In this paper, we propose a novel robust and pragmatic feature selection approach. Unlike those sparse learning based feature selection methods which tackle the approximate problem by imposing sparsity regularization in the objective function, the proposed method only has one l2,1-norm loss term with an explicit l2,0-Norm equality constraint. An efficient algorithm based on augmented Lagrangian method will be derived to solve the above constrained optimization problem to find out the stable local solution. Extensive experiments on four biological datasets show that although our proposed model is not a convex problem, it outperforms the approximate convex counterparts and state-ofart feature selection methods evaluated in terms of classification accuracy by two popular classifiers. What is more, since the regularization parameter of our method has the explicit meaning, i.e. the number of feature selected, it avoids the burden of tuning the parameter, making it a pragmatic feature selection method.

With information about the world implicitly embedded in complex, high-dimensional neural population responses, the brain must perform some sort of statistical inference on a large scale to form hypotheses about the state of the environment. This ability is, in part, acquired after birth and often with very little feedback to guide learning. This is a very difficult learning problem considering the little information about the meaning of neural responses available at birth. In this paper, we address the question of how the brain might solve this problem: We present an unsupervised artificial neural network algorithm which takes from the self-organizing map (SOM) algorithm the ability to learn a latent variable model from its input. We extend the SOM algorithm so it learns about the distribution of noise in the input and computes probability density functions over the latent variables. The algorithm represents these probability density functions using population codes. This is done with very few assumptions about the distribution of noise. Our simulations indicate that our algorithm can learn to perform similar to a maximum likelihood estimator with the added benefit of requiring no a-priori knowledge about the input and computing not only best hypotheses, but also probabilities for alternatives.

We present a novel approach for multilabel classification based on an ensemble of Bayesian networks. The class variables are connected by a tree; each model of the ensemble uses a different class as root of the tree. We assume the features to be conditionally independent given the classes, thus generalizing the naive Bayes assumption to the multiclass case. This assumption allows us to optimally identify the correlations between classes and features; such correlations are moreover shared across all models of the ensemble. Inferences are drawn from the ensemble via logarithmic opinion pooling. To minimize Hamming loss, we compute the marginal probability of the classes by running standard inference on each Bayesian network in the ensemble, and then pooling the inferences. To instead minimize the subset 0/1 loss, we pool the joint distributions of each model and cast the problem as a MAP inference in the corresponding graphical model. Experiments show that the approach is competitive with state-of-the-art methods for multilabel classification.

Bayesian approaches to preference learning using Gaussian Processes(GPs) are attractive due to their ability to explicitly modeluncertainty in users' latent utility functions; unfortunately existingtechniques have cubic time complexity in the number of users, whichrenders this approach intractable for collaborative preferencelearning over a large user base. Exploiting the observation that userpopulations often decompose into communities of shared preferences, wemodel user preferences as an infinite Dirichlet Process (DP) mixtureof communities and learn (a) the expected number of preferencecommunities represented in the data, (b) a GP-based preference model over items tailored to each community, and(c) the mixture weights representing each user's fraction of communitymembership. This results in a learning and inference process thatscales linearly in the number of users rather than cubicly andadditionally provides the ability to analyze individual community preferences and their associated members. We evaluate our approach ona variety of preference data sources including Amazon Mechanical Turkshowing that our method is more scalable and as accurate as previous GP-based preference learning work.

In this paper, the fixed point semantics developed in [Lobo et al., 1992] is generalized to disjunctive logic programs with default negation and over arbitrary structures, and proved to coincide with the stable model semantics. By using the tool of ultraproducts, a preservation theorem, which asserts that a disjunctive logic program without default negation is bounded with respect to the proposed semantics if and only if it has a first-order equivalent, is then obtained. For the disjunctive logic programs with default negation, a sufficient condition assuring the first-order expressibility is also proposed.

The task of explanatory diagnosis conjectures actions to explain observations.This is a common task in real life and an essential ability of intelligent agents.It becomes more complicated in multi-agent scenarios, sinceagents' actions may be partially observable to other agents, andobservations might involve agents' knowledge about the world or other agents' knowledge oreven common knowledge of a group of agents.For example, we might want to explain the observation that $p$ does not hold,but Ann believes $p$, or the observation that Ann, Bob, and Carl commonly believe $p$.In this paper, we formalize the multi-agent explanatory diagnosis task in the framework of dynamic epistemic logic, where Kripke models of actions are used to represent agents' partial observability of actions. Since this task is undecidable in general, we identify important decidable fragments via techniques of reducing the potentially infinite search spaces to finite ones of epistemic states or action sequences.

Many formalisms discussed in the literature on qualitative spatial reasoning are designed for expressing static spatial constraints only. However, dynamic situations arise in virtually all applications of these formalisms, which makes it necessary to study variants and extensions involving change. This paper presents a study on the computational complexity of qualitative change. More precisely, we discuss the reasoning task of finding a solution to a temporal sequence of static reasoning problems where this sequence is subject to additional transition constraints. Our focus is primarily on smoothness and continuity constraints: we show how such transitions can be defined as relations and expressed within qualitative constraint formalisms. Our results demonstrate that for point-based constraint formalisms the interesting fragments become NP-completein the presence of continuity constraints, even if the satisfiability problem of its static descriptions is tractable.

Subset space logics have been introduced and studied as a framework for reasoning about a notion of effort in epistemic logic. The seminal Subset Space Logic (SSL) by Moss and Parikh modeled a single agent, and most work in this area has focused on different extensions of the language, or different model classes resulting from restrictions on subset spaces, while still keeping the single-agent assumption. In this paper we argue that the few existing attempts at multi-agent versions of SSL are unsatisfactory, and propose a new multi-agent subset space logic which is a natural extension of single-agent SSL. The main results are a sound and complete axiomatization of this logic, as well as an alternative and equivalent relational semantics.

In his seminal work [Plaza, 1989], Plaza proposed the public announcement logic (PAL), which is considered as the pilot logic in the field of dynamic epistemic logic. In the same paper, Plaza also introduced an interesting “know-value” operator Kv and listed a few valid formulas of PAL+Kv. However, it is unknown that whether these formulas, on top of the axioms for PAL, completely axiomatize PAL+Kv. In this paper, we first give a negative answer to this open problem. Moreover, we generalize the Kv operator and show that in the setting of PAL, replacing the Kv operator with its generalized version does not increase the expressive power of the resulting logic. This suggests that we can simply use the more flexible generalization instead of the original PAL+Kv. As the main result, we give a complete proof system for PAL plus the generalized operator based on a complete axiomatization of epistemic logic with the same operator in the single-agent setting.

Projection in the situation calculus refers to answering queries about the future evolutions of the modeled domain, while progression refers to updating the logical representation of the initial state so that it reflects the changes due to an executed action. In the general case projection is not decidable and progression may require second-order logic. In this paper we focus on a recent result about the decidability of projection and use it to drive results for the problem of progression. In particular we contribute with the following: (i) a major result showing that for a large class of intuitive action theories with bounded unknowns a first-order progression always exists and can be computed; (ii) a comprehensive classification of the known classes that can be progressed in first-order; (iii) a novel account of nondeterministic actions in the situation calculus.