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Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…

First principles approaches have revolutionized our ability in using computers to predict, explore and design materials. A major advantage commonly associated with these approaches is that they are fully parameter free. However, numerically…

Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…

The deconfounder was proposed as a method for estimating causal parameters in a context with multiple causes and unobserved confounding. It is based on recovery of a latent variable from the observed causes. We disentangle the causal…

Inverse problems are ubiquitous in modern scientific studies and involve recovering an underlying signal from noisy observations often transformed by a measurement operator. These problems are frequently ill-posed, particularly in imaging,…

In inverse problems, distribution-free uncertainty quantification (UQ) aims to obtain error bars with coverage guarantees that are independent of any prior assumptions about the data distribution. In the context of mass mapping,…

We consider statistical inference for a single coordinate of regression coefficients in high-dimensional linear models. Recently, the debiased estimators are popularly used for constructing confidence intervals and hypothesis testing in…

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected…

The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…

We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we…

In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which linear reconstructions will exhibit artifacts. Another consequence of under-sampling is lower signal to noise ratio (SNR) due…

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…

Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…

We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…

Despite the increasing demand for safer machine learning practices, the use of Uncertainty Quantification (UQ) methods in production remains limited. This limitation is exacerbated by the challenge of validating UQ methods in absence of UQ…

In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…

We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under…

Emergence of artificial intelligence techniques in biomedical applications urges the researchers to pay more attention on the uncertainty quantification (UQ) in machine-assisted medical decision making. For classification tasks, prior…

To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…

Large Language Models (LLMs) have become indispensable tools across various applications, making it more important than ever to ensure the quality and the trustworthiness of their outputs. This has led to growing interest in uncertainty…