Domain-specific features are important in representing problem structure throughout machine learning and decision-theoretic planning. In planning, once state features are provided, domain-independent algorithms such as approximate value iteration can learn weighted combinations of those features that often perform well as heuristic estimates of state value (e.g., distance to the goal). Successful applications in real-world domains often require features crafted by human experts. Here, we propose automatic processes for learning useful domain-specific feature sets with little or no human intervention. Our methods select and add features that describe state-space regions of high inconsistency in the Bellman equation (statewise Bellman error) during approximate value iteration. Our method can be applied using any real-valued-feature hypothesis space and corresponding learning method for selecting features from training sets of state-value pairs. We evaluate the method with hypothesis spaces defined by both relational and propositional feature languages, using nine probabilistic planning domains. We show that approximate value iteration using a relational feature space performs at the state-of-the-art in domain-independent stochastic relational planning. Our method provides the first domain-independent approach that plays Tetris successfully (without human-engineered features).

We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the Normal means model. This model, often used in the field of statistics, is a simplified model that provides a laboratory for studying complex procedures.

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when the groups are disjoint or embedded in a specific hierarchical structure, we address here the case of general overlapping groups. To this end, we show that the corresponding optimization problem is related to network flow optimization. More precisely, the proximal problem associated with the norm we consider is dual to a quadratic min-cost flow problem. We propose an efficient procedure which computes its solution exactly in polynomial time. Our algorithm scales up to millions of variables, and opens up a whole new range of applications for structured sparse models. We present several experiments on image and video data, demonstrating the applicability and scalability of our approach for various problems.

In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits multiple modalities, such as acoustic and visual content of video. Integrating such heterogeneous data to form a holistic similarity space is therefore a key challenge to be overcome in many real-world applications. We present a novel multiple kernel learning technique for integrating heterogeneous data into a single, unified similarity space. Our algorithm learns an optimal ensemble of kernel transfor- mations which conform to measurements of human perceptual similarity, as expressed by relative comparisons. To cope with the ubiquitous problems of subjectivity and inconsistency in multi- media similarity, we develop graph-based techniques to filter similarity measurements, resulting in a simplified and robust training procedure.

Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that can achieve considerably stronger pruning than arc consistency. However, existing maxRRC algorithms suffer from overheads and redundancies as they can repeatedly perform many constraint checks without triggering any value deletions. In this paper we propose techniques that can boost the performance of maxRPC algorithms. These include the combined use of two data structures to avoid many redundant constraint checks, and heuristics for the efficient ordering and execution of certain operations. Based on these, we propose two closely related algorithms. The first one which is a maxRPC algorithm with optimal O(end^3) time complexity, displays good performance when used stand-alone, but is expensive to apply during search. The second one approximates maxRPC and has O(en^2d^4) time complexity, but a restricted version with O(end^4) complexity can be very efficient when used during search. Both algorithms have O(ed) space complexity. Experimental results demonstrate that the resulting methods constantly outperform previous algorithms for maxRPC, often by large margins, and constitute a more than viable alternative to arc consistency on many problems.

Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using $l_1/l_2$ regularization upon the activation possibilities of hidden units in restricted Boltzmann machines to capture the loacal dependencies among hidden units. This regularization not only encourages hidden units of many groups to be inactive given observed data but also makes hidden units within a group compete with each other for modeling observed data. Thus, the $l_1/l_2$ regularization on RBMs yields sparsity at both the group and the hidden unit levels. We call RBMs trained with the regularizer \emph{sparse group} RBMs. The proposed sparse group RBMs are applied to three tasks: modeling patches of natural images, modeling handwritten digits and pretaining a deep networks for a classification task. Furthermore, we illustrate the regularizer can also be applied to deep Boltzmann machines, which lead to sparse group deep Boltzmann machines. When adapted to the MNIST data set, a two-layer sparse group Boltzmann machine achieves an error rate of $0.84\%$, which is, to our knowledge, the best published result on the permutation-invariant version of the MNIST task.

The scientific method relies on the iterated processes of inference and inquiry. The inference phase consists of selecting the most probable models based on the available data; whereas the inquiry phase consists of using what is known about the models to select the most relevant experiment. Optimizing inquiry involves searching the parameterized space of experiments to select the experiment that promises, on average, to be maximally informative. In the case where it is important to learn about each of the model parameters, the relevance of an experiment is quantified by Shannon entropy of the distribution of experimental outcomes predicted by a probable set of models. If the set of potential experiments is described by many parameters, we must search this high-dimensional entropy space. Brute force search methods will be slow and computationally expensive. We present an entropy-based search algorithm, called nested entropy sampling, to select the most informative experiment for efficient experimental design. This algorithm is inspired by Skilling's nested sampling algorithm used in inference and borrows the concept of a rising threshold while a set of experiment samples are maintained. We demonstrate that this algorithm not only selects highly relevant experiments, but also is more efficient than brute force search. Such entropic search techniques promise to greatly benefit autonomous experimental design.

Coalitional games serve the purpose of modeling payoff distribution problems in scenarios where agents can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. In the classical Transferable Utility (TU) setting, coalition worths can be freely distributed amongst agents. However, in several application scenarios, this is not the case and the Non-Transferable Utility setting (NTU) must be considered, where additional application-oriented constraints are imposed on the possible worth distributions. In this paper, an approach to define NTU games is proposed which is based on describing allowed distributions via a set of mixed-integer linear constraints applied to an underlying TU game. It is shown that such games allow non-transferable conditions on worth distributions to be specified in a natural and succinct way. The properties and the relationships among the most prominent solution concepts for NTU games that hold when they are applied on (mixed-integer) constrained games are investigated. Finally, a thorough analysis is carried out to assess the impact of issuing constraints on the computational complexity of some of these solution concepts.

The Aviation Safety Reporting System collects voluntarily submitted reports on aviation safety incidents to facilitate research work aiming to reduce such incidents. To effectively reduce these incidents, it is vital to accurately identify why these incidents occurred. More precisely, given a set of possible causes, or shaping factors, this task of cause identification involves identifying all and only those shaping factors that are responsible for the incidents described in a report. We investigate two approaches to cause identification. Both approaches exploit information provided by a semantic lexicon, which is automatically constructed via Thelen and Riloff's Basilisk framework augmented with our linguistic and algorithmic modifications. The first approach labels a report using a simple heuristic, which looks for the words and phrases acquired during the semantic lexicon learning process in the report. The second approach recasts cause identification as a text classification problem, employing supervised and transductive text classification algorithms to learn models from incident reports labeled with shaping factors and using the models to label unseen reports. Our experiments show that both the heuristic-based approach and the learning-based approach (when given sufficient training data) outperform the baseline system significantly.

We use genetic programming to evolve highly successful solvers for two puzzles: Rush Hour and FreeCell. Many NP-Complete puzzles have remained relatively neglected by researchers (see (Kendall, Parkes, and Spoerer 2008) for a review).