Machine Learning (Theory)


Interesting Papers at NIPS 2006

Here are some papers that I found surprisingly interesting.

  1. Yoshua Bengio, Pascal Lamblin, Dan Popovici, Hugo Larochelle, Greedy Layer-wise Training of Deep Networks. Empirically investigates some of the design choices behind deep belief networks.
  2. Long Zhu, Yuanhao Chen, Alan Yuille Unsupervised Learning of a Probabilistic Grammar for Object Detection and Parsing. An unsupervised method for detecting objects using simple feature filters that works remarkably well on the (supervised) caltech-101 dataset.
  3. Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira, Analysis of Representations for Domain Adaptation. This is the first analysis I’ve seen of learning with respect to samples drawn differently from the evaluation distribution which depends on reasonable measurable quantities.

All of these papers turn out to have a common theme—the power of unlabeled data to do generically useful things.


Incentive Compatible Reviewing

Tags: Papers,Research,Reviewing jl@ 10:13 pm

Reviewing is a fairly formal process which is integral to the way academia is run. Given this integral nature, the quality of reviewing is often frustrating. I’ve seen plenty of examples of false statements, misbeliefs, reading what isn’t written, etc…, and I’m sure many other people have as well.

Recently, mechanisms like double blind review and author feedback have been introduced to try to make the process more fair and accurate in many machine learning (and related) conferences. My personal experience is that these mechanisms help, especially the author feedback. Nevertheless, some problems remain.

The game theory take on reviewing is that the incentive for truthful reviewing isn’t there. Since reviewers are also authors, there are sometimes perverse incentives created and acted upon. (Incidentially, these incentives can be both positive and negative.)

Setting up a truthful reviewing system is tricky because their is no final reference truth available in any acceptable (say: subyear) timespan. There are several ways we could try to get around this.

  1. We could try to engineer new mechanisms for finding a reference truth into a conference and then use a ‘proper scoring rule’ which is incentive compatible. For example, we could have a survey where conference participants short list the papers which interested them. There are significant problems here:
    1. Conference presentations mostly function as announcements of results. Consequently, the understanding of the paper at the conference is not nearly as deep as, say, after reading through it carefully in a reading group.
    2. This is inherently useless for judging reviews of rejected papers and it is highly biased for judging reviews of papers presented in two different formats (say, a poster versus an oral presentation).
  2. We could ignore the time issue and try to measure reviewer performance based upon (say) long term citation count. Aside from the bias problems above, there is also a huge problem associated with turnover. Who the reviewers are and how an individual reviewer reviews may change drastically in just a 5 year timespan. A system which can provide track records for only a small subset of current reviewers isn’t very capable.
  3. We could try to manufacture an incentive compatible system even when the truth is never known. This paper by Nolan Miller, Paul Resnick, and Richard Zeckhauser discusses the feasibility of this approach. Essentially, the scheme works by rewarding reviewer i according to a proper scoring rule applied to P(reviewer j’s score | reviewer i’s score). (A simple example of a proper scoring rule is log[P()].) This is approach is pretty fresh, so there are lots of problems, some of which may or may not be fundamental difficulties for application in practice. The significant problem I see is that this mechanism may reward joint agreement instead of a good contribution towards good joint decision making.

None of these mechanisms are perfect, but they may each yield a little bit of information about what was or was not a good decision over time. Combining these sources of information to create some reviewer judgement system may yield another small improvement in the reviewing process.

The important thing to remember is that we are the reviewers as well as the authors. Are we interested in tracking our reviewing performance over time in order to make better judgements? Such tracking often happens on an anecdotal or personal basis, but shifting to an automated incentive compatible system would be a big change in scope.


Two more UAI papers of interest

Tags: Machine Learning,Papers roweis@ 5:08 am

In addition to Ed Snelson’s paper, there were (at least) two other papers that caught my eye at UAI.

One was this paper by Sanjoy Dasgupta, Daniel Hsu and Nakul Verma at UCSD which shows in a surprisingly general and strong way that almost all linear projections of any jointly distributed vector random variable with finite first and second moments look sphereical and unimodal (in fact look like a scale mixture of Gaussians). Great result, as you’d expect from Sanjoy.

The other paper which I found intriguing but which I just haven’t groked yet is this beast by Manfred and Dima Kuzmin.
You can check out the (beautiful) slides
if that helps. I feel like there is something deep here, but my brain is too small to understand it. The COLT and last NIPS papers/slides are also on Manfred’s page. Hopefully someone here can illuminate.


more icml papers

Tags: Machine Learning,Papers roweis@ 7:02 am

Here are a few other papers I enjoyed from ICML06.

Topic Models:

  • Dynamic Topic Models

    David Blei, John Lafferty
    A nice model for how topics in LDA type models can evolve over time,
    using a linear dynamical system on the natural parameters and a very
    clever structured variational approximation (in which the mean field
    parameters are pseudo-observations of a virtual LDS). Like all Blei
    papers, he makes it look easy, but it is extremely impressive.

  • Pachinko Allocation

    Wei Li, Andrew McCallum
    A very elegant (but computationally challenging) model which induces
    correlation amongst topics using a multi-level DAG whose interior nodes
    are “super-topics” and “sub-topics” and whose leaves are the
    vocabulary words. Makes the slumbering monster of structure learning stir.

Sequence Analysis (I missed these talks since I was chairing another session)

  • Online Decoding of Markov Models with Latency Constraints

    Mukund Narasimhan, Paul Viola, Michael Shilman
    An “ah-ha!” paper showing how to trade off latency and decoding
    accuracy when doing MAP labelling (Viterbi decoding) in sequential
    Markovian models. You’ll wish you thought of this yourself.

  • Efficient inference on sequence segmentation model

    Sunita Sarawagi
    A smart way to re-represent potentials in segmentation models
    to reduce the complexity of inference from cubic in the input sequence
    to linear. Also check out her NIPS2004 paper with William Cohen
    on “segmentation CRFs”. Moral of the story: segmentation is NOT just
    sequence labelling.

Optimal Partitionings/Labellings

  • The uniqueness of a good optimum for K-means

    Marina Meila
    Marina shows a stability result for K-means clustering, namely
    that if you find a “good” clustering it is not too “different” than the
    (unknowable) optimal clustering and that all other good clusterings
    are “near” it. So, don’t worry about local minima in K-means as long
    as you get a low objective.

  • Quadratic Programming Relaxations for Metric Labeling and Markov Random Field MAP Estimation

    Pradeep Ravikumar, John Lafferty
    Paradeep and John introduce QP relaxations for the problem of finding
    the best joint labelling of a set of points (connected by a weighted
    graph and with a known metric cost between labels and extended
    the non-metric case). Surprisingly, they show that the QP relaxation
    is both computationally more attractive and more accurate than
    the “natural” LP relaxation or than loopy BP approximations.

Distinguished Paper Award Winners


ICML papers

Tags: Machine Learning,Papers jl@ 7:25 am

Here are some ICML papers which interested me.

  1. Arindam Banerjee had a paper which notes that PAC-Bayes bounds, a core theorem in online learning, and the optimality of Bayesian learning statements share a core inequality in their proof.
  2. Pieter Abbeel, Morgan Quigley and Andrew Y. Ng have a paper discussing RL techniques for learning given a bad (but not too bad) model of the world.
  3. Nina Balcan and Avrim Blum have a paper which discusses how to learn given a similarity function rather than a kernel. A similarity function requires less structure than a kernel, implying that a learning algorithm using a similarity function might be applied in situations where no effective kernel is evident.
  4. Nathan Ratliff, Drew Bagnell, and Marty Zinkevich have a paper describing an algorithm which attempts to fuse A* path planning with learning of transition costs based on human demonstration.

Papers (2), (3), and (4), all seem like an initial pass at solving interesting problems which push the domain in which learning is applicable.

I’d like to encourage discussion of what papers interested you and why. Maybe we’ll all learn a little bit, and it’s very likely that we all missed interesting papers in a multitrack conference.


Online convex optimization at COLT

Tags: Machine Learning,Online,Papers jl@ 2:07 pm

At ICML 2003, Marty Zinkevich proposed the online convex optimization setting and showed that a particular gradient descent algorithm has regret O(T0.5) with respect to the best predictor where T is the number of rounds. This seems to be a nice model for online learning, and there has been some significant follow-up work.

At COLT 2006 Elad Hazan, Adam Kalai, Satyen Kale, and Amit Agarwal presented a modification which takes a Newton step guaranteeing O(log T) regret when the first and second derivatives are bounded. Then they applied these algorithms to portfolio management at ICML 2006 (with Robert Schapire) yielding some very fun graphs.


Bounds greater than 1

Nati Srebro and Shai Ben-David have a paper at COLT which, in the appendix, proves something very striking: several previous error bounds are always greater than 1.

Background One branch of learning theory focuses on theorems which

  1. Assume samples are drawn IID from an unknown distribution D.
  2. Fix a set of classifiers
  3. Find a high probability bound on the maximum true error rate (with respect to D) as a function of the empirical error rate on the training set.

Many of these bounds become extremely complex and hairy.

Current Everyone working on this subject wants “tighter bounds”, however there are different definitions of “tighter”. Some groups focus on “functional tightness” (getting the right functional dependency between the size of the training set and a parameterization of the hypothesis space) while others focus on “practical tightness” (finding bounds which work well on practical problems). (I am definitely in the second camp.)

One of the dangers of striving for “functional tightness” is that the bound can depend on strangely interrelated parameters. In fact, apparently these strange interrelations can become so complex that they end up always larger than 1 (some bounds here and here).

It seems we should ask the question: “Why are we doing the math?” If it is just done to get a paper accepted under review, perhaps this is unsatisfying. The real value of math comes when it guides us in designing learning algorithms. Math from bounds greater than 1 is a dangerously weak motivation for learning algorithm design.

There is a significant danger in taking this “oops” too strongly.

  1. There exist some reasonable arguments (not made here) for aiming at functional tightness.
  2. The value of the research a person does is more related to the best they have done than the worst.


Mad (Neuro)science

One of the questions facing machine learning as a field is “Can we produce a generalized learning system that can solve a wide array of standard learning problems?” The answer is trivial: “yes, just have children”.

Of course, that wasn’t really the question. The refined question is “Are there simple-to-implement generalized learning systems that can solve a wide array of standard learning problems?” The answer to this is less clear. The ability of animals (and people ) to learn might be due to megabytes encoded in the DNA. If this algorithmic complexity is necessary to solve machine learning, the field faces a daunting task in replicating it on a computer.

This observation suggests a possibility: if you can show that few bits of DNA are needed for learning in animals, then this provides evidence that machine learning (as a field) has a hope of big success with relatively little effort.

It is well known that specific portions of the brain have specific functionality across individuals. There are two ways this observation can be explained:

  1. Maybe the specific functionality areas are encoded in the DNA.
  2. Maybe the specific functionality areas arise from the learning process of the brain. This is the answer that machine learning would like to hear because it agrees with the hypothesis that a simple general learning system exists.

It’s important to realize that these choices actually specify a spectrum rather than a dichotomy. There are surely some problem-specific learning hacks in the brain and there is surely some generalized learning ability. The question is: to what degree is learning encoded by genetic heritage vs personal experience?

It is anecdotally well known that people (especially children) can recover from fairly severe brain damage, but of course we would prefer to avoid anecdotal evidence.

There are also neuroscience experiments addressing this question. This paper by Jitendra Sharma, Alessandra Angelucci, and Mriganka Sur provides some evidence. In a nutshell, they rewire the optic nerve of ferrets into the auditory region of the brain. They observe that structures similar to the visual specific region of the brain arise in the auditory region after rewiring (although the new regions may be less capable).

There are doubtless many other experiments addressing this question, but my knowledge of Neuroscience is lacking. (Thanks to Maneesh for pointing this one out.)


“Structural” Learning

Fernando Pereira pointed out Ando and Zhang‘s paper on “structural” learning. Structural learning is multitask learning on subproblems created from unlabeled data.

The basic idea is to take a look at the unlabeled data and create many supervised problems. On text data, which they test on, these subproblems might be of the form “Given surrounding words predict the middle word”. The hope here is that successfully predicting on these subproblems is relevant to the prediction of your core problem.

In the long run, the precise mechanism used (essentially, linear predictors with parameters tied by a common matrix) and the precise problems formed may not be critical. What seems critical is that the hope is realized: the technique provides a significant edge in practice.

Some basic questions about this approach are:

  1. Are there effective automated mechanisms for creating the subproblems?
  2. Is it necessary to use a shared representation?


More NIPS Papers II

Tags: Papers zoubin@ 11:47 pm

I thought this was a very good NIPS with many excellent papers. The following are a few NIPS papers which I liked and I hope to study more carefully when I get the chance. The list is not exhaustive and in no particular order…

  • Preconditioner Approximations for Probabilistic Graphical Models.
    Pradeeep Ravikumar and John Lafferty.
    I thought the use of preconditioner methods from solving linear systems in the context of approximate inference was novel and interesting. The results look good and I’d like to understand the limitations.
  • Rodeo: Sparse nonparametric regression in high dimensions.
    John Lafferty and Larry Wasserman.
    A very interesting approach to feature selection in nonparametric regression from a frequentist framework. The use of lengthscale variables in each dimension reminds me a lot of ‘Automatic Relevance Determination’ in Gaussian process regression — it would be interesting to compare Rodeo to ARD in GPs.
  • Interpolating between types and tokens by estimating power law generators.
    Goldwater, S., Griffiths, T. L., & Johnson, M.
    I had wondered how Chinese restaurant processes and Pitman-Yor processes related to Zipf’s plots and power laws for word frequencies. This paper seems to have the answers.
  • A Bayesian spatial scan statistic.
    Daniel B. Neill, Andrew W. Moore, and Gregory F. Cooper.
    When I first learned about spatial scan statistics I wondered what a Bayesian counterpart would be. I liked the fact they their method was simple, more accurate, and much faster than the usual frequentist method.
  • Q-Clustering.
    M. Narasimhan, N. Jojic and J. Bilmes.
    A very interesting application of sub-modular function optimization to clustering. This feels like a hot area.
  • Worst-Case Bounds for Gaussian Process Models.
    Sham M. Kakade, Matthias W. Seeger, & Dean P. Foster.

    It’s useful for Gaussian process practitioners to know that their approaches don’t do silly things when viewed from a worst-case frequentist setting. This paper provides some relevant theoretical results.


More NIPS Papers

Tags: Papers roweis@ 1:14 am

Let me add to John’s post with a few of my own favourites
from this year’s conference. First, let me say that
Sanjoy’s talk, Coarse Sample Complexity Bounds for Active
was also one of my favourites, as was the

Forgettron paper

I also really enjoyed the last third of
Christos’ talk
on the complexity of finding Nash equilibria.

And, speaking of tagging, I think
the U.Mass Citeseer replacement system
Rexa from the demo track is very cool.

Finally, let me add my recommendations for specific papers:

  • Z. Ghahramani, K. Heller: Bayesian Sets
    [no preprint]
    (A very elegant probabilistic information retrieval style model
    of which objects are “most like” a given subset of objects.)
  • T. Griffiths, Z. Ghahramani: Infinite Latent Feature Models and
    the Indian Buffet Process

    (A Dirichlet style prior over infinite binary matrices with
    beautiful exchangeability properties.)
  • K. Weinberger, J. Blitzer, L. Saul: Distance Metric Learning for
    Large Margin Nearest Neighbor Classification

    (A nice idea about how to learn a linear transformation of your
    feature space which brings nearby points of the same class closer
    together and sends nearby points of differing classes further
    apart. Convex. Kilian gave a very nice talk on this.)
  • D. Blei, J. Lafferty: Correlated Topic Models
    (Nice trick using the lognormal to induce correlations on the simplex
    applied to topic models for text.)

I’ll also post in the comments a list of other papers that caught my eye but
which I haven’t looked at closely enough to be able to out-and-out


Some NIPS papers

Tags: Papers jl@ 4:46 pm

Here is a set of papers that I found interesting (and why).

  1. A PAC-Bayes approach to the Set Covering Machine improves the set covering machine. The set covering machine approach is a new way to do classification characterized by a very close connection between theory and algorithm. At this point, the approach seems to be competing well with SVMs in about all dimensions: similar computational speed, similar accuracy, stronger learning theory guarantees, more general information source (a kernel has strictly more structure than a metric), and more sparsity. Developing a classification algorithm is not very easy, but the results so far are encouraging.
  2. Off-Road Obstacle Avoidance through End-to-End Learning and Learning Depth from Single Monocular Images both effectively showed that depth information can be predicted from camera images (using notably different techniques). This ability is strongly enabling because cameras are cheap, tiny, light, and potentially provider longer range distance information than the laser range finders people traditionally use.
  3. The Forgetron: A Kernel-Based Perceptron on a Fixed Budget proved that a bounded memory kernelized perceptron algorithm (which might be characterizable as “stochastic functional gradient descent with weight decay and truncation”) competes well with respect to an unbounded memory algorithm when the data contains a significant margin. Roughly speaking, this implies that the perceptron approach can learn arbitary (via the kernel) reasonably simple concepts from unbounded quantities of data.

In addition, Sebastian Thrun‘s “How I won the Darpa Grand Challenge” and Sanjoy Dasgupta‘s “Coarse Sample Complexity for Active Learning” talks were both quite interesting.

(Feel free to add any that you found interesting.)


The Everything Ensemble Edge

Tags: Bayesian,Empirical,Papers jl@ 7:38 am

Rich Caruana, Alexandru Niculescu, Geoff Crew, and Alex Ksikes have done a lot of empirical testing which shows that using all methods to make a prediction is more powerful than using any single method. This is in rough agreement with the Bayesian way of solving problems, but based upon a different (essentially empirical) motivation. A rough summary is:

  1. Take all of {decision trees, boosted decision trees, bagged decision trees, boosted decision stumps, K nearest neighbors, neural networks, SVM} with all reasonable parameter settings.
  2. Run the methods on each problem of 8 problems with a large test set, calibrating margins using either sigmoid fitting or isotonic regression.
  3. For each loss of {accuracy, area under the ROC curve, cross entropy, squared error, etc…} evaluate the average performance of the method.

A series of conclusions can be drawn from the observations.

  1. (Calibrated) boosted decision trees appear to perform best, in general although support vector machines and neural networks give credible near-best performance.
  2. The metalearning algorithm which simply chooses the best (based upon a small validation set) performs much better.
  3. A metalearning algorithm which combines the predictors in an ensemble using stepwise refinement of validation set performance appears to perform even better.

There are a number of caveats to this work: it was only applied on large datasets there is no guarantee that the datasets are representative of your problem (although efforts were made to be representative in general), and the size of the training set was fixed rather than using the natural size given by the problem. Despite all these caveats, the story told above seems compelling: if you want maximum performance, you must try many methods and somehow combine them.

The most significant drawback of this method is computational complexity. Techniques for reducing the computational complexity are therefore of significant interest. It seems plausible that there exists some learning algorithm which typically performs well whenever any of the above algorithms can perform well at a computational cost which is significantly less than “run all algorithm on all settings and test”.

A fundamental unanswered question here is “why?” in several forms. Why have the best efforts of many machine learning algorithm designers failed to capture all the potential predictive strength into a single coherent learning algorithm? Why do ensembles give such a significant consistent edge in practice? A great many papers follow the scheme: invent a new way to create ensembles, test, observe that it improves prediction performance at the cost of more computation, and publish. There are several pieces of theory explain individual ensemble methods, but we seem to have no convincing theoretical statement explaining why they almost always work.


Fast Gradient Descent

Tags: Papers,Supervised jl@ 9:27 am

Nic Schaudolph has been developing a fast gradient descent algorithm called Stochastic Meta-Descent (SMD).

Gradient descent is currently untrendy in the machine learning community, but there remains a large number of people using gradient descent on neural networks or other architectures from when it was trendy in the early 1990s. There are three problems with gradient descent.

  1. Gradient descent does not necessarily produce easily reproduced results. Typical algorithms start with “set the initial parameters to small random values”.
  2. The design of the representation that gradient descent is applied to is often nontrivial. In particular, knowing exactly how to build a large neural network so that it will perform well requires knowledge which has not been made easily applicable.
  3. Gradient descent can be slow. Obviously, taking infinitesimal steps in the direction of the gradient would take forever, so some finite step size must be used. What exactly this step size should be is unclear. Many people have developed many algorithms for adjusting the step size (and to some extent the step direction). Unfortunately, many of the more sophisticated algorithms are not robust to noise, scale badly with the number of parameters (Anything worse than O(n) is unacceptable for big applications) or both. Consequently, many people simply use gradient descent where the step size is adjusted by a simple momentum heuristic.

Many people would add point (4): gradient descent on many architectures does not result in a global optima. This seems like a confusion of goals to me. The goal is good performance on future examples in learning rather than achieving a global optima on the training set.

SMD addresses point (3). It is an O(n) algorithm for gradient descent that can compete with the sophisticed methods where the sophisticated methods work but remains fairly robust to noise. Exactly how well it addresses point (3) is not entirely clear, but a few interesting problems have been solved with the algorithm, and perhaps we will see more evidence in the near future.


SVM Adaptability

Tags: Papers,Reductions,structured jl@ 12:33 am

Several recent papers have shown that SVM-like optimizations can be used to handle several large family loss functions.

This is a good thing because it is implausible that the loss function imposed by the world can not be taken into account in the process of solving a prediction problem. Even people used to the hard-core Bayesian approach to learning often note that some approximations are almost inevitable in specifying a prior and/or integrating to achieve a posterior. Taking into account how the system will be evaluated can allow both computational effort and design effort to be focused so as to improve performance.

A current laundry list of capabilities includes:

  1. 2002 multiclass SVM including arbitrary cost matrices
  2. ICML 2003 Hidden Markov Models
  3. NIPS 2003 Markov Networks (see some discussion)
  4. EMNLP 2004 Context free grammars
  5. ICML 2004 Any loss (with much computation)
  6. ICML 2005 Any constrained linear prediction model (that’s my own name).
  7. ICML 2005 Any loss dependent on a contingency table

I am personally interested in how this relates to the learning reductions work which has similar goals, but works at a different abstraction level (the learning problem rather than algorithmic mechanism). The difference in abstraction implies that anything solvable by reduction should be solvable by a direct algorithmic mechanism. However, comparing and constrasting the results I know of it seems that what is solvable via reduction to classification versus what is solvable via direct SVM-like methods is currently incomparable.

  1. Can SVMs be tuned to directly solve (example dependent) cost sensitive classification? Obviously, they can be tuned indirectly via reduction, but it is easy to imagine more tractable direct optimizations.
  2. How efficiently can learning reductions be used to solve structured prediction problems? Structured prediction problems are instances of cost sensitive classification, but the regret transform efficiency which occurs when this embedding is done is too weak to be of interest.
  3. Are there any problems efficiently solvable by SVM-like algorithms which are not efficiently solvable via learning reductions?


Interesting papers at ACL

Tags: Language,Papers hal@ 8:59 am

A recent discussion indicated that one goal of this blog might be to allow people to post comments about recent papers that they liked. I think this could potentially be very useful, especially for those with diverse interests but only finite time to read through conference proceedings. ACL 2005 recently completed, and here are four papers from that conference that I thought were either good or perhaps of interest to a machine learning audience.

David Chiang, A Hierarchical Phrase-Based Model for Statistical Machine Translation. (Best paper award.) This paper takes the standard phrase-based MT model that is popular in our field (basically, translate a sentence by individually translating phrases and reordering them according to a complicated statistical model) and extends it to take into account hierarchy in phrases, so that you can learn things like “X ‘s Y” -> “Y de X” in chinese, where X and Y are arbitrary phrases. This takes a step toward linguistic syntax for MT, which our group is working strongly on, but doesn’t require any linguists to sit down and write out grammars or parse sentences.

Rie Kubota Ando and Tong Zhang, A High-Performance Semi-Supervised Learning Method for Text Chunking. This is more of a machine learning style paper, where they improve a sequence labeling task by augmenting it with models from related tasks for which data is free. I.e., I might train a model that, given a context with a missing word, will predict the word (eg., “The ____ gave a speech” might want you to insert “president”.) By doing so, you can use these other models to give additional useful information to your main task.

Noah A. Smith and Jason Eisner, Contrastive Estimation: Training Log-Linear Models on Unlabeled Data. This paper talks about training sequence labeling models in an unsupervised fashion, basically by contrasting what the model does on the correct string with what the model does on a corrupted version of the string. They get significantly better results than just by using EM in an HMM, and the idea is pretty nice.

Patrick Pantel, Inducing Ontological Co-occurrence Vectors. This is a pretty neat idea (though I’m biased — Patrick is a friend) where one attempts to come up with feature vectors that describe nodes in a semantic hierarchy (ontology) that could enable you to figure out where to insert new words that are not in your ontology. The results are pretty good, and the method is fairly simple; I’d imagine that a more complex model/learning framework could improve the model even further.


Text Entailment at AAAI

Tags: Language,Papers,Problems jl@ 9:53 am

Rajat Raina presented a paper on the technique they used for the PASCAL Recognizing Textual Entailment challenge.

“Text entailment” is the problem of deciding if one sentence implies another. For example the previous sentence entails:

  1. Text entailment is a decision problem.
  2. One sentence can imply another.

The challenge was of the form: given an original sentence and another sentence predict whether there was an entailment. All current techniques for predicting correctness of an entailment are at the “flail” stage—accuracies of around 58% where humans could achieve near 100% accuracy, so there is much room to improve. Apparently, there may be another PASCAL challenge on this problem in the near future.


Not EM for clustering at COLT

Tags: Papers,Unsupervised jl@ 10:06 am

One standard approach for clustering data with a set of gaussians is using EM. Roughly speaking, you pick a set of k random guassians and then use alternating expectation maximization to (hopefully) find a set of guassians that “explain” the data well. This process is difficult to work with because EM can become “stuck” in local optima. There are various hacks like “rerun with t different random starting points”.

One cool observation is that this can often be solved via other algorithm which do not suffer from local optima. This is an early paper which shows this. Ravi Kannan presented a new paper showing this is possible in a much more adaptive setting.

A very rough summary of these papers is that by projecting into a lower dimensional space, it is computationally tractable to pick out the gross structure of the data. It is unclear how well these algorithms work in practice, but they might be effective, especially if used as a subroutine of the form:

  1. Project to low dimensional space.
  2. Pick out gross structure.
  3. Project gross structure into the high dimensional space.
  4. Run EM (or some other local improvement algorithm) to find a final fit.

The effects of steps 1-3 is to “seed” the local optimization algorithm in a good place from which a global optima is plausibly reachable.


A COLT paper

Tags: Papers,Prediction Theory jl@ 2:22 pm

I found Tong Zhang’s paper on Data Dependent Concentration Bounds for Sequential Prediction Algorithms interesting. Roughly speaking, it states a tight bound on the future error rate for online learning algorithms assuming that samples are drawn independently. This bound is easily computed and will make the progressive validation approaches used here significantly more practical.


Dynamic Programming Generalizations and Their Use

Tags: General,Papers jl@ 8:38 pm

David Mcallester gave a talk about this paper (with Pedro Felzenszwalb). I’ll try to give a high level summary of why it’s interesting.

Dynamic programming is most familiar as instantiated by Viterbi decoding in a hidden markov model. It is a general paradigm for problem solving where subproblems are solved and used to solve larger problems. In the Viterbi decoding example, the subproblem is “What is the most probable path ending at each state at timestep t?”, and the larger problem is the same except at timestep t+1. There are a few optimizations you can do here:

  1. Dynamic Programming -> queued Dynamic Programming. Keep track of the “cost so far” (or “most probable path”) and (carefully) only look at extensions to paths likely to yield the shortest path. “Carefully” here is defined by Dijkstra’s shortest path algorithm.
  2. queued Dynamic programming -> A*Add a lower bound on the cost to complete a path (or an upper bound on the probability of a completion) for the priority queue of Dijkstra’s shortest path. This can yield computational speedups varying between negligible and outstanding.
  3. A* -> Hierarchical A* The efficiency of A* search is dependent on the tightness of it’s lower bound, which brings up the question: “Where do you get the lower bound?” One appealing answer is from A* applied to a simplified problem equivalent to the original problem, but with states aliased (many states in original problem = 1 state in new problem). This technique can be applied recursively until the problem is trivial.

Each of these steps has been noted previously (although perhaps not in the generality of this paper). What seems new and interesting is that the entire hierarchy of A* searches can be done simultaneously on one priority queue.

The resulting algorithm can use low level information to optimize high level search as well as high level information to optimize low level search in a holistic process. It’s not clear yet how far this approach can be pushed, but this quality is quite appealing. Naturally, there are many plausible learning-related applications.

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