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We study the problem of estimating the parameters of a Boolean product distribution in $d$ dimensions, when the samples are truncated by a set $S \subset \{0, 1\}^d$ accessible through a membership oracle. This is the first time that the…
The success of neural networks over the past decade has established them as effective models for many relevant data generating processes. Statistical theory on neural networks indicates graceful scaling of sample complexity. For example,…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. We aim to bridge the gap between these two…
We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…
A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear…
Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As…
This work investigates the performance of the final iterate produced by stochastic gradient descent (SGD) under temporally dependent data. We consider two complementary sources of dependence: $(i)$ martingale-type dependence in both the…
Analysis of random censored life-time data along with some related stochastic covariables is of great importance in many applied sciences like medical research, population studies and planning etc. The parametric estimation technique…
This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$,…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy-tailed response variable. In this distribution-free regression setting, we show that boundedness of the conditional second…
Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important measure in risk analysis and stochastic optimization, and is also finding applications beyond these areas. In finance, it…
We study the estimation of distributional parameters when samples are shown only if they fall in some unknown set $S \subseteq \mathbb{R}^d$. Kontonis, Tzamos, and Zampetakis (FOCS'19) gave a $d^{\mathrm{poly}(1/\varepsilon)}$ time…
In semivarying coefficient models for longitudinal/clustered data, usually of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation…
In this paper, we prove strong consistency of an estimator by the truncated singular value decomposition for a multivariate errors-in-variables linear regression model with collinearity. This result is an extension of Gleser's proof of the…
Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…
One of the common challenges faced by researchers in recent data analysis is missing values. In the context of penalized linear regression, which has been extensively explored over several decades, missing values introduce bias and yield a…
We consider an $n$ agents distributed optimization problem with imperfect information characterized in a parametric sense, where the unknown parameter can be solved by a distinct distributed parameter learning problem. Though each agent…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…