Related papers: Core-Elements for Large-Scale Least Squares Estima…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
We devise coresets for kernel $k$-Means with a general kernel, and use them to obtain new, more efficient, algorithms. Kernel $k$-Means has superior clustering capability compared to classical $k$-Means, particularly when clusters are…
With input sizes becoming massive, coresets -- small yet representative summary of the input -- are relevant more than ever. A weighted set $C_w$ that is a subset of the input is an $\varepsilon$-coreset if the cost of any feasible solution…
In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in…
We develop and analyze a method to reduce the size of a very large set of data points in a high dimensional Euclidean space R d to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set…
An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in…
We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…
Model selection in latent block models has been a challenging but important task in the field of statistics. Specifically, a major challenge is encountered when constructing a test on a block structure obtained by applying a specific…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably…
``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…