Related papers: Instance-optimal estimation of L2-norm
We examine three non-negative matrix factorization techniques; L2-norm, L1-norm, and L2,1-norm. Our aim is to establish the performance of these different approaches, and their robustness in real-world applications such as feature selection…
This work develops a sparse and outlier-insensitive method to fit a one-dimensional subspace that can be used as a replacement for eigenvector methods such as principal component analysis (PCA). The method is insensitive to outlier…
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…
We design an $(\varepsilon, \delta)$-differentially private algorithm to estimate the mean of a $d$-variate distribution, with unknown covariance $\Sigma$, that is adaptive to $\Sigma$. To within polylogarithmic factors, the estimator…
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
Consider the design based situation where an $r$-regular set is sampled on a random lattice. A fast algorithm for estimating the integrated mean curvature based on this observation is to use a weighted sum of $2\times \dotsm \times 2$…
This paper extends the empirical minimum divergence approach for models which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to…
We design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…
Classical least squares estimators are well-known to be robust with respect to moment assumptions concerning the error distribution in a wide variety of finite-dimensional statistical problems; generally only a second moment assumption is…
Top-$2$ methods have become popular in solving the best arm identification (BAI) problem. The best arm, or the arm with the largest mean amongst finitely many, is identified through an algorithm that at any sequential step independently…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
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…
We present an algorithm for L1-norm kernel PCA and provide a convergence analysis for it. While an optimal solution of L2-norm kernel PCA can be obtained through matrix decomposition, finding that of L1-norm kernel PCA is not trivial due to…
We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…
In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the best known example of which is Bernoulli convolution. The…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…
The logistic regression model is one of the most popular data generation model in noisy binary classification problems. In this work, we study the sample complexity of estimating the parameters of the logistic regression model up to a given…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…