Related papers: High-dimensional robust regression under heavy-tai…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a…
This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial…
In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses…
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large weights occur with higher probability. This allows the study…
It has repeatedly been observed that loss minimization by stochastic gradient descent (SGD) leads to heavy-tailed distributions of neural network parameters. Here, we analyze a continuous diffusion approximation of SGD, called homogenized…
Considered here are robust subgroup-classifier learning and testing in change-plane regressions with heavy-tailed errors, which can identify subgroups as a basis for making optimal recommendations for individualized treatment. A new…
High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and…
Doubly robust estimators have gained widespread popularity in various fields due to their ability to provide unbiased estimates under model misspecification. However, the asymptotic theory for doubly robust estimators with continuous-time…
We address a parametric joint detection-estimation problem for discrete signals of the form $x(t) = \sum_{n=1}^{N} \alpha_n e^{-i \lambda_n t } + \epsilon_t$, $t \in \mathbb{N}$, with an additive noise represented by independent centered…
Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…
Real-world data is laden with outlying values. The challenge for machine learning is that the learner typically has no prior knowledge of whether the feedback it receives (losses, gradients, etc.) will be heavy-tailed or not. In this work,…
We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…