Related papers: Robust Predictive Uncertainty and Double Descent i…
This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…
The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…
In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior, since this choice is made by the modeler and is often…
Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
Big Data often presents as massive non-probability samples. Not only is the selection mechanism often unknown, but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches…
We revisit the problem of model-based object recognition for intensity images and attempt to address some of the shortcomings of existing Bayesian methods, such as unsuitable priors and the treatment of residuals with a non-robust error…
We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with…
Clinical decision-making demands uncertainty quantification that provides both distribution-free coverage guarantees and risk-adaptive precision, requirements that existing methods fail to jointly satisfy. We present a hybrid…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…
Standard Bayesian inference is known to be sensitive to model misspecification, leading to unreliable uncertainty quantification and poor predictive performance. However, finding generally applicable and computationally feasible methods for…
Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…
We study data-driven decision-making problems in the Bayesian framework, where the expectation in the Bayes risk is replaced by a risk-sensitive entropic risk measure. We focus on problems where calculating the posterior distribution is…
Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…
Change-plane regression identifies subpopulations through an interpretable linear threshold rule, but likelihood-based inference for the hard-threshold boundary is nonregular: objectives are non-smooth, the boundary is weakly identified…
We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…
We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…
This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local…
This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…