Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in \mathbb N$ of possible point evaluations $f(x_i)$, $i=1,...,m$, of $f$, which we are allowed to query in order to construct a uniform approximating function. Under certain smoothness and variation assumptions on the function $g$, and an {\it arbitrary} choice of the matrix $A$, we present in this paper 1. a sampling choice of the points $\{x_i\}$ drawn at random for each function approximation; 2. algorithms (Algorithm 1 and Algorithm 2) for computing the approximating function, whose complexity is at most polynomial in the dimension $d$ and in the number $m$ of points. Due to the arbitrariness of $A$, the choice of the sampling points will be according to suitable random distributions and our results hold with overwhelming probability. Our approach uses tools taken from the {\it compressed sensing} framework, recent Chernoff bounds for sums of positive-semidefinite matrices, and classical stability bounds for invariant subspaces of singular value decompositions.

We review some existing methods for the computation of first order moments on junction trees using Shafer-Shenoy algorithm. First, we consider the problem of first order moments computation as vertices problem in junction trees. In this way, the problem is solved using the memory space of an order of the junction tree edge-set cardinality. After that, we consider two algorithms, Lauritzen-Nilsson algorithm, and Mauá et al. algorithm, which computes the first order moments as the normalization problem in junction tree, using the memory space of an order of the junction tree leaf-set cardinality. K, where A,B U. We assume that the following Shafer-Shenoy axioms hold for combination and marginalization. We omit the parentheses from the notation when it is not prone to misunderstanding.

Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the epsilon-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the epsilon as a choice operator. After reviewing the literature on semantics of Hilbert's epsilon operator, we propose a new semantics with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports proof search optimally and is natural in the sense that it does not only mirror some cases of referential interpretation of indefinite articles in natural language, but may also contribute to philosophy of language. Finally, we ask the question whether our epsilon within our free-variable framework can serve as a paradigm useful in the specification and computation of semantics of discourses in natural language.

Basically, in (one-player) war Real Time Strategy (wRTS) games a human player controls, in real time, an army consisting of a number of soldiers and her aim is to destroy the opponent's assets where the opponent is a virtual (i.e., non-human player controlled) player that usually consists of a pre-programmed decision-making script. These scripts have usually associated some well-known problems (e.g., predictability, non-rationality, repetitive behaviors, and sensation of artificial stupidity among others). This paper describes a method for the automatic generation of virtual players that adapt to the player skills; this is done by building initially a model of the player behavior in real time during the game, and further evolving the virtual player via this model in-between two games. The paper also shows preliminary results obtained on a one player wRTS game constructed specifically for experimentation.

This paper is the continuation of our research work about linguistic truth-valued concept lattice. In order to provide a mathematical tool for mining tacit knowledge, we establish a concrete model of 6-ary linguistic truth-valued concept lattice and introduce a mining algorithm through the structure consistency. Specifically, we utilize the attributes to depict knowledge, propose the 6-ary linguistic truth-valued attribute extended context and congener context to characterize tacit knowledge, and research the necessary and sufficient conditions of forming tacit knowledge. We respectively give the algorithms of generating the linguistic truth-valued congener context and constructing the linguistic truth-valued concept lattice.

The existence of a non-algorithmic side of the mind, conjectured by Penrose on the basis of G\"odel's first incompleteness theorem, is investigated here in terms of a quantum metalanguage. We suggest that, besides human ordinary thought, which can be formalized in a computable, logical language, there is another important kind of human thought, which is Turing-non-computable. This is methatought, the process of thinking about ordinary thought. Metathought can be formalized as a metalanguage, which speaks about and controls the logical language of ordinary thought. Ordinary thought has two computational modes, the quantum mode and the classical mode, the latter deriving from decoherence of the former. In order to control the logical language of the quantum mode, one needs to introduce a quantum metalanguage, which in turn requires a quantum version of Tarski Convention T.

Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinite programming which improves the method sensitivity to a broad variety of deviations from normality. We also discuss the procedures which allows to recover the structure when its effective dimension is unknown.

A specific type of neural network, the Restricted Boltzmann Machine (RBM), is implemented for classification and feature detection in machine learning. RBM is characterized by separate layers of visible and hidden units, which are able to learn efficiently a generative model of the observed data. We study a "hybrid" version of RBM's, in which hidden units are analog and visible units are binary, and we show that thermodynamics of visible units are equivalent to those of a Hopfield network, in which the N visible units are the neurons and the P hidden units are the learned patterns. We apply the method of stochastic stability to derive the thermodynamics of the model, by considering a formal extension of this technique to the case of multiple sets of stored patterns, which may act as a benchmark for the study of correlated sets. Our results imply that simulating the dynamics of a Hopfield network, requiring the update of N neurons and the storage of N(N-1)/2 synapses, can be accomplished by a hybrid Boltzmann Machine, requiring the update of N+P neurons but the storage of only NP synapses. In addition, the well known glass transition of the Hopfield network has a counterpart in the Boltzmann Machine: It corresponds to an optimum criterion for selecting the relative sizes of the hidden and visible layers, resolving the trade-off between flexibility and generality of the model. The low storage phase of the Hopfield model corresponds to few hidden units and hence a overly constrained RBM, while the spin-glass phase (too many hidden units) corresponds to unconstrained RBM prone to overfitting of the observed data.

For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other with respect to the metric are expected to be stronger than the dependencies between variables that are further apart. The purpose of this paper is to describe a method that combines such a problem-specific distance metric with information mined from probabilistic models obtained in previous runs of estimation of distribution algorithms with the goal of solving future problem instances of similar type with increased speed, accuracy and reliability. While the focus of the paper is on additively decomposable problems and the hierarchical Bayesian optimization algorithm, it should be straightforward to generalize the approach to other model-directed optimization techniques and other problem classes. Compared to other techniques for learning from experience put forward in the past, the proposed technique is both more practical and more broadly applicable.

Blogs-Online digital diary like application on web 2.0 has opened new and easy way to voice opinion, thoughts, and like-dislike of every Internet user to the World. Blogosphere has no doubt the largest user-generated content repository full of knowledge. The potential of this knowledge is still to be explored. Knowledge discovery from this new genre is quite difficult and challenging as it is totally different from other popular genre of web-applications like World Wide Web (WWW). Blog-posts unlike web documents are small in size, thus lack in context and contain relaxed grammatical structures. Hence, standard text similarity measure fails to provide good results. In this paper, specialized requirements for comparing a pair of blog-posts is thoroughly investigated. Based on this we proposed a novel algorithm for sentence oriented semantic similarity measure of a pair of blog-posts. We applied this algorithm on a subset of political blogosphere of Pakistan, to cluster the blogs on different issues of political realm and to identify the influential bloggers.