Computational approaches to transcription factor binding site identification have been actively researched for the past decade. Negative examples have long been utilized in de novo motif discovery and have been shown useful in transcription factor binding site search as well. However, understanding of the roles of negative examples in binding site search is still very limited. We propose the 2-centroid and optimal discriminating vector methods, taking into account negative examples. Cross-validation results on E. coli transcription factors show that the proposed methods benefit from negative examples, outperforming the centroid and position-specific scoring matrix methods. We further show that our proposed methods perform better than a state-of-the-art method. We characterize the proposed methods in the context of the other compared methods and show that, coupled with motif subtype identification, the proposed methods can be effectively applied to a wide range of transcription factors. Finally, we argue that the proposed methods are well-suited for eukaryotic transcription factors as well. Software tools are available at: http://biogrid.engr.uconn.edu/tfbs_search/.

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify nonparametric regression against outliers - that is, data markedly deviating from the postulated models. A variational counterpart to least-trimmed squares regression is shown closely related to an L0-(pseudo)norm-regularized estimator, that encourages sparsity in a vector explicitly modeling the outliers. This connection suggests efficient solvers based on convex relaxation, which lead naturally to a variational M-type estimator equivalent to the least-absolute shrinkage and selection operator (Lasso). Outliers are identified by judiciously tuning regularization parameters, which amounts to controlling the sparsity of the outlier vector along the whole robustification path of Lasso solutions. Reduced bias and enhanced generalization capability are attractive features of an improved estimator obtained after replacing the L0-(pseudo)norm with a nonconvex surrogate. The novel robust spline-based smoother is adopted to cleanse load curve data, a key task aiding operational decisions in the envisioned smart grid system. Computer simulations and tests on real load curve data corroborate the effectiveness of the novel sparsity-controlling robust estimators.

Many web-search queries serve as the beginning of an exploration of an unknown space of information, rather than looking for a specific web page. To answer such queries effec- tively, the search engine should attempt to organize the space of relevant information in a way that facilitates exploration. We describe the Aspector system that computes aspects for a given query. Each aspect is a set of search queries that together represent a distinct information need relevant to the original search query. To serve as an effective means to explore the space, Aspector computes aspects that are orthogonal to each other and to have high combined coverage. Aspector combines two sources of information to compute aspects. We discover candidate aspects by analyzing query logs, and cluster them to eliminate redundancies. We then use a mass-collaboration knowledge base (e.g., Wikipedia) to compute candidate aspects for queries that occur less frequently and to group together aspects that are likely to be semantically related. We present a user study that indicates that the aspects we compute are rated favorably against three competing alternatives related searches proposed by Google, cluster labels assigned by the Clusty search engine, and navigational searches proposed by Bing.

In this paper, auto-associative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word "manifold" refers to the topology properties of the structure. The approximating manifold is built by a projection pursuit algorithm. At each step of the algorithm, the dimension of the manifold is incremented. Some theoretical properties are provided. In particular, we can show that, at each step of the algorithm, the mean residuals norm is not increased. Moreover, it is also established that the algorithm converges in a finite number of steps. Some particular auto-associative models are exhibited and compared to the classical PCA and some neural networks models. Implementation aspects are discussed. We show that, in numerous cases, no optimization procedure is required. Some illustrations on simulated and real data are presented.

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a linear regression can benefit from knowledge that the underlying regression vector is sparse. The combinatorial problem of selecting the nonzero components of this vector can be "relaxed" by regularizing the squared error with a convex penalty function like the $\ell_1$ norm. However, in many applications, additional conditions on the structure of the regression vector and its sparsity pattern are available. Incorporating this information into the learning method may lead to a significant decrease of the estimation error. In this paper, we present a family of convex penalty functions, which encode prior knowledge on the structure of the vector formed by the absolute values of the regression coefficients. This family subsumes the $\ell_1$ norm and is flexible enough to include different models of sparsity patterns, which are of practical and theoretical importance. We establish the basic properties of these penalty functions and discuss some examples where they can be computed explicitly. Moreover, we present a convergent optimization algorithm for solving regularized least squares with these penalty functions. Numerical simulations highlight the benefit of structured sparsity and the advantage offered by our approach over the Lasso method and other related methods.

One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while specifying the unreliable ones is critical for robust sensing. This sensing task is formulated here as that of finding the maximum number of feasible subsystems of linear equations, and proved to be NP-hard. Useful links are established with compressive sampling, which aims at recovering vectors that are sparse. In contrast, the signals here are not sparse, but give rise to sparse residuals. Capitalizing on this form of sparsity, four sensing schemes with complementary strengths are developed. The first scheme is a convex relaxation of the original problem expressed as a second-order cone program (SOCP). It is shown that when the involved sensing matrices are Gaussian and the reliable measurements are sufficiently many, the SOCP can recover the optimal solution with overwhelming probability. The second scheme is obtained by replacing the initial objective function with a concave one. The third and fourth schemes are tailored for noisy sensor data. The noisy case is cast as a combinatorial problem that is subsequently surrogated by a (weighted) SOCP. Interestingly, the derived cost functions fall into the framework of robust multivariate linear regression, while an efficient block-coordinate descent algorithm is developed for their minimization. The robust sensing capabilities of all schemes are verified by simulated tests.

The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing methods. In our method, a solution is computed by iteratively performing dependence estimation and maximization: Dependence estimation is analytically carried out by recently-proposed least-squares mutual information (LSMI), and dependence maximization is also analytically carried out by utilizing the Epanechnikov kernel. Through large-scale experiments on real-world image classification and audio tagging problems, the proposed method is shown to compare favorably with existing dimension reduction approaches.

We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images that have been pre-segmented into smaller regions. We propose generalizations of the restricted Boltzmann machine (RBM) that are appropriate in this context and explore how to incorporate different assumptions about the relationship between the input sets and the target class within the RBM. In experiments on standard multiple-instance learning datasets, we demonstrate the competitiveness of approaches based on RBMs and apply the proposed variants to the problem of incoming mail classification.

We consider a collection of prediction experiments, which are clustered in the sense that groups of experiments ex- hibit similar relationship between the predictor and response variables. The experiment clusters as well as the regres- sion relationships are unknown. The regression relation- ships define the experiment clusters, and in general, the predictor and response variables may not exhibit any clus- tering. We call this prediction problem clustered regres- sion with unknown clusters (CRUC) and in this paper we focus on linear regression. We study and compare several methods for CRUC, demonstrate their applicability to the Yahoo Learning-to-rank Challenge (YLRC) dataset, and in- vestigate an associated mathematical model. CRUC is at the crossroads of many prior works and we study several prediction algorithms with diverse origins: an adaptation of the expectation-maximization algorithm, an approach in- spired by K-means clustering, the singular value threshold- ing approach to matrix rank minimization under quadratic constraints, an adaptation of the Curds and Whey method in multiple regression, and a local regression (LoR) scheme reminiscent of neighborhood methods in collaborative filter- ing. Based on empirical evaluation on the YLRC dataset as well as simulated data, we identify the LoR method as a good practical choice: it yields best or near-best prediction performance at a reasonable computational load, and it is less sensitive to the choice of the algorithm parameter. We also provide some analysis of the LoR method for an asso- ciated mathematical model, which sheds light on optimal parameter choice and prediction performance.

Applications range from the detection of potential all times t 1,...T (m 1)τ. We refer to such a sequence problems (such as an elderly person who has fallen down as a model of the system. Note that these models are in their home) to general monitoring of disease progression nonparametric. Theoretically, under some smoothness assumptions (e.g. in Parkinson's disease), or simply tracking the amount (Takens, 1981), if m is big enough, and τ is not of exercise and physical activity that a person gets. Ideally, a multiple of the period of the system, such a model captures such activities should be monitored as precisely as possible, all the relevant dynamics. However, real data is noisy, but using cheap or easily available devices, and in a way that so nonparametric models of the same activity can have high does not interfere with daily life.