Hyperspectral images (HIS) classification is a high technical remote sensing tool. The goal is to reproduce a thematic map that will be compared with a reference ground truth map (GT), constructed by expecting the region. The HIS contains more than a hundred bidirectional measures, called bands (or simply images), of the same region. They are taken at juxtaposed frequencies. Unfortunately, some bands contain redundant information, others are affected by the noise, and the high dimensionality of features made the accuracy of classification lower. The problematic is how to find the good bands to classify the pixels of regions. Some methods use Mutual Information (MI) and threshold, to select relevant bands, without treatment of redundancy. Others control and eliminate redundancy by selecting the band top ranking the MI, and if its neighbors have sensibly the same MI with the GT, they will be considered redundant and so discarded. This is the most inconvenient of this method, because this avoids the advantage of hyperspectral images: some precious information can be discarded. In this paper we'll accept the useful redundancy. A band contains useful redundancy if it contributes to produce an estimated reference map that has higher MI with the GT.nTo control redundancy, we introduce a complementary threshold added to last value of MI. This process is a Filter strategy; it gets a better performance of classification accuracy and not expensive, but less preferment than Wrapper strategy.

This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be solved via a block coordinate descent algorithm. Statistical estimation performance can be established for our method. The proposed approach has competitive empirical performance compared to existing methods, as demonstrated by various experiments on synthetic and real datasets.

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.

There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. Motivated by such a dataset on genomic instability collected from tumor samples of several types, we propose a sparse covariate dependent Ising model to study both the conditional dependency within the binary data and its relationship with the additional covariates. This results in subject-specific Ising models, where the subject's covariates influence the strength of association between the genes. As in all exploratory data analysis, interpretability of results is important, and we use L1 penalties to induce sparsity in the fitted graphs and in the number of selected covariates. Two algorithms to fit the model are proposed and compared on a set of simulated data, and asymptotic results are established. The results on the tumor dataset and their biological significance are discussed in detail.

Automatic extraction of temporal relations between event pairs is an important task for several natural language processing applications such as Question Answering, Information Extraction, and Summarization. Since most existing methods are supervised and require large corpora, which for many languages do not exist, we have concentrated our efforts to reduce the need for annotated data as much as possible. This paper presents two different algorithms towards this goal. The first algorithm is a weakly supervised machine learning approach for classification of temporal relations between events. In the first stage, the algorithm learns a general classifier from an annotated corpus. Then, inspired by the hypothesis of "one type of temporal relation per discourse'', it extracts useful information from a cluster of topically related documents. We show that by combining the global information of such a cluster with local decisions of a general classifier, a bootstrapping cross-document classifier can be built to extract temporal relations between events. Our experiments show that without any additional annotated data, the accuracy of the proposed algorithm is higher than that of several previous successful systems. The second proposed method for temporal relation extraction is based on the expectation maximization (EM) algorithm. Within EM, we used different techniques such as a greedy best-first search and integer linear programming for temporal inconsistency removal. We think that the experimental results of our EM based algorithm, as a first step toward a fully unsupervised temporal relation extraction method, is encouraging.

Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sample data. Solving this convex optimization problem is very challenging, especially for large problems. In this paper, we propose two alternating direction methods for solving this problem. The first method is to apply the classical alternating direction method of multipliers to solve the problem as a consensus problem. The second method is a proximal gradient based alternating direction method of multipliers. Our methods exploit and take advantage of the special structure of the problem and thus can solve large problems very efficiently. Global convergence result is established for the proposed methods. Numerical results on both synthetic data and gene expression data show that our methods usually solve problems with one million variables in one to two minutes, and are usually five to thirty five times faster than a state-of-the-art Newton-CG proximal point algorithm.

In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive results, albeit with some loss of accuracy. Bayesian statistics have been widely used in the development of probability models in machine learning in recent years and these methods have many advantages, including their abilities to avoid overfitting. In this paper, we develop two Bayesian mixture models with the Dirichlet distribution prior and the Dirichlet process (DP) prior to improve the previous non-Bayesian mixture model developed for transaction dataset mining. We implement the inference of both mixture models using two methods: a collapsed Gibbs sampling scheme and a variational approximation algorithm. Experiments in several benchmark problems have shown that both mixture models achieve better performance than a non-Bayesian mixture model. The variational algorithm is the faster of the two approaches while the Gibbs sampling method achieves a more accurate results. The Dirichlet process mixture model can automatically grow to a proper complexity for a better approximation. Once the model is built, it can be very fast to query and run analysis on (typically 10 times faster than Eclat, as we will show in the experiment section). However, these approaches also show that mixture models underestimate the probabilities of frequent itemsets. Consequently, these models have a higher sensitivity but a lower specificity.

We develop a model of issue-specific voting behavior. This model can be used to explore lawmakers' personal voting patterns of voting by issue area, providing an exploratory window into how the language of the law is correlated with political support. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout prediction performance and the model's utility in interpreting an inherently multi-dimensional space.

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.