Related papers: Optimal query complexity for estimating the trace …
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
Consider the task of matrix estimation in which a dataset $X \in \mathbb{R}^{n\times m}$ is observed with sparsity $p$, and we would like to estimate $\mathbb{E}[X]$, where $\mathbb{E}[X_{ui}] = f(\alpha_u, \beta_i)$ for some Holder smooth…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
In this paper we study the problem of testing of constrained samplers over high-dimensional distributions with $(\varepsilon,\eta,\delta)$ guarantees. Samplers are increasingly used in a wide range of safety-critical ML applications, and…
We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…
We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
Multi-fidelity methods that use an ensemble of models to compute a Monte Carlo estimator of the expectation of a high-fidelity model can significantly reduce computational costs compared to single-model approaches. These methods use oracle…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
Given data drawn from a collection of Gaussian variables with a common mean but different and unknown variances, what is the best algorithm for estimating their common mean? We present an intuitive and efficient algorithm for this task. As…
We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider…
The problem of estimating certain distributions over $\{0,1\}^d$ is considered here. The distribution represents a quantum system of $d$ qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is…
Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. This problem is magnified in high-dimensional settings where the number of variables $p$ diverges with the sample size $n$, as well…
Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…
A problem of statistical estimation of a Hermitian nonnegatively definite matrix of unit trace (for instance, a density matrix in quantum state tomography) is studied. The approach is based on penalized least squares method with a…
We consider the sensitivity of algorithms for the maximum matching problem against edge and vertex modifications. Algorithms with low sensitivity are desirable because they are robust to edge failure or attack. In this work, we show a…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…