We describe theoretical bounds and a practical algorithm for teaching a model by demonstration in a sequential decision making environment. Unlike previous efforts that have optimized learners that watch a teacher demonstrate a static policy, we focus on the teacher as a decision maker who can dynamically choose different policies to teach different parts of the environment. We develop several teaching frameworks based on previously defined supervised protocols, such as Teaching Dimension, extending them to handle noise and sequences of inputs encountered in an MDP. We provide theoretical bounds on the learnability of several important model classes in this setting and suggest a practical algorithm for dynamic teaching.

In practical machine learning systems, graph based data representation has been widely used in various learning paradigms, ranging from unsupervised clustering to supervised classification. Besides those applications with natural graph or network structure data, such as social network analysis and relational learning, many other applications often involve a critical step in converting data vectors to an adjacency graph. In particular, a sparse subgraph extracted from the original graph is often required due to both theoretic and practical needs. Previous study clearly shows that the performance of different learning algorithms, e.g., clustering and classification, benefits from such sparse subgraphs with balanced node connectivity. However, the existing graph construction methods are either computationally expensive or with unsatisfactory performance. In this paper, we utilize a scalable method called auction algorithm and its parallel extension to recover a sparse yet nearly balanced subgraph with significantly reduced computational cost. Empirical study and comparison with the stateof-art approaches clearly demonstrate the superiority of the proposed method in both efficiency and accuracy.

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items are scored independently by their similarity to the query in the latent embedding space. The structure of the ranked list (i.e. considering the set of items returned as a whole) is not taken into account. This can be a problem because the set of top predictions can be either too diverse (contain results that contradict each other) or are not diverse enough. In this paper we introduce a method for learning latent structured rankings that improves over existing methods by providing the right blend of predictions at the top of the ranked list. Particular emphasis is put on making this method scalable. Empirical results on large scale image annotation and music recommendation tasks show improvements over existing approaches.

Active Learning (AL) is increasingly important in a broad range of applications. Two main AL principles to obtain accurate classification with few labeled data are refinement of the current decision boundary and exploration of poorly sampled regions. In this paper we derive a novel AL scheme that balances these two principles in a natural way. In contrast to many AL strategies, which are based on an estimated class conditional probability ^p(y|x), a key component of our approach is to view this quantity as a random variable, hence explicitly considering the uncertainty in its estimated value. Our main contribution is a novel mathematical framework for uncertainty-based AL, and a corresponding AL scheme, where the uncertainty in ^p(y|x) is modeled by a second-order distribution. On the practical side, we show how to approximate such second-order distributions for kernel density classification. Finally, we find that over a large number of UCI, USPS and Caltech4 datasets, our AL scheme achieves significantly better learning curves than popular AL methods such as uncertainty sampling and error reduction sampling, when all use the same kernel density classifier.

Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in social sciences and marketing, "analytical ability" in educational testing, or "inflation" in economics). This leads to the development of measurement instruments to record noisy indirect evidence for such unobserved variables such as surveys, tests and price indexes. In such problems, there are postulated latent variables and a given measurement model. At the same time, other unantecipated latent variables can add further unmeasured confounding to the observed variables. The problem is how to deal with unantecipated latents variables. In this paper, we provide a method loosely inspired by canonical correlation that makes use of background information concerning the "known" latent variables. Given a partially specified structure, it provides a structure learning approach to detect "unknown unknowns," the confounding effect of potentially infinitely many other latent variables. This is done without explicitly modeling such extra latent factors. Because of the special structure of the problem, we are able to exploit a new variation of composite likelihood fitting to efficiently learn this structure. Validation is provided with experiments in synthetic data and the analysis of a large survey done with a sample of over 100,000 staff members of the National Health Service of the United Kingdom.

Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is well-understood, with efficient computations taking O(DlogD) time. Yet efficient marginalization and sampling have not been addressed as thoroughly in the machine learning community. We show that there exists a simple algorithm for computing marginal probabilities and drawing exact joint samples that runs in O(Dlog2 D) time, and we show how to frame the algorithm as efficient belief propagation in a low order tree-structured model that includes additional auxiliary variables. We then develop a new, more general class of models, termed Recursive Cardinality models, which take advantage of this efficiency. Finally, we show how to do efficient exact inference in models composed of a tree structure and a cardinality potential. We explore the expressive power of Recursive Cardinality models and empirically demonstrate their utility.

Recently, Petrik et al. demonstrated that L1Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and value function approximation steps simultaneously. RALP's performance guarantees become looser if sampled next states are used. For very noisy domains, RALP requires an accurate model rather than samples, which can be unrealistic in some practical scenarios. In this paper, we demonstrate this weakness, and then introduce Locally Smoothed L1-Regularized Approximate Linear Programming (LS-RALP). We demonstrate that LS-RALP mitigates inaccuracies stemming from noise even without an accurate model. We show that, given some smoothness assumptions, as the number of samples increases, error from noise approaches zero, and provide experimental examples of LS-RALP's success on common reinforcement learning benchmark problems.

This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to minimization of convex functions in highdimensional spaces. Unlike traditional gradient methods, mirror descent undertakes gradient updates of weights in both the dual space and primal space, which are linked together using a Legendre transform. Mirror descent can be viewed as a proximal algorithm where the distance generating function used is a Bregman divergence. A new class of proximal-gradient based temporal-difference (TD) methods are presented based on different Bregman divergences, which are more powerful than regular TD learning. Examples of Bregman divergences that are studied include p-norm functions, and Mahalanobis distance based on the covariance of sample gradients. A new family of sparse mirror-descent reinforcement learning methods are proposed, which are able to find sparse fixed points of an l1-regularized Bellman equation at significantly less computational cost than previous methods based on second-order matrix methods. An experimental study of mirror-descent reinforcement learning is presented using discrete and continuous Markov decision processes.

Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arising from multiple modalities or make restrictive assumptions about the form of the functions or transformations, limiting their generality. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is determined in a data-driven fashion through the use of a Dirichlet process prior, and it can accommodate any transformation function parameterized by a continuous parameter vector. As a result, it is applicable to a wide range of data types, and transformation functions. We present positive results on synthetic two-dimensional data, on a set of one-dimensional curves, and on various image data sets, showing large improvements over previous work. We discuss several variations of the model and conclude with directions for future work.

Learning a Bayesian network structure from data is an NP-hard problem and thus exact algorithms are feasible only for small data sets. Therefore, network structures for larger networks are usually learned with various heuristics. Another approach to scaling up the structure learning is local learning. In local learning, the modeler has one or more target variables that are of special interest; he wants to learn the structure near the target variables and is not interested in the rest of the variables. In this paper, we present a score-based local learning algorithm called SLL. We conjecture that our algorithm is theoretically sound in the sense that it is optimal in the limit of large sample size. Empirical results suggest that SLL is competitive when compared to the constraint-based HITON algorithm. We also study the prospects of constructing the network structure for the whole node set based on local results by presenting two algorithms and comparing them to several heuristics.