Related papers: Minimax rates in variance and covariance changepoi…
Lower bounds involving $f$-divergences between the underlying probability measures are proved for the minimax risk in estimation problems. Our proofs just use simple convexity facts. Special cases and straightforward corollaries of our…
Consider the problem of estimating the Shannon entropy of a distribution over $k$ elements from $n$ independent samples. We show that the minimax mean-square error is within universal multiplicative constant factors of $$\Big(\frac{k }{n…
We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset $\mathcal{C}$ of $\mathbb{R}^d$. We adopt a minimax point of view and our primary…
We consider here the identification of change-points on large-scale data streams. The objective is to find the most efficient way of combining information across data stream so that detection is possible under the smallest detectable change…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…
This paper addresses hypothesis testing for the mean of matrix-valued data in high-dimensional settings. We investigate the minimum discrepancy test, originally proposed by Cragg (1997), which serves as a rank test for lower-dimensional…
In this paper, we study the minimax rates and provide an implementable convex algorithm for Poisson inverse problems under weak sparsity and physical constraints. In particular we assume the model $y_i \sim \mbox{Poisson}(Ta_i^{\top}f^*)$…
We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse…
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…
We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method…
We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived…
Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates $x$) of training and testing samples $\mathrm{p}_\text{tr}(x)$ and $\mathrm{p}_\text{te}(x)$ are different but the label…
Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…
We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…
We study a plug in least squares estimator for the change point parameter where change is in the mean of a high dimensional random vector under subgaussian or subexponential distributions. We obtain sufficient conditions under which this…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…
A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…