Related papers: Minimax optimal transfer learning for high-dimensi…
This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…
We generalize the notion of average Lipschitz smoothness proposed by Ashlagi et al. (COLT 2021) by extending it to H\"older smoothness. This measure of the "effective smoothness" of a function is sensitive to the underlying distribution and…
We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where…
Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial…
Modern data analytics take advantage of ensemble learning and transfer learning approaches to tackle some of the most relevant issues in data analysis, such as lack of labeled data to use to train the analysis models, sparsity of the…
Generalization error bounds are essential for comprehending how well machine learning models work. In this work, we suggest a novel method, i.e., the Auxiliary Distribution Method, that leads to new upper bounds on expected generalization…
We propose a novel adaptive transfer learning framework, learning to transfer learn (L2TL), to improve performance on a target dataset by careful extraction of the related information from a source dataset. Our framework considers…
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…
We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…
In this paper, we focus on the high-dimensional double sparse structure, where the parameter of interest simultaneously encourages group-wise sparsity and element-wise sparsity in each group. By combining the Gilbert-Varshamov bound and its…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…
The shapes of functions provide highly interpretable summaries of their trajectories. This article develops a novel transfer learning methodology to tackle the challenge of data scarcity in functional linear models. The methodology…
The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While many empirical studies illustrate the benefits of transfer learning, few theoretical results are…