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We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms.…
Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…
This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an $m$-by-$n$ nonnegative matrix $X$ and an integer $k$, the PSD factorization…
Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to…
Manifold regularization methods for matrix factorization rely on the cluster assumption, whereby the neighborhood structure of data in the input space is preserved in the factorization space. We argue that using the k-neighborhoods of all…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
Training machine learning models with differential privacy (DP) has received increasing interest in recent years. One of the most popular algorithms for training differentially private models is differentially private stochastic gradient…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
Imbalanced domain learning aims to produce accurate models in predicting instances that, though underrepresented, are of utmost importance for the domain. Research in this field has been mainly focused on classification tasks.…
We study the Maximum Independent Set of Rectangles (MISR) problem, where we are given a set of axis-parallel rectangles in the plane and the goal is to select a subset of non-overlapping rectangles of maximum cardinality. In a recent…
Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…
We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy…
We propose a method to fit arbitrarily accurate blendshape rig models by solving the inverse rig problem in realistic human face animation. The method considers blendshape models with different levels of added corrections and solves the…