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We establish theoretical results concerning all local optima of various regularized M-estimators, where both loss and penalty functions are allowed to be nonconvex. Our results show that as long as th...
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and comm...
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kerne...
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterp...
In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular ta...
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis ...
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closel...
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closel...
We use L\'evy processes to generate joint prior distributions for a location parameter $\bbeta = (\beta_1,...,\beta_p) $ as $p$ grows large. This leads to the class of local-global shrinkage rules. We...
We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of...
Let (X,,t~ [0, 11) be a oentred stationary Gaussian process defined on (D,A , P) with covariance function satisfying Define the regularized process X' = cp, * X and YE = Xc/oe, where CT~ = var Xf ,...
The aim of this paper is to compare three regularized particle filters in an online data processing context. We carry out the comparison in terms of hidden states filtering and parameter estimation, c...
We consider the problem of constructing a nonlinear discriminant procedure, using a regularized local likelihood method. The local likelihood method is effective for analyzing data with complex struct...

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