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Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which…
Simplicity bias is an intriguing phenomenon prevalent in various input-output maps, characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these maps typically feature high-probability outputs with simple…
The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its…
Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these…
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,…
Learning and decision-making in domains with naturally high noise-to-signal ratio, such as Finance or Healthcare, is often challenging, while the stakes are very high. In this paper, we study the problem of learning and acting under a…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we…
Learning with noisy labels has gained increasing attention because the inevitable imperfect labels in real-world scenarios can substantially hurt the deep model performance. Recent studies tend to regard low-loss samples as clean ones and…
Conformal Prediction (CP) quantifies network uncertainty by building a small prediction set with a pre-defined probability that the correct class is within this set. In this study we tackle the problem of CP calibration based on a…
Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the…
Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…
We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical…
This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Labelling of data for supervised learning can be costly and time-consuming and the risk of incorporating label noise in large data sets is imminent. When training a flexible discriminative model using a strictly proper loss, such noise will…
Class imbalance and label noise are pervasive in large-scale datasets, yet much of machine learning research assumes well-labeled, balanced data, which rarely reflects real world conditions. Existing approaches typically address either…
We study online classification of features into labels with general hypothesis classes. In our setting, true labels are determined by some function within the hypothesis class but are corrupted by unknown stochastic noise, and the features…
This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting. We propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design…