Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such models can be very computationally expensive when there are many datapoints and many continuous variables with complex nonlinear relationships, particularly when no good ways of decomposing the joint distribution are known a priori. In such situations, previous research has generally focused on the use of discretization techniques in which each continuous variable has a single discretization that is used throughout the entire network. \ In this paper, we present and compare a wide variety of tree-based algorithms for learning and evaluating conditional density estimates over continuous variables. These trees can be thought of as discretizations that vary according to the particular interactions being modeled; however, the density within a given leaf of the tree need not be assumed constant, and we show that such nonuniform leaf densities lead to more accurate density estimation. We have developed Bayesian network structure-learning algorithms that employ these tree-based conditional density representations, and we show that they can be used to practically learn complex joint probability models over dozens of continuous variables from thousands of datapoints. We focus on finding models that are simultaneously accurate, fast to learn, and fast to evaluate once they are learned.

We develop a qualitative theory of Markov Decision Processes (MDPs) and Partially Observable MDPs that can be used to model sequential decision making tasks when only qualitative information is available. Our approach is based upon an order-of-magnitude approximation of both probabilities and utilities, similar to epsilon-semantics. The result is a qualitative theory that has close ties with the standard maximum-expected-utility theory and is amenable to general planning techniques.

The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the definition and analysis of one such search space. We use a theoretically motivated neighbourhood, the inclusion boundary, and represent equivalence classes by essential graphs. We show that this search space is connected and that the score of the neighbours can be evaluated incrementally. We devise a practical way of building this neighbourhood for an essential graph that is purely graphical and does not explicitely refer to the underlying independences. We find that its size can be intractable, depending on the complexity of the essential graph of the equivalence class. The emphasis is put on the potential use of this space with greedy hill -climbing search

We introduce a new method for training deep Boltzmann machines jointly. Prior methods require an initial learning pass that trains the deep Boltzmann machine greedily, one layer at a time, or do not perform well on classifi- cation tasks.

We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a convex optimization problem that involves searching over the forest and hyperforest polytopes with special structures, independently. A supergradient method is used to solve the dual problem, with a run-time complexity of $O(k^3 n^{k+2} \log n)$ for each iteration, where $n$ is the number of variables and $k$ is a bound on the treewidth. We compare our approach to state-of-the-art methods on synthetic datasets and classical benchmarks, showing the gains of the novel convex approach.

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diverge only in their marginals, i.e. they have the same labeling function. Another popular approach is to consider an hypothesis class that moves closer the two distributions while implying a low-error for both tasks. This is a VC-dim approach that restricts the complexity of an hypothesis class in order to get good generalization. Instead, we propose a PAC-Bayesian approach that seeks for suitable weights to be given to each hypothesis in order to build a majority vote. We prove a new DA bound in the PAC-Bayesian context. This leads us to design the first DA-PAC-Bayesian algorithm based on the minimization of the proposed bound. Doing so, we seek for a \rho-weighted majority vote that takes into account a trade-off between three quantities. The first two quantities being, as usual in the PAC-Bayesian approach, (a) the complexity of the majority vote (measured by a Kullback-Leibler divergence) and (b) its empirical risk (measured by the \rho-average errors on the source sample). The third quantity is (c) the capacity of the majority vote to distinguish some structural difference between the source and target samples.

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces. Keywords: Markov decision processes, hierarchical reinforcement learning, transfer, multiscale analysis.

Machine Learning manuscript No. (will be inserted by the editor) Abstract This paper considers the challenge of evaluating a set of classifiers, as done in shared task evaluations like the KDD Cup or NIST TREC, without expert labels. While expert labels provide the traditional cornerstone for evaluating statistical learners, limited or expensive access to experts represents a practical bottleneck. Instead, we seek methodology for estimating performance of the classifiers (relative and absolute) which is more scalable than expert labeling yet preserves high correlation with evaluation based on expert labels. We consider both: 1) using only labels automatically generated by the classifiers themselves (blind evaluation); and 2) using labels obtained via crowdsourcing. While crowdsourcing methods are lauded for scalability, using such data for evaluation raises serious concerns given the prevalence of label noise. In regard to blind evaluation, two broad strategies are investigated: combine & score and score & combine. Combine & Score methods infer a single "pseudo-gold" label set by aggregating classifier labels; classifiers are then evaluated based on this single pseudo-gold label set. On the other hand, score & combine methods: i) sample multiple label sets from classifier outputs, ii) evaluate classifiers on each label set, and iii) average classifier performance across label sets. When additional crowd labels are also collected, we investigate two alternative avenues for exploiting them: 1) direct evaluation of classifiers; or 2) supervision of combine-and-score methods. To assess generality of our techniques, classifier performance is measured using four common classification metrics, with statistical significance tests establishing relative performance of the classifiers for each metric. Finally, we measure both score and rank correlations between estimated classifier performance vs. actual performance according to expert judgments. Rigorous evaluation of classifiers from the TREC 2011 Crowdsourcing Track shows reliable evaluation can be achieved without reliance on expert labels.

The standard training method of Conditional Random Fields (CRFs) is very slow for large-scale applications. As an alternative, piecewise training divides the full graph into pieces, trains them independently, and combines the learned weights at test time. In this paper, we present \emph{separate} training for undirected models based on the novel Co-occurrence Rate Factorization (CR-F). Separate training is a local training method. In contrast to MEMMs, separate training is unaffected by the label bias problem. Experiments show that separate training (i) is unaffected by the label bias problem; (ii) reduces the training time from weeks to seconds; and (iii) obtains competitive results to the standard and piecewise training on linear-chain CRFs.

Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in parallel (and possibly interacting) have summed time-evolution operators. From this foundation, algorithms for simulation, inference and model reduction may be systematically derived. The useful consequences are potentially far-reaching in computational science, machine learning and beyond. Hybrid compositional stochastic modeling/probabilistic programming approaches may also be possible.