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Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…
In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…
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…
We consider the minimum spanning tree problem in a setting where the edge weights are stochastic from unknown distributions, and the only available information is a single sample of each edge's weight distribution. In this setting, we…
The decision whether a measured distribution complies with an equidistribution is a central element of many biostatistical methods. High throughput differential expression measurements, for instance, necessitate to judge possible…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by…
We introduce single-set spectral sparsification as a deterministic sampling based feature selection technique for regularized least squares classification, which is the classification analogue to ridge regression. The method is unsupervised…
Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…
In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this…
We study the column subset selection problem with respect to the entrywise $\ell_1$-norm loss. It is known that in the worst case, to obtain a good rank-$k$ approximation to a matrix, one needs an arbitrarily large $n^{\Omega(1)}$ number of…
Modern datasets span billions of samples, making training on all available data infeasible. Selecting a high quality subset helps in reducing training costs and enhancing model quality. Submodularity, a discrete analogue of convexity, is…
We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…
A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proportions. Training machine learning models on biased data sets…
Given a finite set of unknown distributions or arms that can be sampled, we consider the problem of identifying the one with the maximum mean using a $\delta$-correct algorithm (an adaptive, sequential algorithm that restricts the…