The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2 under L2-norm for real valued matrices.

In many fields where human understanding plays a crucial role, such as bioprocesses, the capacity of extracting knowledge from data is of critical importance. Within this framework, fuzzy learning methods, if properly used, can greatly help human experts. Amongst these methods, the aim of orthogonal transformations, which have been proven to be mathematically robust, is to build rules from a set of training data and to select the most important ones by linear regression or rank revealing techniques. The OLS algorithm is a good representative of those methods. However, it was originally designed so that it only cared about numerical performance. Thus, we propose some modifications of the original method to take interpretability into account. After recalling the original algorithm, this paper presents the changes made to the original method, then discusses some results obtained from benchmark problems. Finally, the algorithm is applied to a real-world fault detection depollution problem.

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we uniformly sample polynomially many samples from the (exponentially large) state space. This way, the complexity of our algorithm becomes polynomial in the size of the fMDP description length. We prove that the algorithm is convergent. We also derive an upper bound on the difference between our approximate solution and the optimal one, and also on the error introduced by sampling. We analyze various projection operators with respect to their computation complexity and their convergence when combined with approximate value iteration.

This report describes experimental results for a set of benchmarks on program verification. It compares the capabilities of CPBVP "Constraint Programming framework for Bounded Program Verification" [4] with the following frameworks: ESC/Java, CBMC, Blast, EUREKA and Why.

In this article we review standard null-move pruning and introduce our extended version of it, which we call verified null-move pruning. In verified null-move pruning, whenever the shallow null-move search indicates a fail-high, instead of cutting off the search from the current node, the search is continued with reduced depth. Our experiments with verified null-move pruning show that on average, it constructs a smaller search tree with greater tactical strength in comparison to standard null-move pruning. Moreover, unlike standard null-move pruning, which fails badly in zugzwang positions, verified null-move pruning manages to detect most zugzwangs and in such cases conducts a re-search to obtain the correct result. In addition, verified null-move pruning is very easy to implement, and any standard null-move pruning program can use verified null-move pruning by modifying only a few lines of code.

Over two decades ago a "quite revolution" overwhelmingly replaced knowledgebased approaches in natural language processing (NLP) by quantitative (e.g., statistical, corpus-based, machine learning) methods. Although it is our firm belief that purely quantitative approaches cannot be the only paradigm for NLP, dissatisfaction with purely engineering approaches to the construction of large knowledge bases for NLP are somewhat justified. In this paper we hope to demonstrate that both trends are partly misguided and that the time has come to enrich logical semantics with an ontological structure that reflects our commonsense view of the world and the way we talk about in ordinary language. In this paper it will be demonstrated that assuming such an ontological structure a number of challenges in the semantics of natural language (e.g., metonymy, intensionality, copredication, nominal compounds, etc.) can be properly and uniformly addressed.

We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a conditional probability simplex.

Statistical topic models provide a general data-driven framework for automated discovery of high-level knowledge from large collections of text documents. While topic models can potentially discover a broad range of themes in a data set, the interpretability of the learned topics is not always ideal. Human-defined concepts, on the other hand, tend to be semantically richer due to careful selection of words to define concepts but they tend not to cover the themes in a data set exhaustively. In this paper, we propose a probabilistic framework to combine a hierarchy of human-defined semantic concepts with statistical topic models to seek the best of both worlds. Experimental results using two different sources of concept hierarchies and two collections of text documents indicate that this combination leads to systematic improvements in the quality of the associated language models as well as enabling new techniques for inferring and visualizing the semantics of a document.

The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. We show that the reconstruction weights computed by LLE capture the high-dimensional structure of the neighborhoods, and not the low-dimensional manifold structure. Consequently, the weight vectors are highly sensitive to noise. Moreover, this causes LLE to converge to a linear projection of the input, as opposed to its non-linear embedding goal. To overcome both of these problems, we propose to compute the weight vectors using a low-dimensional neighborhood representation. We prove theoretically that this straightforward and computationally simple modification of LLE reduces LLE's sensitivity to noise. This modification also removes the need for regularization when the number of neighbors is larger than the dimension of the input. We present numerical examples demonstrating both the perturbation and linear projection problems, and the improved outputs using the low-dimensional neighborhood representation.

The ongoing discussion whether modern vision systems have to be viewed as visually-enabled cognitive systems or cognitively-enabled vision systems is groundless, because perceptual and cognitive faculties of vision are separate components of human (and consequently, artificial) information processing system modeling.