This paper considers the fragment ∃∀SO of second-order logic. Many interesting problems, such as conformant planning, can be naturally expressed as finite domain satisfiability problems of this logic. Such satisfiability problems are computationally hard (ΣP2) and many of these problems are often solved approximately. In this paper, we develop a general approximative method, i.e., a sound but incomplete method, for solving ∃∀SO satisfiability problems. We use a syntactic representation of a constraint propagation method for first-order logic to transform such an ∃∀SO satisfiability problem to an ∃SO(ID) satisfiability problem (second-order logic, extended with inductive definitions). The finite domain satisfiability problem for the latter language is in NP and can be handled by several existing solvers. Inductive definitions are a powerful knowledge representation tool, and this moti- vates us to also approximate ∃∀SO(ID) problems. In order to do this, we first show how to perform propagation on such inductive definitions. Next, we use this to approximate ∃∀SO(ID) satisfiability problems. All this provides a general theoretical framework for a number of approximative methods in the literature. Moreover, we also show how we can use this framework for solving practical useful problems, such as conformant planning, in an effective way.

Collective classification models attempt to improve classification performance by taking into account the class labels of related instances. However, they tend not to learn patterns of interactions between classes and/or make the assumption that instances of the same class link to each other (assortativity assumption). Blockmodels provide a solution to these issues, being capable of modelling assortative and disassortative interactions, and learning the pattern of interactions in the form of a summary network. The Supervised Blockmodel provides good classification performance using link structure alone, whilst simultaneously providing an interpretable summary of network interactions to allow a better understanding of the data. This work explores three variants of supervised blockmodels of varying complexity and tests them on four structurally different real world networks.

This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons equipped with spiking timing dependent plasticity (STDP) and (ii) is amenable to theoretical analysis. We show that the selectron encodes reward estimates into spikes and that an error bound on spikes is controlled by a spiking margin and the sum of synaptic weights. Moreover, the efficacy of spikes (their usefulness to other reward maximizing selectrons) also depends on total synaptic strength. Finally, based on our analysis, we propose a regularized version of STDP, and show the regularization improves the robustness of neuronal learning when faced with multiple stimuli.

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel estimators for the cases of noisy, missing and/or dependent data. Many standard approaches to noisy or missing data, such as those using the EM algorithm, lead to optimization problems that are inherently nonconvex, and it is difficult to establish theoretical guarantees on practical algorithms. While our approach also involves optimizing nonconvex programs, we are able to both analyze the statistical error associated with any global optimum, and more surprisingly, to prove that a simple algorithm based on projected gradient descent will converge in polynomial time to a small neighborhood of the set of all global minimizers. On the statistical side, we provide nonasymptotic bounds that hold with high probability for the cases of noisy, missing and/or dependent data. On the computational side, we prove that under the same types of conditions required for statistical consistency, the projected gradient descent algorithm is guaranteed to converge at a geometric rate to a near-global minimizer. We illustrate these theoretical predictions with simulations, showing close agreement with the predicted scalings.

Synaptic plasticity seems to be a capital aspect of the dynamics of neural networks. It is about the physiological modifications of the synapse, which have like consequence a variation of the value of the synaptic weight. The information encoding is based on the precise timing of single spike events that is based on the relative timing of the pre- and post-synaptic spikes, local synapse competitions within a single neuron and global competition via lateral connections. In order to classify temporal sequences, we present in this paper how to use a local hebbian learning, spike-timing dependent plasticity for unsupervised competitive learning, preserving self-organizing maps of spiking neurons. In fact we present three variants of self-organizing maps (SOM) with spike-timing dependent Hebbian learning rule, the Leaky Integrators Neurons (LIN), the Spiking_SOM and the recurrent Spiking_SOM (RSSOM) models. The case study of the proposed SOM variants is phoneme classification and word recognition in continuous speech and speaker independent.

Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative features kept constant over changes. The aim of this paper is to identify one such feature, namely interactions or dependencies among variables that are common across multiple datasets collected under different conditions. To that end, we propose a common substructure learning (CSSL) framework based on a graphical Gaussian model. We further present a simple learning algorithm based on the Dual Augmented Lagrangian and the Alternating Direction Method of Multipliers. We confirm the performance of CSSL over other existing techniques in finding unchanging dependency structures in multiple datasets through numerical simulations on synthetic data and through a real world application to anomaly detection in automobile sensors.

It is a meaningful issue that under what condition neighborhoods induced by a covering are equal to the covering itself. A necessary and sufficient condition for this issue has been provided by some scholars. In this paper, through a counter-example, we firstly point out the necessary and sufficient condition is false. Second, we present a necessary and sufficient condition for this issue. Third, we concentrate on the inverse issue of computing neighborhoods by a covering, namely giving an arbitrary covering, whether or not there exists another covering such that the neighborhoods induced by it is just the former covering. We present a necessary and sufficient condition for this issue as well. In a word, through the study on the two fundamental issues induced by neighborhoods, we have gained a deeper understanding of the relationship between neighborhoods and the covering which induce the neighborhoods.

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough set is established through the lower approximation operator. Second, the dual of the matroid and its properties such as independent sets, bases and rank function are investigated. Finally, the relationships between the contraction of the dual matroid to the complement of a single point set and the contraction of the dual matroid to the complement of the equivalence class of this point are studied.

Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some necessary and sufficient conditions. However, there exists one common trait among these conditions, that is they are established on the basis of all neighborhoods have been obtained. In this paper, we provide a necessary and sufficient condition directly based on the covering itself. First, we investigate the influence of that there are reducible elements in the covering on neighborhoods. Second, we propose the definition of uniform block and obtain a sufficient condition from it. Third, we propose the definitions of repeat degree and excluded number. By means of the two concepts, we obtain a necessary and sufficient condition for neighborhoods to form a partition. In a word, we have gained a deeper and more direct understanding of the essence over that neighborhoods form a partition.

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the terminology of linear algebra and graph theory. We can combine rough set theory with matroid theory through using rough sets to study some characteristics of matroids. In this paper, we apply rough sets to matroids through defining a family of sets which are constructed from the upper approximation operator with respect to an equivalence relation. First, we prove the family of sets satisfies the support set axioms of matroids, and then we obtain a matroid. We say the matroids induced by the equivalence relation and a type of matroid, namely support matroid, is induced. Second, through rough sets, some characteristics of matroids such as independent sets, support sets, bases, hyperplanes and closed sets are investigated.