We consider the problem of covariance matrix estimation in the presence of latent variables. Under suitable conditions, it is possible to learn the marginal covariance matrix of the observed variables via a tractable convex program, where the concentration matrix of the observed variables is decomposed into a sparse matrix (representing the graphical structure of the observed variables) and a low rank matrix (representing the marginalization effect of latent variables). We present an efficient first-order method based on split Bregman to solve the convex problem. The algorithm is guaranteed to converge under mild conditions. We show that our algorithm is significantly faster than the state-of-the-art algorithm on both artificial and real-world data. Applying the algorithm to a gene expression data involving thousands of genes, we show that most of the correlation between observed variables can be explained by only a few dozen latent factors.

This essay explores the limits of Turing machines concerning the modeling of minds and suggests alternatives to go beyond those limits.

In this paper, we present a supervised learning approach to training submodular scoring functions for extractive multi-document summarization. By taking a structured predicition approach, we provide a large-margin method that directly optimizes a convex relaxation of the desired performance measure. The learning method applies to all submodular summarization methods, and we demonstrate its effectiveness for both pairwise as well as coverage-based scoring functions on multiple datasets. Compared to state-of-the-art functions that were tuned manually, our method significantly improves performance and enables high-fidelity models with numbers of parameters well beyond what could reasonbly be tuned by hand.

Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the objective of a matchmaking process is to discover best available offers to a given request. We address the problem of matchmaking from a knowledge representation perspective, with a formalization based on Description Logics. We devise Concept Abduction and Concept Contraction as non-monotonic inferences in Description Logics suitable for modeling matchmaking in a logical framework, and prove some related complexity results. We also present reasonable algorithms for semantic matchmaking based on the devised inferences, and prove that they obey to some commonsense properties. Finally, we report on the implementation of the proposed matchmaking framework, which has been used both as a mediator in e-marketplaces and for semantic web services discovery.

PDDL was originally conceived and constructed as a lingua franca for the International Planning Competition. PDDL2.1 embodies a set of extensions intended to support the expression of something closer to real planning problems. This objective has only been partially achieved, due in large part to a deliberate focus on not moving too far from classical planning models and solution methods.

In this commentary I argue that although PDDL is a very useful standard for the planning competition, its design does not properly consider the issue of domain modeling. Hence, I would not advocate its use in specifying planning domains outside of the context of the planning competition. Rather, the field needs to explore different approaches and grapple more directly with the problem of effectively modeling and utilizing all of the diverse pieces of knowledge we typically have about planning domains.

This paper studies bilateral multi-issue negotiation between self-interested autonomous agents. Now, there are a number of different procedures that can be used for this process; the three main ones being the package deal procedure in which all the issues are bundled and discussed together, the simultaneous procedure in which the issues are discussed simultaneously but independently of each other, and the sequential procedure in which the issues are discussed one after another. Since each of them yields a different outcome, a key problem is to decide which one to use in which circumstances. Specifically, we consider this question for a model in which the agents have time constraints (in the form of both deadlines and discount factors) and information uncertainty (in that the agents do not know the opponents utility function). For this model, we consider issues that are both independent and those that are interdependent and determine equilibria for each case for each procedure. In so doing, we show that the package deal is in fact the optimal procedure for each party. We then go on to show that, although the package deal may be computationally more complex than the other two procedures, it generates Pareto optimal outcomes (unlike the other two), it has similar earliest and latest possible times of agreement to the simultaneous procedure (which is better than the sequential procedure), and that it (like the other two procedures) generates a unique outcome only under certain conditions (which we define).

Allocating scarce resources among agents to maximize global utility is, in general, computationally challenging. We focus on problems where resources enable agents to execute actions in stochastic environments, modeled as Markov decision processes (MDPs), such that the value of a resource bundle is defined as the expected value of the optimal MDP policy realizable given these resources. We present an algorithm that simultaneously solves the resource-allocation and the policy-optimization problems. This allows us to avoid explicitly representing utilities over exponentially many resource bundles, leading to drastic (often exponential) reductions in computational complexity. We then use this algorithm in the context of self-interested agents to design a combinatorial auction for allocating resources. We empirically demonstrate the effectiveness of our approach by showing that it can, in minutes, optimally solve problems for which a straightforward combinatorial resource-allocation technique would require the agents to enumerate up to 2^100 resource bundles and the auctioneer to solve an NP-complete problem with an input of that size.

In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules.

We describe how to convert the heuristic search algorithm A* into an anytime algorithm that finds a sequence of improved solutions and eventually converges to an optimal solution. The approach we adopt uses weighted heuristic search to find an approximate solution quickly, and then continues the weighted search to find improved solutions as well as to improve a bound on the suboptimality of the current solution. When the time available to solve a search problem is limited or uncertain, this creates an anytime heuristic search algorithm that allows a flexible tradeoff between search time and solution quality. We analyze the properties of the resulting Anytime A* algorithm, and consider its performance in three domains; sliding-tile puzzles, STRIPS planning, and multiple sequence alignment. To illustrate the generality of this approach, we also describe how to transform the memory-efficient search algorithm Recursive Best-First Search (RBFS) into an anytime algorithm.