We present a fast, fully parameterizable GPU implementation of Convolutional Neural Network variants. Our feature extractors are neither carefully designed nor pre-wired, but rather learned in a supervised way. Our deep hierarchical architectures achieve the best published results on benchmarks for object classification (NORB, CIFAR10) and handwritten digit recognition (MNIST), with error rates of 2.53%, 19.51%, 0.35%, respectively. Deep nets trained by simple back-propagation perform better than more shallow ones. Learning is surprisingly rapid. NORB is completely trained within five epochs. Test error rates on MNIST drop to 2.42%, 0.97% and 0.48% after 1, 3 and 17 epochs, respectively.

Boolean Satisfiability solvers have gone through dramatic improvements in their performances and scalability over the last few years by considering symmetries. It has been shown that by using graph symmetries and generating symmetry breaking predicates (SBPs) it is possible to break symmetries in Conjunctive Normal Form (CNF). The SBPs cut down the search space to the nonsymmetric regions of the space without affecting the satisfiability of the CNF formula. The symmetry breaking predicates are created by representing the formula as a graph, finding the graph symmetries and using some symmetry extraction mechanism (Crawford et al.). Here in this paper we take one non-trivial CNF and explore its symmetries. Finally, we generate the SBPs and adding it to CNF we show how it helps to prune the search tree, so that SAT solver would take short time. Here we present the pruning procedure of the search tree from scratch, starting from the CNF and its graph representation. As we explore the whole mechanism by a non-trivial example, it would be easily comprehendible. Also we have given a new idea of generating symmetry breaking predicates for breaking symmetry in CNF, not derived from Crawford's conditions. At last we propose a backtrack SAT solver with inbuilt SBP generator.

Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower and upper approximations. It seems somewhat unreasonable since the basic idea of rough set theory aims at describing vague concepts by the lower and upper approximations. In this paper, we thus define new information-theoretic entropy and co-entropy functions associated to the partition and the approximations to measure the uncertainty and granularity of an approximation space. After introducing the novel notions of entropy and co-entropy, we then examine their properties. In particular, we discuss the relationship of co-entropies between different universes. The theoretical development is accompanied by illustrative numerical examples.

We offer a new understanding of some aspects of practical SAT-solvers that are based on DPLL with unit-clause propagation, clause-learning, and restarts. We do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, before making any new decision or restart, the solver repeatedly applies the unit-resolution rule until saturation, and leaves no component to the mercy of non-determinism except for some internal randomness. We prove the perhaps surprising fact that, although the solver is not explicitly designed for it, with high probability it ends up behaving as width-k resolution after no more than O(n^{2k+2}) conflicts and restarts, where n is the number of variables. In other words, width-k resolution can be thought of as O(n^{2k+2}) restarts of the unit-resolution rule with learning.

Learning to rank has been a task of significant interest during the recent years. The ranking problem has been largely motivated by applications in areas such as web search and recommender systems. Due to the large amounts of data available in these domains, it is necessary for the used algorithms to scale well, preferably close to linear time methods are needed. For a detailed introduction to the topic of learning to rank, we refer to (Liu, 2009; Fürnkranz and Hüllermeier, 2011). In this work we assume the so-called scoring setting, where each data instance is associated with a utility score reflecting its goodness with respect to the ranking criterion. A successful approach for learning ranking functions has been to consider pairwise preferences (Fürnkranz and Hüllermeier, 2005). In this setting, the aim is to minimize the number of pairwise mis-orderings in the ranking produced when ordering a set of examples according to predicted utility scores. A number of machine learning algorithms optimizing relaxations of this criterion have been proposed, such as the RankBoost (Freund et al., 2003), RankNet (Burges et al., 2005), RankRLS (Pahikkala et al., 2007, 2009), and the subject of this study, the ranking support vector machine (RankSVM) algorithm (Herbrich et al., 1999; Joachims, 2002). The original solution proposed for RankSVM optimization was to train a support vector machine (SVM) classifier on pairs of data examples.

Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the correlations between the projections are maximized. The solution is invariant to any linear transformation of either or both of the views; for tasks with small sample size such flexibility implies overfitting, which is even worse for more flexible nonparametric or kernel-based dependency discovery methods. We develop variants which reduce the degrees of freedom by assuming constraints on similarity of the projections in the two views. A particular example is provided by a cancer gene discovery application where chromosomal distance affects the dependencies between gene copy number and activity levels. Similarity constraints are shown to improve detection performance of known cancer genes.

In action domains where agents may have erroneous beliefs, reasoning about the effects of actions involves reasoning about belief change. In this paper, we use a transition system approach to reason about the evolution of an agent's beliefs as actions are executed. Some actions cause an agent to perform belief revision while others cause an agent to perform belief update, but the interaction between revision and update can be non-elementary. We present a set of rationality properties describing the interaction between revision and update, and we introduce a new class of belief change operators for reasoning about alternating sequences of revisions and updates. Our belief change operators can be characterized in terms of a natural shifting operation on total pre-orderings over interpretations. We compare our approach with related work on iterated belief change due to action, and we conclude with some directions for future research.

In 1992, Bartholdi, Tovey, and Trick opened the study of control attacks on elections---attempts to improve the election outcome by such actions as adding/deleting candidates or voters. That work has led to many results on how algorithms can be used to find attacks on elections and how complexity-theoretic hardness results can be used as shields against attacks. However, all the work in this line has assumed that the attacker employs just a single type of attack. In this paper, we model and study the case in which the attacker launches a multipronged (i.e., multimode) attack. We do so to more realistically capture the richness of real-life settings. For example, an attacker might simultaneously try to suppress some voters, attract new voters into the election, and introduce a spoiler candidate. Our model provides a unified framework for such varied attacks. By constructing polynomial-time multiprong attack algorithms we prove that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time.

Recursive Least Squares (RLS) is a widely used method for adaptive filtering and prediction in signal processing and related fields. Its applications include: acoustic echo cancelation; wireless channel equalization; interference cancelation and data streaming predictors. In these applications a measurement stream is recursively fitted to a linear model, described by the coefficients of an FIR prediction filter, in such a way to minimize a weighted average of squared residual prediction errors. Compared to other adaptive filtering algorithms such as Least Mean Square (LMS) filters, RLS is popular because of its fast convergence and low steady-state error. In many applications it is natural to constrain the predictor coefficients to be sparse.

Leading agent-based trust models address two important needs. First, they show how an agent may estimate the trustworthiness of another agent based on prior interactions. Second, they show how agents may share their knowledge in order to cooperatively assess the trustworthiness of others. However, in real-life settings, information relevant to trust is usually obtained piecemeal, not all at once. Unfortunately, the problem of maintaining trust has drawn little attention. Existing approaches handle trust updates in a heuristic, not a principled, manner. This paper builds on a formal model that considers probability and certainty as two dimensions of trust. It proposes a mechanism using which an agent can update the amount of trust it places in other agents on an ongoing basis. This paper shows via simulation that the proposed approach (a) provides accurate estimates of the trustworthiness of agents that change behavior frequently; and (b) captures the dynamic behavior of the agents. This paper includes an evaluation based on a real dataset drawn from Amazon Marketplace, a leading e-commerce site.