Related papers: Batch List-Decodable Linear Regression via Higher …
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted…
Motivated by problems in controlled experiments, we study the discrepancy of random matrices with continuous entries where the number of columns $n$ is much larger than the number of rows $m$. Our first result shows that if $\omega(1) = m =…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
We introduce a new regression problem which we call the Sum-Based Hierarchical Smoothing problem. Given a directed acyclic graph and a non-negative value, called target value, for each vertex in the graph, we wish to find non-negative…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can,…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions…
We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…
In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true…
We describe a numerical scheme for evaluating the posterior moments of Bayesian linear regression models with partial pooling of the coefficients. The principal analytical tool of the evaluation is a change of basis from coefficient space…
We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…
We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…