Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy algorithm design, which plays an important role in attribute reduction. Therefore, it is meaningful to combine matroids with rough sets to solve the optimization problems. In this paper, we introduce an existing algebraic structure called dependence space to study the reduction problem in terms of matroids. First, a dependence space of matroids is constructed. Second, the characterizations for the space such as consistent sets and reducts are studied through matroids. Finally, we investigate matroids by the means of the space and present two expressions for their bases. In a word, this paper provides new approaches to study attribute reduction.

In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a $d$-dimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational approach and showed in simulation and real data experiments that it can work quite satisfactorily. The results presented in the present paper provide theoretical underpinning of the method. In particular, we show how to tune the priors on the hyper parameters of the model in order for the procedure to automatically adapt to the degree of smoothness of the unknown intensity and to achieve optimal convergence rates.

We consider an autonomous agent facing a partially observable, stochastic, multiagent environment where the unknown policies of other agents are represented as finite state controllers (FSCs). We show how an agent can (i) learn the FSCs of the other agents, and (ii) exploit these models during interactions. To separate the issues of off-line versus on-line learning we consider here an off-line two-phase approach. During the first phase the agent observes as the other player(s) are interacting with the environment (the observations may be imperfect and the learning agent is not taking part in the interaction.) The collected data is used to learn an ensemble of FSCs that explain the behavior of the other agent(s) using a Bayesian non-parametric (BNP) approach. We verify the quality of the learned models during the second phase by allowing the agent to compute its own optimal policy and interact with the observed agent. The optimal policy for the learning agent is obtained by solving an interactive POMDP in which the states are augmented by the other agent(s)' possible FSCs. The advantage of using the Bayesian nonparametric approach in the first phase is that the complexity (number of nodes) of the learned controllers is not bounded a priori. Our two-phase approach is preliminary and separates the learning using BNP from the complexities of learning on-line while the other agent may be modifying its policy (on-line approach is subject of our future work.) We describe our implementation and results in a multiagent Tiger domain. Our results show that learning improves the agent's performance, which increases with the amount of data collected during the learning phase.

Although the concept of ecological integrity is referred in many country legislations there is no consensus on how to formalize and implement it. One possible definition is as the capacity of an ecosystem to support and maintain a balanced, integrated, and adaptive community of organisms having a species composition, diversity, and functional organization comparable to that of a natural habitat of the region. Our objective is to model this interpretation of ecological integrity from a set of ecological measures that can be estimated from ecological inventory data.

A fundamental challenge in calcium imaging has been to infer the timing of action potentials from the measured noisy calcium fluorescence traces. We systematically evaluate a range of spike inference algorithms on a large benchmark dataset recorded from varying neural tissue (V1 and retina) using different calcium indicators (OGB-1 and GCamp6). We show that a new algorithm based on supervised learning in flexible probabilistic models outperforms all previously published techniques, setting a new standard for spike inference from calcium signals. Importantly, it performs better than other algorithms even on datasets not seen during training. Future data acquired in new experimental conditions can easily be used to further improve its spike prediction accuracy and generalization performance. Finally, we show that comparing algorithms on artificial data is not informative about performance on real population imaging data, suggesting that a benchmark dataset may greatly facilitate future algorithmic developments.

Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional magnetic resonance imaging (fMRI) blood oxygen level dependent (BOLD) signal. Since the BOLD signal is a proxy for neuronal activity, it is of interest to learn the latent functional network structure. Additionally, despite a core set of observations about functional networks such as small-worldness, modularity, exponentially truncated degree distributions, and presence of various types of hubs, very little is known about the computational principles which can give rise to these observations. This paper introduces a Hidden Markov Random Field framework for the purpose of representing, estimating, and evaluating latent neuronal functional relationships between different brain regions using fMRI data.

Mean field variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, it is well known that a major failing of MFVB is that it underestimates the uncertainty of model variables (sometimes severely) and provides no information about model variable covariance. We develop a fast, general methodology for exponential families that augments MFVB to deliver accurate uncertainty estimates for model variables -- both for individual variables and coherently across variables. MFVB for exponential families defines a fixed-point equation in the means of the approximating posterior, and our approach yields a covariance estimate by perturbing this fixed point. Inspired by linear response theory, we call our method linear response variational Bayes (LRVB). We also show how LRVB can be used to quickly calculate a measure of the influence of individual data points on parameter point estimates. We demonstrate the accuracy and scalability of our method by learning Gaussian mixture models for both simulated and real data.

Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding parameters. This paper discusses unsupervised learning of mixture models using the Bayesian Minimum Message Length (MML) criterion. To demonstrate the effectiveness of search and inference of mixture parameters using the proposed approach, we select two key probability distributions, each handling fundamentally different types of data: the multivariate Gaussian distribution to address mixture modelling of data distributed in Euclidean space, and the multivariate von Mises-Fisher (vMF) distribution to address mixture modelling of directional data distributed on a unit hypersphere. The key contributions of this paper, in addition to the general search and inference methodology, include the derivation of MML expressions for encoding the data using multivariate Gaussian and von Mises-Fisher distributions, and the analytical derivation of the MML estimates of the parameters of the two distributions. Our approach is tested on simulated and real world data sets. For instance, we infer vMF mixtures that concisely explain experimentally determined three-dimensional protein conformations, providing an effective null model description of protein structures that is central to many inference problems in structural bioinformatics. The experimental results demonstrate that the performance of our proposed search and inference method along with the encoding schemes improve on the state of the art mixture modelling techniques.

This paper deals with the binary classification task when the target class has the lower probability of occurrence. In such situation, it is not possible to build a powerful classifier by using standard methods such as logistic regression, classification tree, discriminant analysis, etc. To overcome this short-coming of these methods which yield classifiers with low sensibility, we tackled the classification problem here through an approach based on the association rules learning. This approach has the advantage of allowing the identification of the patterns that are well correlated with the target class. Association rules learning is a well known method in the area of data-mining. It is used when dealing with large database for unsupervised discovery of local patterns that expresses hidden relationships between input variables. In considering association rules from a supervised learning point of view, a relevant set of weak classifiers is obtained from which one derives a classifier that performs well.

We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing approximate inference techniques such as belief propagation, mean field, and variants. We show that a recently proposed variational approach to inference in log-supermodular models -L-FIELD- reduces to the widely-studied minimum norm problem for submodular minimization. This insight allows to leverage powerful existing tools, and hence to solve the variational problem orders of magnitude more efficiently than previously possible. We then provide another natural interpretation of L-FIELD, demonstrating that it exactly minimizes a specific type of R\'enyi divergence measure. This insight sheds light on the nature of the variational approximations produced by L-FIELD. Furthermore, we show how to perform parallel inference as message passing in a suitable factor graph at a linear convergence rate, without having to sum up over all the configurations of the factor. Finally, we apply our approach to a challenging image segmentation task. Our experiments confirm scalability of our approach, high quality of the marginals, and the benefit of incorporating higher-order potentials.