We study constraint satisfaction problems on the so-called planted random ensemble. We show that for a certain class of problems, e.g. We study the structural phase transitions, and the easy/hard/easy pattern in the average computational complexity. We also discuss the finite temperature phase diagram, finding a close connection with the liquid/glass/solid phenomenology. Constraint satisfaction problems (CSPs) stand at the root of the theory of computational complexity [1] and arise in computer science, physics, engineering and many other fields of science.

The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure $\mu$ belongs to an arbitrary class $\C$ of stochastic processes. We are interested in predictors $\rho$ whose conditional probabilities converge to the "true" $\mu$-conditional probabilities if any $\mu\in\C$ is chosen to generate the data. We show that if such a predictor exists, then a predictor can also be obtained as a convex combination of a countably many elements of $\C$. In other words, it can be obtained as a Bayesian predictor whose prior is concentrated on a countable set. This result is established for two very different measures of performance of prediction, one of which is very strong, namely, total variation, and the other is very weak, namely, prediction in expected average Kullback-Leibler divergence.

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006) allows to express the exact partition function of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in (Certkov et al., 2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze the performance of the algorithm for the partition function approximation for models with binary variables and pairwise interactions on grids and other planar graphs. We study in detail both the loop series and the equivalent Pfaffian series and show that the first term of the Pfaffian series for the general, intractable planar model, can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.

Complex questions that require inferencing and synthesizing information from multiple documents can be seen as a kind of topic-oriented, informative multi-document summarization where the goal is to produce a single text as a compressed version of a set of documents with a minimum loss of relevant information. In this paper, we experiment with one empirical method and two unsupervised statistical machine learning techniques: K-means and Expectation Maximization (EM), for computing relative importance of the sentences. We compare the results of these approaches. Our experiments show that the empirical approach outperforms the other two techniques and EM performs better than K-means. However, the performance of these approaches depends entirely on the feature set used and the weighting of these features. In order to measure the importance and relevance to the user query we extract different kinds of features (i.e. lexical, lexical semantic, cosine similarity, basic element, tree kernel based syntactic and shallow-semantic) for each of the document sentences. We use a local search technique to learn the weights of the features. To the best of our knowledge, no study has used tree kernel functions to encode syntactic/semantic information for more complex tasks such as computing the relatedness between the query sentences and the document sentences in order to generate query-focused summaries (or answers to complex questions). For each of our methods of generating summaries (i.e. empirical, K-means and EM) we show the effects of syntactic and shallow-semantic features over the bag-of-words (BOW) features.

When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these presentations are neither intended nor suitable for human use. A challenge therefore is to develop user- and goal-adaptive proof presentation techniques that obey common mathematical practice. We present a flexible and adaptive approach to proof presentation that exploits machine learning techniques to extract a model of the specific granularity of proof examples and employs this model for the automated generation of further proofs at an adapted level of granularity.

We relate tag clouds to other forms of visualization, including planar or reduced dimensionality mapping, and Kohonen self-organizing maps. Using a modified tag cloud visualization, we incorporate other information into it, including text sequence and most pertinent words. Our notion of word pertinence goes beyond just word frequency and instead takes a word in a mathematical sense as located at the average of all of its pairwise relationships. We capture semantics through context, taken as all pairwise relationships. Our domain of application is that of filmscript analysis. The analysis of filmscripts, always important for cinema, is experiencing a major gain in importance in the context of television. Our objective in this work is to visualize the semantics of filmscript, and beyond filmscript any other partially structured, time-ordered, sequence of text segments. In particular we develop an innovative approach to plot characterization.

We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised arc consistency on such a multiset ordering constraint. Experimental results on several problem domains show considerable promise.

Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework, based on both CP-nets and soft constraints, that handles both hard and soft constraints as well as conditional preferences efficiently and uniformly. We study the complexity of testing the consistency of preference statements, and show how soft constraints can faithfully approximate the semantics of conditional preference statements whilst improving the computational complexity.

We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the ALLDIFFERENT constraint.

We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudo-Boolean solver.