are nonlinear. (Thanks to Drew for pointing it out.) In making this post, I ran across this two day tutorial which discusses extensions of this idea to nonlinear systems. Unfortunately, I’ll miss the tutorial, and I haven’t found the related paper.

The point of this paper at ICML is that some dynamic systems (those which are “invertible”), can be decomposed into separate bounded resource prediction problems which, when solved, create an implicit definition of state. This allows us to use any general purpose supervised learning algorithm to solve the state formation problem without requiring linearity or any specific representation. When writing papers you don’t generally gush too hard, but it’s fair to say that I’m excited by this approach.

  1. It’s not a known dead end.
  2. It doesn’t require lots of prior specification & information when you have lots of data.
  3. It leverages the huge amount of work that has gone into supervised learning algorithm design.
  4. It works in controlled systems also, where the control is simply another observation.
  5. It works with generalization from the start, rather than requiring the (often awkward) addition of generalization later.
  6. It doesn’t require predicting everything in order to predict what you want.
  7. It can work with very large observation spaces, and can even work better the larger the observation space, because larger observations imply more invertibility.

I expect some people reading this paper will be disappointed that it doesn’t solve all problems. That’s good news for anyone interested in research. For those who aren’t note that this is (in some sense) a generalization of subspace ID, and hence that there are other applications of the approach known to work in practice. Furthermore, we have some sample complexity analysis in the linear case.

It’s relatively rare to have a paper about a new approach to solving a problem as intractable as nonlinear dynamics has proved to be, so if you see a flaw please speak up.

6/1/2009

Multitask Poisoning

Tags: Mathematics, Research jl@ 2:25 am

There are many ways that interesting research gets done. For example it’s common at a conference for someone to discuss a problem with a partial solution, and for someone else to know how to solve a piece of it, resulting in a paper. In some sense, these are the easiest results we can achieve, so we should ask: Can all research be this easy?

The answer is certainly no for fields where research inherently requires experimentation to discover how the real world works. However, mathematics, including parts of physics, computer science, statistics, etc… which are effectively mathematics don’t require experimentation. In effect, a paper can be simply a pure expression of thinking. Can all mathematical-style research be this easy?

What’s going on here is research-by-communication. Someone knows something, someone knows something else, and as soon as someone knows both things, a problem is solved. The interesting thing about research-by-communication is that it is becoming radically easier with improved technology. It’s already possible to communicate with nearly anyone anywhere in the world via {voice, video, text, shared program/website/blog}. As these mechanisms become cheaper in cost and ease of use, we’ll surely see their adoption into many activities. If all mathematical-style research can be sped up by communication, that’s great news for research.

However, I don’t believe it. The essential difficulty is that doing good research often requires the simultaneous understanding of several different things—the problem, all the broken approaches to solving some problem, why they break, and some hint about where to look for a solution. Absorbing and simultaneously keeping in mind this information requires a substantial amount of effort.

The extent of effort required is perhaps most easily understood in collaboration with yourself. Often, a problem is not immediately solved the first time it is thought of, instead a researcher must attack it again and again, until either giving up or finding a solution. A basic parameter in attacking a problem is: How hard is it to resume where you left off?

For many of the problems I’ve worked on, the answer is pretty hard. After weeks of not working on a problem, it might take several hours to refresh my memory with all the simultaneous concerns that go into a solution. Even if I worked on such a problem yesterday, it might take a half hour or an hour to reach a state where I’m prepared to make progress.

Given the difficulty of research, I (and many other people) often struggle in dealing with interruptions. Modern technology has made communication very easy, implying a stream of potential interruptions throughout the day, some of which are undeniably fruitful. And yet, an interruption means the overhead of getting back to thinking must be paid yet again.

Trading off properly between the value of avoiding the overhead and the value of dealing with interruptions is a constant struggle which typically did not exist before before modern communication technology made it prevalent. I think it is common to give in to the interrupts, and effectively cease to be able to do research other than research-by-communication. I’m not ready to do that, so I’ve found it essential to arrange large unused and uninterrupted periods of time for the purpose of doing research.

Although the solution is simple, I’ve often found implementing it challenging in several ways. There is the standard problem that people you deal with don’t understand the overhead of switching tasks in research. However, there is also a more insidious problem. Coping with the modern world requires that at least some portion of our time be devoted to interrupts, which are almost always easier to deal with than research. Dealing with these interrupts therefore can create a bad habit where you seek interrupts to achieve the (short term, easy) gratification of dealing with them. Thus, multitasking creates an internal expectation of multitasking, which makes multitasking preferred, eliminating the ability to do careful research. This is what I think of as multitask poisoning—it’s not just the time lost to swapping some context back in, but also the bad habits of self-interruption that it creates.

I don’t have a good answer to this problem, other than continuing the struggle to preserve substantial contiguous chunks of time for thinking. An alternative sometimes-applicable solution is to reduce the overhead of starting to solve a problem by decomposing the problem into subproblems. Where possible, this is of course valuable, but mathematical research is often almost uniquely undecomposable, because the nature of the problem is that it’s solution is unknown and hence undecomposable. Restated, the real problem is finding a valid decomposition.

I self-interrupted at least 3 times in making this post.

5/30/2009

Many ways to Learn this summer

There are at least 3 summer schools related to machine learning this summer.

  1. The first is at University of Chicago June 1-11 organized by Misha Belkin, Partha Niyogi, and Steve Smale. Registration is closed for this one, meaning they met their capacity limit. The format is essentially an extended Tutorial/Workshop. I was particularly interested to see Valiant amongst the speakers. I’m also presenting Saturday June 6, on logarithmic time prediction.
  2. Praveen Srinivasan points out the second at Peking University in Beijing, China, July 20-27. This one differs substantially, as it is about vision, machine learning, and their intersection. The deadline for applications is June 10 or 15. This is also another example of the growth of research in China, with active support from NSF.
  3. The third one is at Cambridge, England, August 29-September 10. It’s in the MLSS series. Compared to the Chicago one, this one is more about the Bayesian side of ML, although effort has been made to create a good cross section of topics. It’s also more focused on tutorials over workshop-style talks.

5/24/2009

2009 ICML discussion site

Mark Reid has setup a discussion site for ICML papers again this year and Monica Dinculescu has linked it in from the ICML site. Last year’s attempt appears to have been an acceptable but not wild success as a little bit of fruitful discussion occurred. I’m hoping this year will be a bit more of a success—please don’t be shy :-)

I’d like to also point out that ICML’s early registration deadline has a few hours left, while UAI’s and COLT’s are in a week.

5/19/2009

CI Fellows

Tags: CS, Funding, Machine Learning jl@ 3:37 pm

Lev Reyzin points out the CI Fellows Project. Essentially, NSF is funding 60 postdocs in computer science for graduates from a wide array of US places to a wide array of US places. This is particularly welcome given a tough year for new hires. I expect some fraction of these postdocs will be in ML. The time frame is quite short, so those interested should look it over immediately.

5/17/2009

Server Update

Tags: Meta jl@ 3:32 pm

The hunch.net server has been updated. I’ve taken the opportunity to upgrade the version of wordpress which caused cascading changes.

  1. Old threaded comments are now flattened. The system we used to use (Brian’s threaded comments) appears incompatible with the new threading system built into wordpress. I haven’t yet figured out a workaround.
  2. I setup a feedburner account.
  3. I added an RSS aggregator for both Machine Learning and other research blogs that I like to follow. This is something that I’ve wanted to do for awhile.
  4. Many other minor changes in font and format, with some help from Alina.

If you have any suggestions for site tweaks, please speak up.

5/8/2009

Computability in Artificial Intelligence

Normally I do not blog, but John kindly invited me to do so. Since computability issues play a major role in Artificial Intelligence and Machine Learning, I would like to take the opportunity to comment on that and raise some questions.

The general attitude is that AI is about finding efficient smart algorithms. For large parts of machine learning, the same attitude is not too dangerous. If you want to concentrate on conceptual problems, simply become a statistician. There is no analogous escape for modern research on AI (as opposed to GOFAI rooted in logic).

Let me show by analogy why limiting research to computational questions is bad for any field.

Except in computer science, computational aspects play little role in the development of fundamental theories: Consider e.g. set theory with axiom of choice, foundations of logic, exact/full minimax for zero-sum games, quantum (field) theory, string theory, … Indeed, at least in physics, every new fundamental theory seems to be less computable than previous ones. Of course, once a subject has been formalized, further research (a) analyzes the structure of the theory and (b) tries to compute efficient approximations. Only in (b) do computational aspects play a role.

So my question is: Why are computational questions so prevalent in AI research? Here are some unconvincing arguments I’ve heard:

A) Because AI is a subfield of computer science, and the task of computer scientists is to find (efficient) algorithms for well-defined problems?

I think it does not do any (real-world) problem any good to confine it to computer science. Of course, philosophers and cognitive scientists also care about AI, but where are the mathematicians?

B) Because formalizing AI and finding efficient smart programs goes hand-in-hand? Separating these two issues would lead to no, or at best to results which are misleading or useless in the construction of intelligent machines?

I am not aware of any convincing argument that separating the issues of “axiomatizing a field” and “finding efficient solutions” will (likely) fail for AI. The examples above of other fields actually indicate the opposite. Of course, interaction is important to avoid both sides running wild. For instance, von Neumann’s minimax solution for games, albeit infeasible for most games, is the cornerstone of most practical approximations.

C) Because there is some deep connection between intelligence and computation which can not be disentangled?

Sure, you could say that intelligence is by definition about computationally efficient decision making. This is as unconvincing as argument (A). Pointing out that the human brain is a computational device is quite useful in many ways, but doesn’t proves (C) either. Of course, ultimately we want a “fast” smart algorithm. How is AI different from wanting a fast algorithm computing primes, which you derive from a non-algorithmic definition of primes; or drawing fractals?

D) Because AI is trivial if computational issues are ignored? All conceptual problems have already been solved?

Many have expressed ideas that some form of exhaustive search over all possible solutions and picking the “best” one does the job. This works essentially for exactly those problems that are well-defined. For instance, optimal minimax play of a zero-sum game or solving NP complete problems are conceptually trivial, i.e. if computation time is ignored. But in general AI and machine learning, there is not a universally agreed-upon objective function. The Turing test is informal (involves a human judge in the loop), maximizing expected reward (the true distribution is not known, so expectation w.r.t. to what?), etc. The AIXI model, briefly discussed at this blog, is the first complete and formal such criterion, for which, let me phrase it that way, no flaw has yet been identified. Shane Legg’s award-winning thesis gives an informal introduction and contains lots of discussion.

Conceptual and computational problems in AI should be studied jointly as well as separately, but the latter is not (yet) fashionable. When AI was more logic oriented, some good logicians helped develop the foundations of “deductive” AI. Where are the researchers giving modern “inductive” AI its foundation? I am talking about generic learning agents, not classifying i.i.d. data. Reinforcement learners? Well, most of the hard results are from adaptive control theorists, but it’s reassuring to see parts of these communities merging. It’s a pity that so few mathematicians are interested in AI. A field “mathematical AI” with the prestige of “mathematical physics” would be exciting. As a start: 40% of the COLT & ALT papers on generic learning agents, 30% induction, 20% time-series forecasting, 10% i.i.d. Currently it’s reversed.

5/6/2009

Machine Learning to AI

Tags: AI, Machine Learning, Reinforcement jl@ 2:46 am

I recently had fun discussions with both Vikash Mansinghka and Thomas Breuel about approaching AI with machine learning. The general interest in taking a crack at AI with machine learning seems to be rising on many fronts including DARPA.

As a matter of history, there was a great deal of interest in AI which died down before I began research. There remain many projects and conferences spawned in this earlier AI wave, as well as a good bit of experience about what did not work, or at least did not work yet. Here are a few examples of failure modes that people seem to run into:

  1. Supply/Product confusion. Sometimes we think “Intelligences use X, so I’ll create X and have an Intelligence.” An example of this is the Cyc Project which inspires some people as “intelligences use ontologies, so I’ll create an ontology and a system using it to have an Intelligence.” The flaw here is that Intelligences create ontologies, which they use, and without the ability to create ontologies you don’t have an Intelligence. If we are lucky, the substantial effort invested in Cyc won’t be wasted, as it has a large quantity of information stored in a plausibly useful format. If we are unlucky, it fails to even be partially useful, because the format is unnatural for the internal representations of an Intelligence.
  2. Uncertainty second. Many of the older AI programs had no role for uncertainty. If you asked the people working on them, they might agree that uncertainty was an important but secondary concern to be solved after the main problem. Unfortunately, it seems that uncertainty is a primary concern in practice. One example of this is blocks world where a system for planning how to rearrange blocks on a table might easily fail in practice because the robot fails to grab a block properly. Many people think of uncertainty as a second order concern, because they don’t experience uncertainty in their daily lives. I believe this is incorrect—a mental illusion due to the effect that focusing attention on a specific subject implies reducing uncertainty on that subject. More generally, because any Intelligence is a small part of the world, the ability of any intelligence to perceive, understand, and manipulate the world is inherently limited, requiring the ability to deal with uncertainty. For statistics & ML people, it’s important to not breath a sigh of relief too easily, as the problem is pernicious. For example many ML techniques based around conditional independence routinely suffer from excess certainty.
  3. Computation second. Some people try to create an intelligence without reference to efficient computation. AIXI is an extreme example of this sort. The algorithm is very difficult to deploy in practice because there were no computational constraints other than computability designed into it’s creation. It’s important to understand that computational constraints and uncertainty go together: because there are computational constraints, an intelligence is forced to deal with uncertainty since not everything which might follow at a mathematical level can be inferred in the available computational budget.
  4. AI-Hard problems. There was a time when some people thought, “If we could just get a program that mastered chess so well it could beat the best humans, we will learn enough about AI to create an AI.” Deep Blue put that theory to rest. Current efforts on Poker and Go seem more promising, but no one believes they are “AI-Hard” for good reason. It’s not even clear that the Turing Test is a reliable indicator, because (for example) we might imagine that there is Intelligence which can not imitate a human, or that there are programs that can imitate humans well enough to fool humans without being able to achieve everything that an Intelligence could. Perhaps the best evidence is something singularity-style: AI exists when it can substantially improve it’s own abilities.
  5. Asymptopia. In machine learning there are many theorems of the form “learning algorithm A can solve any learning problem in the limit of infinite data”. Here A might be nearest neighbors, decision trees, two-layer neural networks, support vector machines, nonparametric statistics, nonparametric Bayes, or something else. These theorem are ok, but insufficient. Often the algorithms are not computationally acceptable, and even if so, they are not sufficiently efficient with respect to the amount of experience required to learn.

Solving AI is undeniably hard, as evidenced by the amount of time spent on it, and the set of approaches which haven’t succeeded. There are a couple reasons for hope this time. The first is that there is, or soon will be sufficient computation available, unlike the last time. The second is that the machine learning approach fails well, because there are industrial uses for machine learning. Consequently, we can expect a lack of success to still see substantial use in practice. This might sound like “a good downside”, but it’s actually an upside, because it implies that incremental progress has the potential for ultimate success.

Restated at an abstract level: a hard problem can generally be decomposed in many ways into subproblems. Amongst all such decompositions, a good decomposition is one with the property that solutions to the subproblems are immediately useful. The machine learning approach to AI has this goodness property, unlike many other approaches, which partially explains why the ML approach is successful despite “failing” so far to achieve AI.

One reason why AI is hard, is that it turns out tackling general problems in the world undeniably requires a substantial number of different strategies, including learning, searching, and chunking (= constructing macros), all while respecting constraints of computation and robustness to uncertainty. Given this, a fair strategy seems to be first mastering one strategy, and then incorporating others, always checking that that incorporation properly addresses real world problems. In doing this, considering the constraint ignoring approaches as limiting cases of the real system may be helpful.

5/2/2009

Wielding a New Abstraction

This post is partly meant as an advertisement for the reductions tutorial Alina, Bianca, and I are planning to do at ICML. Please come, if you are interested.

Many research programs can be thought of as finding and building new useful abstractions. The running example I’ll use is learning reductions where I have experience. The basic abstraction here is that we can build a learning algorithm capable of solving classification problems up to a small expected regret. This is used repeatedly to solve more complex problems.

In working on a new abstraction, I think you typically run into many substantial problems of understanding, which make publishing particularly difficult.

  1. It is difficult to seriously discuss the reason behind or mechanism for abstraction in a conference paper with small page limits. People rarely see such discussions and hence have little basis on which to think about new abstractions. Another difficulty is that when building an abstraction, you often don’t know the right way to state things.

    Here’s my current attempt: The process of abstraction for learning reductions can start with sample complexity bounds (or online learning against an adversary analysis). A very simple sample complexity bound is that for all sets of hypotheses H, for all distributions D on examples (x,y), and for all confidence parameters d

    Pr(x,y)m~Dm(for all h in H: |e(h,D)-e(h,(x,y)m)| < (ln( |H|/ d )/m)0.5 ) > 1 – d

    Here (x,y)m is a sequence of m IID samples, e(h,D) is the error rate of h on D and e(h,(x,y)m) is the empirical error rate of h on the set of IID samples.

    The previous bound is a very simple example, and yet remarkably complex both to state and to interpret—many people have been lost by the meaning of d. The impact of this complexity is that it is difficult to effectively use these bounds in practical learning algorithm design, particularly in solving more complex learning problems where much more than one bit of prediction is required. This was a central frustration that I ran into in my thesis work. Some progress has been made since then, but it is still quite difficult. The abstraction in the learning reduction setting is:

    1. You throw away d, because it only has a logarithmic dependence anyways.
    2. You eliminate H and m on the theory that intelligent choices for H and m are made in practice.
    3. You eliminate the IID assumption, because it is no longer needed to define things

    The statement then is

    e(A((x,y)m),D)-e(h*,D) < eps

    where A() is the hypothesis output by the learning algorithm, h* is the best possible predictor, and eps is used to parameterize the theorems. This abstraction is radical in some sense, but something radical was needed to yield tractable and useful analysis on the complex problems people need to solve in practice.

  2. A consequence of lack of familiarity, is that people often misread. In reading a paper, there is a temptation to not read carefully and fill in your understanding of things. Most of the time this works out well, but not here. For example, we saw many instances where people inserted IID sample assumptions or other things that simply weren’t there.
  3. Once you get past the lack of familiarity and misunderstandings, there is a feeling that the new abstraction is cheating. To some extent I understand, as I remember learning about abstractions in class, and I remember feeling that they were in some real sense cheating by dropping important details. For example:
    1. Big-O notation provides an upper bound specified up to constants. For example O(log n) computational complexity means there exists a constant c such that the number of operations requires is less than c log n. Big-O can be abused by hiding “constants” larger than the plausible values for the parameters. In machine learning, a particularly egregious case occurs in Bandit analysis where the punchline of some papers is “logarithmic regret”, hiding an arbitrarily large problem dependent constant.
    2. TCP provides a mechanism for reliable transport over an unreliable network. It is a very commonly used mechanism for sending information over the internet—you used TCP in reading this. TCP is both a programming construct and a mechanism for abstracting communicating over a network. The TCP abstraction is broken when the network is too unreliable for it to recover, such as on sketchy wireless networks where the programmer built for the TCP abstraction which wasn’t delivered.
    3. Dimensional analysis is a technique for quick analysis in physics. The basic idea is to just look at the units when estimating some quantity and combine them to get the right unit answer. For example, to compute the distance d traveled after time t with acceleration a, you simply use at2, since that formula is the only way to combine a with units of distance/time2 and t with units of time to get units of distance. This answer is off by a factor of 2 from what a more detailed analysis using integration yields, which is typical. Dimensional analysis can be misleading when the constants are very large. One example is in Gravitation where there is a table with time and distance equated since they are related by a constant—the speed of light 3*108 m/s. For example, E=mc2 becomes E=m.

    Although the above breakages are real, the usefulness of these abstractions, in terms of allowing us to quickly think about and make decisions more than offsets the drawbacks. Indeed, even the breakages stated above are thought provoking or useful enough that I can’t even say it is wrong to consider them. This property that abstractions can be abused is generically essential to the process of abstraction itself. Abstraction is about neglecting details, and when these details are not neglectable, the abstraction is abused or ineffective. Because of this, any abstraction is insufficient for analyzing and solving real problems where the neglected details matter.

    Just as for these abstractions, the learning reduction abstraction can be abused—the chosen learning algorithm can be pathetic yielding vacuous bounds, or the reduction can scramble the feature information with an encryption algorithm making it so no reasonable learning algorithm could yield other than pathetic performance. Similarly, there are situations in which I don’t know how to effectively use a learning reduction to build a learning algorithm, and it seems implausible that observation changes as more is learned in the future.

For a good abstraction, the drawbacks are matched by the advantages. The principle advantage is that there is a new way to examine and solve problems. This has several interesting effects.

  1. A good abstraction can capture a more complete specification of the problem. As an example, the sample complexity view of learning is broken in practice, because when insufficient performance is achieved people choose a different set of hypotheses H by throwing in additional features or choosing a different learning algorithm. Capturing this process in the sample complexity view requires an additional level of complexity. In the reduction view, this is entirely natural, because any means for achieving a better generalization—more/better features, a better learning algorithm, a better prior, sticking a human in the learning process, etc… are legitimate. This is particularly powerful when architecting solutions, providing a partial answer to the “What?” question Yehuda pointed out.
  2. A higher level abstraction can let you accidentally solve problems in other areas as well. A good example of this is error correcting tournaments which are useful for tournament design to select the best player/team/paper in real tournaments. Recently, I was amused to learn that a standard betting procedure for basketball tournaments exactly mirrors the importance weights suggested for the final elimination of ECTs. The first phase of ECTs provides a sound and practical method to seed a final elimination tournament, eliminating the need for (and biases of) a committee.
  3. Perhaps the most interesting effect is that the new abstraction can aid you in finding effective solutions to new problems. For learning reductions, there are about 3 compelling instances I’ve seen so far.
    1. Given training-time access to a good policy oracle, Searn provides a method for decomposing any complex prediction problem into simple problems, such that low regret solutions to the simple problems imply a low regret solution to the original problem. While Searn competes well (computationally and prediction-wise) with existing methods for linear chain style structured prediction, it really shines on more complex problems. Hal used Searn for automatic document summarization (see section 6.2) which previously wasn’t really solved via ML. More generally, when I learn about the details of other complex prediction systems for machine translation or vision, the base algorithms are tweaked, typically in ways that Searn would suggest. This suggests that Searn formalizes and automates the intuitions of practical people.
    2. The “one step RL” reduction in Bianca’s thesis (page 119) provided tractable and effective approaches to learning in partial feedback problems where only the loss of a chosen label is learned. An even simpler reduction exists as a matter of folklore—estimate the the value of each label and then take an argmax. However, we have found classification approaches generally work better, where applicable, and as the theory suggests.
    3. Many commonly used algorithms for prediction have a running time linear (or worse) in the number of labels with decision trees a good exception. While simply predicting faster isn’t normally solving a “new problem”, an exponential improvement in computational time seems to merit this description because it allows entirely new kinds of applications. It turns out that it is both very easy to do logarithmic time prediction wrong, and that this problem is often fixable. Furthermore, it appears logarthmic time prediction can really work in practice over very many labels.

When we started working on learning reductions, I had no idea what either the difficulties or rewards were going to be—it simply seemed like a natural and compelling direction of investigation. Given the substantial difficulties encountered, it’s not at all clear that this pursuit was personally worthwhile. It has cost much time which could have been put to good use in other ways.

On the other hand, the advantages are also substantial. I’ve learned something about architecting solutions to problems, both expanding the domain of application for the field and providing a personal edge that I can bring to many conversations about ML. It’s also progress towards the AI goal, which interests me. When I think of what I could have worked on instead to achieve these goals, I don’t have any more compelling answer yet. Learning reductions seem to have accomplished more per unit thought than any other theoretical approach I can identify over the last 5 or 6 years. Furthermore, they are composable by design, so they should stay relevant (and perhaps even become more so), when people use an online active deep semisupervised probabilistic convolutional algorithm to solve a problem, particularly for complex problems.

As I said at the beginning, please join us for the tutorial, if you are interested.

4/23/2009

Jonathan Chang at Slycoder

Tags: Announcements, Machine Learning jl@ 3:00 pm

Jonathan Chang has a research blog on aspects of machine learning.

4/21/2009

Interesting Presentations at Snowbird

Here are a few of presentations interesting me at the snowbird learning workshop (which, amusingly, was in Florida with AIStat).

  1. Thomas Breuel described machine learning problems within OCR and an open source OCR software/research platform with modular learning components as well has a 60Million size dataset derived from Google’s scanned books.
  2. Kristen Grauman and Fei-Fei Li discussed using active learning with different cost labels and large datasets for image ontology. Both of them used Mechanical Turk as a labeling system, which looks to become routine, at least for vision problems.
  3. Russ Tedrake discussed using machine learning for control, with a basic claim that it was the way to go for problems involving a medium Reynold’s number such as in bird flight, where simulation is extremely intense.
  4. Yann LeCun presented a poster on an FPGA for convolutional neural networks yielding a factor of 100 speedup in processing. In addition to the graphics processor approach Rajat has worked on, this seems like an effective approach to deal with the need to compute many dot products.

4/2/2009

Asymmophobia

One striking feature of many machine learning algorithms is the gymnastics that designers go through to avoid symmetry breaking. In the most basic form of machine learning, there are labeled examples composed of features. Each of these can be treated symmetrically or asymmetrically by algorithms.

  1. feature symmetry Every feature is treated the same. In gradient update rules, the same update is applied whether the feature is first or last. In metric-based predictions, every feature is just as important in computing the distance.
  2. example symmetry Every example is treated the same. Batch learning algorithms are great exemplars of this approach.
  3. label symmetry Every label is treated the same. This is particularly noticeable in multiclass classification systems which predict according to arg maxl wl x but it occurs in many other places as well.

Empirically, breaking symmetry well seems to yield great algorithms.

  1. feature asymmetry For those who like the “boosting is stepwise additive regression on exponential loss” viewpoint (I don’t entirely), boosting is an example of symmetry breaking on features.
  2. example asymmetry Online learning introduces an example asymmetry. Aside from providing a mechanism for large scale learning, it also enables learning in entirely new (online) settings.
  3. label asymmetry Tree structured algorithms are good instances of example asymmetry. This includes both the older decision tree approaches like C4.5 and some newer ones we’ve worked on. These approaches are exponentially faster in the number of labels than more symmetric approaches.

The examples above are notably important, with good symmetry breaking approaches yielding substantially improved prediction or computational performance. Given such strong evidence that symmetry breaking is a desirable property, a basic question is: Why isn’t it more prevalent, and more thoroughly studied? One reasonable answer is that doing symmetry breaking well requires more serious thought about learning algorithm design, so researchers simply haven’t gotten to it. This answer appears incomplete.

A more complete answer is that many researchers seem to reflexively avoid symmetry breaking. A simple reason for this is the now pervasive use of Matlab in machine learning. Matlab is a handy tool for fast prototyping of learning algorithms, but it has an intrinsic language-level bias towards symmetric approaches since there are builtin primitives for matrix operations. A more complex reason is a pervasive reflex belief in fairness. While this is admirable when reviewing papers, it seems less so when designing learning algorithms. A third related reason seems to be a fear of doing unmotivated things. Anytime symmetry breaking is undertaken, the method for symmetry breaking is in question, and many people feel uncomfortable without a theorem suggesting the method is the right one. Since there are few theorems motivating symmetry breaking methods, it is often avoided.

What methods for symmetry breaking exist?

  1. Randomization. Neural Network learning algorithms which initialize the weights randomly exemplify this. I consider the randomization approach particularly weak. It makes experiments non-repeatable, and it seems like the sort of solution that someone with asymmophobia would come up with if they were forced to do something asymmetric.
  2. Arbitrary. Arbitrary symmetry breaking is something like random, except there is no randomness—you simply declare this feature/label/example comes first and that one second. This seems mildly better than the randomized approach, but still not inspiring.
  3. Data-driven. Boosting is a good example where a data-driven approach drives symmetry breaking (over features). Data-driven approaches for symmetry breaking seem the most sound, as they can result in improved performance.

While there are examples of learning algorithms doing symmetry breaking for features, labels, and examples individually, there aren’t any I know which do all three, well. What would such an algorithm look like?

3/26/2009

Machine Learning is too easy

Tags: Machine Learning jl@ 3:05 pm

One of the remarkable things about machine learning is how diverse it is. The viewpoints of Bayesian learning, reinforcement learning, graphical models, supervised learning, unsupervised learning, genetic programming, etc… share little enough overlap that many people can and do make their careers within one without touching, or even necessarily understanding the others.

There are two fundamental reasons why this is possible.

  1. For many problems, many approaches work in the sense that they do something useful. This is true empirically, where for many problems we can observe that many different approaches yield better performance than any constant predictor. It’s also true in theory, where we know that for any set of predictors representable in a finite amount of RAM, minimizing training error over the set of predictors does something nontrivial when there are a sufficient number of examples.
  2. There is nothing like a unifying problem defining the field. In many other areas there are unifying problems for which finer distinctions in approaches matter.

The implications of this observation agrees with inspection of the field.

  1. Particular problems are often “solved” by the first technique applied to them. This is particularly exacerbated when some other field first uses machine learning, as people there may not be aware of other approaches. A popular example of this is Naive Bayes for spam. In other fields, the baseline method is a neural network, an SVM, a graphical model, etc…
  2. The analysis of new learning algorithms is often subject to assumptions designed for the learning algorithm. Examples include large margins for support vector machines, a ‘correct’ Bayesian prior, correct conditional independence assumptions for graphical models, etc… Given such assumptions, it’s unsurprising to learn that the algorithm is the right method, and justifying a new algorithm becomes an exercise in figuring out an assumption which seems natural sounding under which the algorithm performs well. This assumption set selection problem is the theoretician’s version of the data set selection problem.

A basic problem is: How do you make progress in a field with this (lack of) structure? And what does progress even mean? Some possibilities are:

  1. Pick an approach and push it. [Insert your favorite technique] everywhere.
  2. Find new real problems and apply ML. The fact that ML is easy means there is a real potential for doing great things this way.
  3. Find a hard problem and work on it. Although almost anyone can do something nontrivial on most problems, achieving best-possible performance on some problems is not at all easy.
  4. Make the problem harder. Create algorithms that work fast online, in real time, with very few or no labeled examples, but very many examples, very many features, and very many things to predict.

I am least fond of approach (1), although many people successfully follow approach (1) for their career. What’s frustrating about approach (1), is that there does not seem to be any single simple philosophy capable of solving all the problems we might recognize as machine learning problems. Consequently, people following approach (1) are at risk of being outpersuaded by someone sometime in the future.

Approach (2) is perhaps the easiest way to accomplish great things, and in some sense much advance comes from new applications.

Approach (3) seems solid, promoting a different kind of progress than approach (2).

Approach (4) seems particularly cool to me at the moment. It is not as specialized as (2) or (3), and it seems many constraints are complementary. For example, there is large scale learning = online learning.

3/18/2009

Parallel ML primitives

Tags: Computation, Machine Learning jl@ 4:47 am

Previously, we discussed parallel machine learning a bit. As parallel ML is rather difficult, I’d like to describe my thinking at the moment, and ask for advice from the rest of the world. This is particularly relevant right now, as I’m attending a workshop tomorrow on parallel ML.

Parallelizing slow algorithms seems uncompelling. Parallelizing many algorithms also seems uncompelling, because the effort required to parallelize is substantial. This leaves the question: Which one fast algorithm is the best to parallelize? What is a substantially different second?

One compellingly fast simple algorithm is online gradient descent on a linear representation. This is the core of Leon’s sgd code and Vowpal Wabbit. Antoine Bordes showed a variant was competitive in the large scale learning challenge. It’s also a decades old primitive which has been reused in many algorithms, and continues to be reused. It also applies to online learning rather than just online optimization, implying the algorithm can be used in a host of situations where batch algorithms are awkward or unviable.

If we start with a fast learning algorithm as a baseline, there seem to be two directions we can go with parallel ML:

  1. (easier) Try to do more in the same amount of time. For example, Paul and Neil suggest using parallelism to support ensemble methods.
  2. (harder) Try to use parallelism to reduce the amount of time required to effectively learn on large amounts of data. For this approach, bandwidth and latency become uncomfortably critical implementation details. Due to these issues, it appears important to at least loosen the goal to competing with learning on large amounts of data. Alternatively, we could consider this as evidence some other learning primitive is desirable, although I’m not sure which one.

3/8/2009

Prediction Science

One view of machine learning is that it’s about how to program computers to predict well. This suggests a broader research program centered around the more pervasive goal of simply predicting well.
There are many distinct strands of this broader research program which are only partially unified. Here are the ones that I know of:

  1. Learning Theory. Learning theory focuses on several topics related to the dynamics and process of prediction. Convergence bounds like the VC bound give an intellectual foundation to many learning algorithms. Online learning algorithms like Weighted Majority provide an alternate purely game theoretic foundation for learning. Boosting algorithms yield algorithms for purifying prediction abiliity. Reduction algorithms provide means for changing esoteric problems into well known ones.
  2. Machine Learning. A great deal of experience has accumulated in practical algorithm design from a mixture of paradigms, including bayesian, biological, optimization, and theoretical.
  3. Mechanism Design. The core focus in game theory is on equilibria, mostly typically Nash equilibria, but also many other kinds of equilibria. The point of equilibria, to a large extent, is predicting how agents will behave. When this is employed well, principally in mechanism design for auctions, it can be a very powerful concept.
  4. Prediction Markets. The basic idea in a prediction market is that commodities can be designed so that their buy/sell price reflects a form of wealth-weighted consensus estimate of the probability of some event. This is not simply mechanism design, because (a) the thin market problem must be dealt with and (b) the structure of plausible guarantees is limited.
  5. Predictive Statistics. Part of statistics focuses on prediction, essentially becoming indistinguishable from machine learning. The canonical example of this is tree building algorithms such as CART, random forests, and some varieties of boosting. Similarly the notion of probability, counting, and estimation are all handy.
  6. Robust Search. I have yet to find an example of robust search which isn’t useful—and there are several varieties. This includes active learning, robust min finding, and (more generally) compressed sensing and error correcting codes.

The lack of unification is fertile territory for new research, so perhaps it’s worthwhile to think about how these different research programs might benefit from each other.

  1. Learning Theory. The concept of mechanism design is mostly missing from learning theory, but it is sure to be essential when interactive agents are learning. We’ve found several applications for robust search as well as new settings for robust search such as active learning, and error correcting tournaments, but there are surely others.
  2. Machine Learning and Predictive Statistics. Machine learning has been applied to auction design. There is a strong relationship between incentive compatibility and choice of loss functions, both for choosing proxy losses and approximating the real loss function imposed by the world. It’s easy to imagine designer loss functions from the study of incentive compatibility mechanisms giving learning algorithm an edge. I found this paper thought provoking that way. Since machine learning and information markets share a design goal, are there hybrid approaches which can outperform either?
  3. Mechanism Design. There are some notable similarities between papers in ML and mechanism design. For example there are papers about learning on permutations and pricing in combinatorial markets. I haven’t yet taken the time to study these carefully, but I could imagine that one suggests advances for the other, and perhaps vice versa. In general, the idea of using mechanism design with context information (as is done in machine learning), could also be extremely powerful.
  4. Prediction Markets. Prediction markets are partly an empirical field and partly a mechanism design field. There seems to be relatively little understanding about how well and how exactly information from multiple agents is supposed to interact to derive a good probability estimate. For example, the current global recession reminds us that excess leverage is a very bad idea. The same problem comes up in machine learning and is solved by the weighted majority algorithm (and even more thoroughly by the hedge algorithm). Can an information market be designed with the guarantee that an imperfect but best player decides the vote after not-too-many rounds? How would this scale as a function of the ratio of a participants initial wealth to the total wealth?
  5. Robust Search. Investigations into robust search are extremely diverse, essentially only unified in a mathematically based analysis. For people interested in robust search, machine learning and information markets provide a fertile ground for empirical application and new settings. Can all mechanisms for robust search be done with context information, as is common in learning? Do these approaches work empirically in machine learning or information markets?

There are almost surely many other interesting research topics and borrowable techniques here, and probably even other communities oriented around prediction. While the synthesis of these fields is almost sure to eventually happen, I’d like to encourage it sooner rather than later. For someone working on one of these branches, attending a conference on one of the other branches might be a good start. At a lesser time investment, Oddhead is a good start.

2/22/2009

Effective Research Funding

Tags: Funding, Research jl@ 10:17 am

With a worldwide recession on, my impression is that the carnage in research has not been as severe as might be feared, at least in the United States. I know of two notable negative impacts:

  1. It’s quite difficult to get a job this year, as many companies and universities simply aren’t hiring. This is particularly tough on graduating students.
  2. Perhaps 10% of IBM research was fired.

In contrast, around the time of the dot com bust, ATnT Research and Lucent had one or several 50% size firings wiping out much of the remainder of Bell Labs, triggering a notable diaspora for the respected machine learning group there. As the recession progresses, we may easily see more firings as companies in particular reach a point where they can no longer support research.

There are a couple positives to the recession as well.

  1. Both the implosion of Wall Street (which siphoned off smart people) and the general difficulty of getting a job coming out of an undergraduate education suggest that the quality of admitted phd students may increase. In half a decade when they start graduating, we might have some new and very creative ideas.
  2. The latest stimulus bill includes substantial additional research funding. This is particularly welcome news for those at universities, because it will compensate for other cutbacks which may be necessary there as endowments or state funding fall. It’s also particularly good for young researchers at universities who just got a position or succeed this year, as the derivative on research funding particularly impacts them.

There are two effects going on: Does a recession cause us to refocus on other possibly better ideas? Or does it cause us to focus on short term survival? The first effect helps research while the second effect does not. By far, most of the money invested by governments to fight the recession has gone towards survival, but a small fraction in the US is going towards other possibly better ideas, with a portion of that going towards research.

We could hope for a larger fraction of money heading towards new ideas, rather than rescuing old, but there is a basic issue: the apparatus for creation and use of new ideas in the US is simply too small—it may not be able to effectively use more funding. In order to justify further funding for research, we may need to be more creative than simply “give us more”.

However, this is easy. Throughout much of the 1900s, Bell Labs created many inventions which are fundamental to modern society, including the transistor, C(++), Unix, the laser, information theory, etc… In my view the vital ingredients for success are:

  1. Access to cutting edge problems. Even extraordinarily intelligent researchers can simply end up working on the wrong problem. Without direct access to and knowledge of such problems researchers can end up inventing their own, which occasionally works out well, but more often does not.
  2. Free time. This is both obvious and yet a common failure mode. Researchers at universities have many more demands on their time, including teaching, fundraising, mentoring, and running a university. Similarly, researchers at corporations can be sucked into patching an existing system rather than thinking about the best way to really solve a problem.
  3. Concentration. Two researchers working together can often manage much more than one apart, as each can bring relevant expertise and viewpoints necessary to solve a problem. This remains true up to the point where communication becomes a substantial overhead, which in my experience is about 5, but which we might imagine technology helps improve.

Bell Labs managed to satisfy all three of these desiderata. Some research universities manage to achieve at least access and concentration to some extent, but hidden difficulties exist. For example, professors often don’t work with other professors, because they are both too busy with students and they must make a case for tenure based on work which is unambiguously their own. I’m not extremely familiar with existing national labs, but I believe they often fail at (a)—at least research at national labs have had relatively little impact on newer fields such as computer science.

So, my suggestion would be funding research in modes which satisfy all three desiderata. The natural and easy way to do this is by the government partially subsidizing basic research at those corporations which have decided to fund basic research. In computer science at least, this includes Microsoft, IBM, Yahoo, Google, and what’s left of Bell Labs at ATnT and Alcatel. While this is precisely the conclusion you might expect from someone doing research at one of these places, it’s also what you would expect of someone intensely interested in research who sought out the best environment for research. In economic terms, these companies have for reasons of their own decided to provide a public good. As long as we are interested, as a nation, or as a civilization, in subsidizing this public good, it is desirable to do this as efficiently as possible.

Some people might think that basic research done at a university is inherently more desirable than the same in industry. I don’t see any reason for this. For example, it seems that patentable research is about as likely to be patented at a university as elsewhere, and hence equally restricted for public use over the duration of a patent. Other people might think that basic research only really happens at universities or national labs, but that simply doesn’t agree with history.

Given this, it’s odd that the rules for NSF funding, which is the premier source of funding for basic science in the US, generally requires university participation on proposals. This restriction naturally makes it easier for researchers at universities to acquire grant money than researchers not at universities. I don’t understand why this restriction is desirable from the viewpoint of a government wanting to effectively subsidize research.

2/18/2009

Decision by Vetocracy

Few would mistake the process of academic paper review for a fair process, but sometimes the unfairness seems particularly striking. This is most easily seen by comparison:

Paper Banditron Offset Tree Notes
Problem Scope Multiclass problems where only the loss of one choice can be probed. Strictly greater: Cost sensitive multiclass problems where only the loss of one choice can be probed. Often generalizations don’t matter. That’s not the case here, since every plausible application I’ve thought of involves loss functions substantially different from 0/1.
What’s new Analysis and Experiments Algorithm, Analysis, and Experiments As far as I know, the essence of the more general problem was first stated and analyzed with the EXP4 algorithm (page 16) (1998). It’s also the time horizon 1 simplification of the Reinforcement Learning setting for the random trajectory method (page 15) (2002). The Banditron algorithm itself is functionally identical to One-Step RL with Traces (page 122) (2003) in Bianca’s thesis with the epsilon greedy strategy and a multiclass perceptron with update scaled by the importance weight.
Computational Time O(k) per example where k is the number of choices O(log k) per example Lower bounds on the sample complexity of learning in this setting are a factor of k worse than for supervised learning, implying that many more examples may be needed in practice. Consequently, learning algorithm speed is more important than in standard supervised learning.
Analysis Incomparable. An online regret analysis showing that if a small hinge loss predictor exists, a bounded number of mistakes occur. Also, an algorithm independent analysis of the fully realizable case. Incomparable. A learning reduction analysis showing how the regret of any base classifier bounds policy regret. Also contains a lower bound and comparable analysis of all plausible alternative reductions.
Experiments 1 dataset, comparing with no other approaches to solving the problem. 13 datasets, comparing with 2 other approaches to solve the problem.
Outcome Accepted at ICML Rejected at ICML, NIPS, UAI, and NIPS.

The reviewers of the Banditron paper made the right call. The subject is interesting, and analysis of a new learning domain is of substantial interest. Real advances in machine learning often come as new domains of application. The talk was well attended and generated substantial interest. It’s also important to remember the reviewers of the two papers probably did not overlap, so there was no explicit preference for A over B.

Why was the Offset Tree rejected? One of these rejections is easily explained as a fluke—we ran into a reviewer at UAI who believes that learning by memorization is the way to go. I, and virtually all machine learning people, disagree but some reviewers at UAI aren’t interested or expert in machine learning.

The striking thing about the other 3 rejects is that they all contain a reviewer who doesn’t read the paper. Instead, the reviewer asserts that learning reductions are bogus because for an alternative notion of learning reduction, made up by the reviewer, an obviously useless approach yields a factor of 2 regret bound. I believe this is the same reviewer each time, because the alternative theorem statement drifted over the reviews fixing bugs we pointed out in the author response.

The first time we encountered this review, we assumed the reviewer was just cranky that day—maybe we weren’t quite clear enough in explaining everything as it’s always difficult to get every detail clear in new subject matter. I have sometimes had a very strong negative impression of a paper which later turned out to be unjustified upon further consideration. Sometimes when a reviewer is cranky, they change their mind after the authors respond, or perhaps later, or perhaps never but you get a new set of reviewers the next time.

The second time the review came up, we knew there was a problem. If we are generous to the reviewer, and taking into account the fact that learning reduction analysis is a relatively new form of analysis, the fear that because an alternative notion of reduction is vacuous our notion of reduction might also be vacuous isn’t too outlandish. Fortunately, there is a way to completely address that—we added an algorithm independent lower bound to the draft (which was the only significant change in content over the submissions). This lower bound conclusively proves that our notion of learning reduction is not vacuous as is the reviewer’s notion of learning reduction.

The review came up a third time. Despite pointing out the lower bound quite explicitly, the reviewer simply ignored it. This more-or-less confirms our worst fears. Some reviewer is bidding for the paper with the intent to torpedo review it. They are uninterested in and unwiling to read the content itself.

Shouldn’t author feedback address this? Not if the reviewer ignores it.

Shouldn’t Double Blind reviewing help? Not if the paper only has one plausible source. The general problem area and method of analysis were freely discussed on hunch.net. We withheld public discussion of the algorithm itself for much of the time (except for a talk at CMU) out of respect for the review process.

Why doesn’t the area chair/program chair catch it? It took us 3 interactions to get it, so it seems unrealistic to expect someone else to get it in one interaction. In general, these people are strongly overloaded and the reviewer wasn’t kind enough to boil down the essence of the stated objection as I’ve done above. Instead, they phrase it as an example and do not clearly state the theorem they have in mind or distinguish the fact that the quantification of that theorem differs from the quantification of our theorems. More generally, my observation is that area chairs rarely override negative reviews because:

  1. It risks their reputation since defending a criticized work requires the kind of confidence that can only be inspired by a thorough personal review they don’t have time for.
  2. They may offend the reviewer they invited to review and personally know.
  3. They figure that the average review is similar to the average perception/popularity by the community anyways.
  4. Even if they don’t agree with the reviewer, it’s hard to fully discount the review in their consideration.

I’ve seen these effects create substantial mental gymnastics elsewhere.

Maybe you just ran into a cranky reviewer 3 times randomly Maybe so. However, the odds seem low enough and the 1/2 year cost of getting another sample high enough, that going with the working hypothesis seems indicated.

Maybe the writing needs improving. Often that’s a reasonable answer for a rejection, but in this case I believe not. We’ve run the paper by several people, who did not have substantial difficulties understanding it. They even understand the draft well enough to make a suggestion or two. More generally, no paper is harder to read than the one you picked because you want to reject it.

What happens next? With respect to the Offset Tree, I’m hopeful that we eventually find reviewers who appreciate an exponentially faster algorithm, good empirical results, or the very tight and elegant analysis, or even all three. For the record, I consider the Offset Tree a great paper. It remains a substantial advance on the state of the art, even 2 years later, and as far as I know the Offset Tree (or the Realizable Offset Tree) consistently beat all reasonable contenders both in prediction and computational performance. This is rare and precious, as many papers tradeoff one for the other. It yields a practical algorithm applicable to real problems. It substantially addresses the RL to classification reduction problem. It also has the first nonconstant algorithm independent lower bound for learning reductions.

With respect to the reviewer, I expect remarkably little. The system is designed to protect reviewers, so they have virtually no responsibility for their decisions. This reviewer has a demonstrated capability to sabotage the review process at ICML and NIPS and a demonstrated willingness to continue doing so indefinitely. The process of bidding for papers and making up reasons to reject them seems tedious, but there is no fundamental reason why they can’t continue doing so for several decades if they remain active in academia.

This experience has substantially altered my understanding and appreciation of the review process at conferences. The bidding mechanism commonly used, coupled with responsibility-free reviewing is an invitation to abuse. A clever abusive reviewer can sabotage perhaps 5 papers per conference (out of 8 reviewed), while maintaining a typical average score. While I don’t believe most people choose papers with intent to sabotage, the capability is there and used by at least one person and possibly others. If, for example, 5% of reviewers are willing to abuse the process this way and there are 100 reviewers, every paper must survive 5 vetoes. If there are 200 reviewers, every paper must survive 10 vetoes. And if there are 400 reviewers, every paper must survive 20 vetoes. This makes publishing any paper that offends someone difficult. The surviving papers are typically inoffensive or part of a fad strong enough that vetoes are held back. Neither category is representative of high quality decision making. These observations suggest that the conference with the most reviewers tend strongly toward faddy and inoffensive papers, both of which often lack impact in the long term. Perhaps this partly explains why NIPS is so weak when people start citation counting. Conversely, this would suggest that smaller conferences and workshops have a natural advantage. Similarly, the reviewing style in theory conferences seems better—the set of bidders for any paper is substantially smaller, implying papers must survive fewer vetos.

This decision making process can be modeled as a group of n decision makers, each of which has the opportunity to veto any action. When n is relatively small, this decision making process might work ok, depending on the decision makers, but as n grows larger, it’s difficult to imagine a worse decision making process. The closest representatives outside of academia I know are deeply bureacratic governments and other large organizations where many people must sign off on something before it takes place. These vetocracies are universally frustrating to interact with. A reasonable conjecture is that any decision making process with a large veto number has poor characteristics.

A basic question is: Is a vetocracy inevitable for large organizations? I believe the answer is no. The basic observation is that the value of n can be logarithmic in the number of participants in an organization rather than linear, as per reviewing under a bidding process. An essential force driving vetocracy creation is a desire to offload responsibility for decisions, so there is no clear decision maker. A large organization not deciding by vetocracy must have a very different structure, with clearly dilineated responsibility.

NIPS provides an almost perfect natural experiment in it’s workshop organization, which involves the very same community of people and subject matter, yet works in a very different manner. There are one or two workshop chairs who are responsible for selecting amongst workshop proposals, after which the content of the workshop is entirely up to the workshop organizers. If a workshop is rejected, it’s clear who is at fault, and if a workshop presentation is rejected, it is often clear by who. Some workshop chairs use a small set of reviewers, but even then the effective veto number remains small. Similarly, if a workshop ends up a flop, it’s relatively easy to see who to blame—either the workshop chair for not predicting it, or the organizers for failing to organize. I can’t think of a single time when I attended both the workshops and the conference that the workshops were less interesting than the conference. My understanding is that this observation is common. Given this discussion, it will be particularly interesting to see how the review process Michael and Leon setup for ICML this year pans out, as it is a system with notably more responsibility assignment than in previous years.

Journals end up looking relatively good with respect to vetocracy avoidance. The ones I’m familiar with have a chief editor who bears responsibility for routing papers to an action editor, who bears responsibility for choosing good reviewers. Every agent except the reviewers is often known by the authors, and the reviewers don’t act as additional vetoers in nearly as strong a manner as reviewers with the opportunity to bid.

This experience has also altered my view of blogging and research. On one hand, I’m very enthusiastic about research in general, and my research in particular, where we are regularly cracking conventionally impossible problems. On the other hand, it seems that some small number of people viewing a discussion silently decide they don’t like it, and veto it given the opportunity. It only takes one to turn strong paper into a years-long odyssey, so public discussion of research directions and topics in a vetocracy is akin to voluntarily wearing a “kick me” sign. While this a problem for me, I expect it to be even worse for the members of a vetocracy in the long term.

It’s hard to imagine any research community surviving without a serious online presence. When a prospective new researcher looks around at existing research, if they don’t find serious online discussion, they’ll assume it doesn’t exist under the “not on the internet so it doesn’t exist” principle. This will starve a field of new people. More generally, there is an opportunity to get feedback about research directions and problems much more rapidly than is otherwise possible, allowing us to avoid research on dead end topics which are pervasive. At some point, it may even seem that people not willing to discuss their research simply avoid doing so because it is critically lacking in one way or another. Since a vetocracy creates a substantial disincentive to discuss research directions online, we can expect that communities sticking with decision by vetocracy to be at a substantial disadvantage.

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