Machine Learning (Theory)


Vowpal Wabbit 8.5.0 & NIPS tutorial

Yesterday, I tagged VW version 8.5.0 which has many interactive learning improvements (both contextual bandit and active learning), better support for sparse models, and a new baseline reduction which I’m considering making a part of the default update rule.

If you want to know the details, we’ll be doing a mini-tutorial during the Friday lunch break at the Extreme Classification workshop at NIPS. Please join us if interested.

Edit: also announced at the Learning Systems workshop


The End of the Beginning of Active Learning

Tags: Active,Machine Learning Daniel@ 12:18 pm

This post is by Daniel Hsu and John Langford.

In selective sampling style active learning, a learning algorithm chooses which examples to label. We now have an active learning algorithm that is:

  1. Efficient in label complexity, unlabeled complexity, and computational complexity.
  2. Competitive with supervised learning anywhere that supervised learning works.
  3. Compatible with online learning, with any optimization-based learning algorithm, with any loss function, with offline testing, and even with changing learning algorithms.
  4. Empirically effective.

The basic idea is to combine disagreement region-based sampling with importance weighting: an example is selected to be labeled with probability proportional to how useful it is for distinguishing among near-optimal classifiers, and labeled examples are importance-weighted by the inverse of these probabilities. The combination of these simple ideas removes the sampling bias problem that has plagued many previous heuristics for active learning, and yet leads to a general and flexible method that enjoys the desirable traits described above. None of these desirable criteria are individually sufficient, but the simultaneous satisfaction of all criteria by one algorithm is compelling.

This combination of traits implies that active learning is a viable choice in most places where supervised learning is a viable choice. 6 years ago, we didn’t know how to deal with adversarial label noise, and didn’t know how to characterize where active learning helped over supervised learning. 5.5 years ago we had the first breakthroughs in characterization and learning with adversarial label noise. Several more substantial improvements occurred, leading to a tutorial 2 years ago and discussion about what’s next. Since then, we cracked question (2) here and applied it to get an effective absurdly efficient active learning algorithm. Directions for experimenting with it are here, page 47.

As research programs go, we’d like to declare victory, but can’t. Victory in research is when ideas get used, becoming part of the standard repertoire of tools and ways people think. Instead, it seems fair to declare “theory victory” which is more like a milestone in the grand scheme. We’ve hit a point where anyone versed in these results can comfortably and effectively apply active learning instead of supervised learning (caveats below). Whether or not this leads to a real victory depends a great deal on how this gets used. In achieving “theory victory”, the key people were:

  1. Nina Balcan*
  2. Alina Beygelzimer
  3. Sanjoy Dasgupta
  4. Steve Hanneke*
  5. Daniel Hsu*
  6. Matti Kääriäinen
  7. Nikos Karampatziakis
  8. [Added from Daniel] Vladimir Koltchinskii
  9. John Langford
  10. Claire Monteleoni*
  11. Tong Zhang

(*)=thesis work.

Naturally, there are many caveats to the above. We moved as fast as we could towards an effective sound useful algorithm according to the standard IID-only assumption criteria of supervised learning. This means that our understanding is not particularly broad, and a number of questions remain including 1,3,4 here.

  1. The existing solution is a simple algorithm with a complex analysis. Simplifying and tightening this analysis would be quite helpful—it’s not even clear we have the best-possible functional form yet. In addition, we rely on the abstraction of a learning algorithm as an effective ERM algorithm when applying the algorithm in practice. That’s plausibly reasonable, but it may also breakdown, implying that experiments beyond linear and decision tree architectures could be helpful.
  2. The extreme efficiency of active learning achieved opens up the possibility of using it for efficient parallel learning and other information-distillation purposes.
  3. Our understanding of the limits of active learning is not complete: various lower bounds have been identified, but a gap remains relative to the known upper bounds. Are the label complexity upper bounds achieved by the general scheme tight for a general class of active learning algorithms, or can the algorithms be improved using new techniques without sacrificing consistency?
  4. Can active learning succeed under different generative / statistical assumptions (e.g., fully-adversarial data, alternative labeling oracles)? Some recent progress on fully-adversarial active learning has been made by Nicolo Cesa-Bianchi, Claudio Gentile, and Francesco Orabona and Ofer Dekel, Claudio Gentile, and Karthik Sridharan, with the latter also providing a solution for learning with multiple heterogeneous labeling oracles (e.g. Mechanical Turk). At the other end of the spectrum, the work of Andrew Guillory and Jeff Bilmes and Daniel Golovin and Andreas Krause (building on some earlier findings of Sanjoy Dasgupta) looks at average-case / Bayesian analyses of greedy algorithms. The resulting approximation factor-type guarantees can be reassuring to the practitioner when justifying a particular choice of sampling strategy; the trade-off here is that the guarantee holds in a somewhat limited sense.
  5. Can active learning be effectively combined with semi-supervised and unsupervised learning? It is known from the rich area of semi-supervised learning that unlabeled data can suggest learning biases (e.g., large margin separators, low dimensional structure) that may improve performance over supervised learning, especially when labeled data are few. When these biases are not aligned with reality, however, performance can be significantly degraded; this is a common but serious criticism of semi-supervised learning. A basic observation is that active learning provides the opportunity to validate or refute these biases using label queries, and also to subsequently revise them. Thus, it seems that active learners ought to be able to pursue learning biases much more aggressively than passive learners. A few works on cluster-based sampling and multi-view active learning have appeared, but much remains to be discovered.


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?


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.


An Active Learning Survey

Tags: Active,Machine Learning jl@ 5:11 am

Burr Settles wrote a fairly comprehensive survey of active learning. He intends to maintain and update the survey, so send him any suggestions you have.

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