We address the scalability of symbolic planning under uncertainty with factored states and actions. Prior work has focused almost exclusively on factored states but not factored actions, and on value iteration (VI) compared to policy iteration (PI). Our first contribution is a novel method for symbolic policy backups via the application of constraints, which is used to yield a new efficient symbolic imple- mentation of modified PI (MPI) for factored action spaces. While this approach improves scalability in some cases, naive handling of policy constraints comes with its own scalability issues. This leads to our second and main contribution, symbolic Opportunistic Policy Iteration (OPI), which is a novel convergent al- gorithm lying between VI and MPI. The core idea is a symbolic procedure that applies policy constraints only when they reduce the space and time complexity of the update, and otherwise performs full Bellman backups, thus automatically adjusting the backup per state. We also give a memory bounded version of this algorithm allowing a space-time tradeoff. Empirical results show significantly improved scalability over the state-of-the-art.

The receptive field (RF) of a sensory neuron describes how the neuron integrates sensory stimuli over time and space. In typical experiments with naturalistic or flickering spatiotemporal stimuli, RFs are very high-dimensional, due to the large number of coefficients needed to specify an integration profile across time and space. Estimating these coefficients from small amounts of data poses a variety of challenging statistical and computational problems. Here we address these challenges by developing Bayesian reduced rank regression methods for RF estimation. This corresponds to modeling the RF as a sum of several space-time separable (i.e., rank-1) filters, which proves accurate even for neurons with strongly oriented space-time RFs. This approach substantially reduces the number of parameters needed to specify the RF, from 1K-100K down to mere 100s in the examples we consider, and confers substantial benefits in statistical power and computational efficiency. In particular, we introduce a novel prior over low-rank RFs using the restriction of a matrix normal prior to the manifold of low-rank matrices. We then use a localized'' prior over row and column covariances to obtain sparse, smooth, localized estimates of the spatial and temporal RF components. We develop two methods for inference in the resulting hierarchical model: (1) a fully Bayesian method using blocked-Gibbs sampling; and (2) a fast, approximate method that employs alternating coordinate ascent of the conditional marginal likelihood. We develop these methods under Gaussian and Poisson noise models, and show that low-rank estimates substantially outperform full rank estimates in accuracy and speed using neural data from retina and V1."

We propose an efficient Bayesian nonparametric model for discovering hierarchical community structure in social networks. Our model is a tree-structured mixture of potentially exponentially many stochastic blockmodels. We describe a family of greedy agglomerative model selection algorithms whose worst case scales quadratically in the number of vertices of the network, but independent of the number of communities. Our algorithms are two orders of magnitude faster than the infinite relational model, achieving comparable or better accuracy.

Today, with respect to the increasing growth of demand to get credit from the customers of banks and finance and credit institutions, using an effective and efficient method to decrease the risk of non-repayment of credit given is very necessary. Assessment of customers' credit is one of the most important and the most essential duties of banks and institutions, and if an error occurs in this field, it would leads to the great losses for banks and institutions. Thus, using the predicting computer systems has been significantly progressed in recent decades. The data that are provided to the credit institutions' managers help them to make a straight decision for giving the credit or not-giving it. In this paper, we will assess the customer credit through a combined classification using artificial neural networks, genetics algorithm and Bayesian probabilities simultaneously, and the results obtained from three methods mentioned above would be used to achieve an appropriate and final result. We use the K_folds cross validation test in order to assess the method and finally, we compare the proposed method with the methods such as Clustering-Launched Classification (CLC), Support Vector Machine (SVM) as well as GA+SVM where the genetics algorithm has been used to improve them.

A new approach for functional data description is proposed in this paper. It consists of a regression model with a discrete hidden logistic process which is adapted for modeling curves with abrupt or smooth regime changes. The model parameters are estimated in a maximum likelihood framework through a dedicated Expectation Maximization (EM) algorithm. From the proposed generative model, a curve discrimination rule is derived using the Maximum A Posteriori rule. The proposed model is evaluated using simulated curves and real world curves acquired during railway switch operations, by performing comparisons with the piecewise regression approach in terms of curve modeling and classification.

Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such data. A new approach for time series modeling is proposed in this paper. It consists of a regression model incorporating a discrete hidden logistic process allowing for activating smoothly or abruptly different polynomial regression models. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The M step of the EM algorithm uses a multi-class Iterative Reweighted Least-Squares (IRLS) algorithm to estimate the hidden process parameters. To evaluate the proposed approach, an experimental study on simulated data and real world data was performed using two alternative approaches: a heteroskedastic piecewise regression model using a global optimization algorithm based on dynamic programming, and a Hidden Markov Regression Model whose parameters are estimated by the Baum-Welch algorithm. Finally, in the context of the remote monitoring of components of the French railway infrastructure, and more particularly the switch mechanism, the proposed approach has been applied to modeling and classifying time series representing the condition measurements acquired during switch operations.

Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful approaches in cluster analysis. The mixture density estimation is generally performed by maximizing the observed-data log-likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the EM algorithm initialization is crucial. In addition, the standard EM algorithm requires the number of clusters to be known a priori. Some solutions have been provided in [31, 12] for model-based clustering with Gaussian mixture models for multivariate data. In this paper we focus on model-based curve clustering approaches, when the data are curves rather than vectorial data, based on regression mixtures. We propose a new robust EM algorithm for clustering curves. We extend the model-based clustering approach presented in [31] for Gaussian mixture models, to the case of curve clustering by regression mixtures, including polynomial regression mixtures as well as spline or B-spline regressions mixtures. Our approach both handles the problem of initialization and the one of choosing the optimal number of clusters as the EM learning proceeds, rather than in a two-fold scheme. This is achieved by optimizing a penalized log-likelihood criterion. A simulation study confirms the potential benefit of the proposed algorithm in terms of robustness regarding initialization and funding the actual number of clusters.

We present a new mixture model-based discriminant analysis approach for functional data using a specific hidden process regression model. The approach allows for fitting flexible curve-models to each class of complex-shaped curves presenting regime changes. The model parameters are learned by maximizing the observed-data log-likelihood for each class by using a dedicated expectation-maximization (EM) algorithm. Comparisons on simulated data with alternative approaches show that the proposed approach provides better results.

A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The parameters of the hidden logistic process, in the inner loop of the EM algorithm, are estimated using a multi-class Iterative Reweighted Least-Squares (IRLS) algorithm. An experimental study using simulated and real data reveals good performances of the proposed approach.

A new approach for feature extraction from time series is proposed in this paper. This approach consists of a specific regression model incorporating a discrete hidden logistic process. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The parameters of the hidden logistic process, in the inner loop of the EM algorithm, are estimated using a multi-class Iterative Reweighted Least-Squares (IRLS) algorithm. A piecewise regression algorithm and its iterative variant have also been considered for comparisons. An experimental study using simulated and real data reveals good performances of the proposed approach.