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In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…
K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes…
We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of…
We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…
A common computational problem in multiple change-point models is to recover the segmentations with $1$ to $K_{max}$ change-points of minimal cost with respect to some loss function. Here we present an algorithm to prune the set of…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…
Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…
Let $K$ be a field and $P=K[x_1,\dots,x_n]$. The technique of elimination by substitution is based on discovering a coherently $Z=(z_1,\dots,z_s)$-separating tuple of polynomials $(f_1,\dots,f_s)$ in an ideal $I$, i.e., on finding…
We study the Bayesian approach to variable selection in the context of linear regression. Motivated by a recent work by Rockova and George (2014), we propose an EM algorithm that returns the MAP estimate of the set of relevant variables.…
We provide an approximation algorithm for k-means clustering in the one-round (aka non-interactive) local model of differential privacy (DP). This algorithm achieves an approximation ratio arbitrarily close to the best non private…
In this paper we provide a fully distributed implementation of the k-means clustering algorithm, intended for wireless sensor networks where each agent is endowed with a possibly high-dimensional observation (e.g., position, humidity,…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
In this paper, we propose a maximum smoothed likelihood method to estimate the component density functions of mixture models, in which the mixing proportions are known and may differ among observations. The proposed estimates maximize a…
The coresets approach, also called subsampling or subset selection, aims to select a subsample as a surrogate for the observed sample and has found extensive applications in large-scale data analysis. Existing coresets methods construct the…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
We consider a generalization of the criterion minimized by the K-means algorithm, where a neighborhood structure is used in the calculus of the variance. Such tool is used, for example with Kohonen maps, to measure the quality of the…
We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…