Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features. Our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints. We experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state-of-the-art, yet non-adaptive, subgradient algorithms.

Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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Adaptive Subgradient Methods for Online Learning and Stochastic Optimization

The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer training labels if it is allowed to choose the data from which it learns. An active learner may pose queries, usually in the form of unlabeled data instances to be labeled by an oracle (e.g., a human annotator). Active learning is well-motivated in many modern machine learning problems, where unlabeled data may be abundant or easily obtained, but labels are difficult, time-consuming, or expensive to obtain. This report provides a general introduction to active learning and a survey of the literature. This includes a discussion of the scenarios in which queries can be formulated, and an overview of the query strategy frameworks proposed in the literature to date. An analysis of the empirical and theoretical evidence for successful active learning, a summary of problem setting variants and practical issues, and a discussion of related topics in machine learning research are also presented.

Active Learning Literature Survey

We give an efficient algorithm for learning a binary function in a given class C of bounded VC dimension, with training data distributed according to P and test data according to Q, where P and Q may be arbitrary distributions over X. This is the generic form of what is called covariate shift, which is impossible in general as arbitrary P and Q may not even overlap. However, recently guarantees were given in a model called PQ-learning (Goldwasser et al., 2020) where the learner has: (a) access to unlabeled test examples from Q (in addition to labeled samples from P, i.e., semi-supervised learning); and (b) the option to reject any example and abstain from classifying it (i.e., selective classification). The algorithm of Goldwasser et al. (2020) requires an (agnostic) noise tolerant learner for C. The present work gives a polynomial-time PQ-learning algorithm that uses an oracle to a "reliable" learner for C, where reliable learning (Kalai et al., 2012) is a model of learning with one-sided noise. Furthermore, our reduction is optimal in the sense that we show the equivalence of reliable and PQ learning.

Efficient Learning with Arbitrary Covariate Shift

Current state-of-the-art language models (LMs) are notorious for generating text with"hallucinations,"a primary example being book and paper references that lack any solid basis in their training data. However, we find that many of these fabrications can be identified using the same LM, using only black-box queries without consulting any external resources. Consistency checks done with direct queries about whether the generated reference title is real (inspired by Kadavath et al. 2022, Lin et al. 2022, Manakul et al. 2023) are compared to consistency checks with indirect queries which ask for ancillary details such as the authors of the work. These consistency checks are found to be partially reliable indicators of whether or not the reference is a hallucination. In particular, we find that LMs in the GPT-series will hallucinate differing authors of hallucinated references when queried in independent sessions, while it will consistently identify authors of real references. This suggests that the hallucination may be more a result of generation techniques than the underlying representation.

Do Language Models Know When They're Hallucinating References?

A common challenge across all areas of machine learning is that training data is not distributed like test data, due to natural shifts, "blind spots," or adversarial examples. We consider a model where one may abstain from predicting, at a fixed cost. In particular, our transductive abstention algorithm takes labeled training examples and unlabeled test examples as input, and provides predictions with optimal prediction loss guarantees. The loss bounds match standard generalization bounds when test examples are i.i.d. from the training distribution, but add an additional term that is the cost of abstaining times the statistical distance between the train and test distribution (or the fraction of adversarial examples). For linear regression, we give a polynomial-time algorithm based on Celis-Dennis-Tapia optimization algorithms. For binary classification, we show how to efficiently implement it using a proper agnostic learner (i.e., an Empirical Risk Minimizer) for the class of interest. Our work builds on a recent abstention algorithm of Goldwasser, Kalais, and Montasser (2020) for transductive binary classification.

Adam Tauman Kalai

Papers

Efficient Learning with Arbitrary Covariate Shift

Do Language Models Know When They're Hallucinating References?

Towards optimally abstaining from prediction.