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We study least-squares trace regression when the parameter is the sum of a $r$-low-rank matrix and a $s$-sparse matrix and a fraction $\epsilon$ of the labels is corrupted. For subgaussian distributions and feature-dependent noise, we…
Assured AI in unrestricted settings is a critical problem. Our framework addresses AI assurance challenges lying at the intersection of domain adaptation, fairness, and counterfactuals analysis, operating via the discovery and intervention…
We observe an unknown function of $d$ variables $f(\boldsymbol{t})$, $\boldsymbol{t} \in[0,1]^d$, in the Gaussian white noise model of intensity $\varepsilon>0$. We assume that the function $f$ is regular and that it is a sum of $k$-variate…
We consider an additive regression model consisting of two components $f^0$ and $g^0$, where the first component $f^0$ is in some sense "smoother" than the second $g^0$. Smoothness is here described in terms of a semi-norm on the class of…
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial…
Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the…
Active learning is typically used to label data, when the labeling process is expensive. Several active learning algorithms have been theoretically proved to perform better than their passive counterpart. However, these algorithms rely on…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
In this paper, we consider the so-called Shape Invariant Model which stands for the estimation of a function f0 submitted to a random translation of law g0 in a white noise model. We are interested in such a model when the law of the…
We consider the Stochastic Boolean Function Evaluation (SBFE) problem in the well-studied case of $k$-of-$n$ functions: There are independent Boolean random variables $x_1,\dots,x_n$ where each variable $i$ has a known probability $p_i$ of…
Gaussian smoothing combined with a probabilistic framework for denoising via the empirical Bayes formalism, i.e., the Tweedie-Miyasawa formula (TMF), are the two key ingredients in the success of score-based generative models in Euclidean…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
In the present paper, we consider the estimation of a periodic two-dimensional function $f(\cdot,\cdot)$ based on observations from its noisy convolution, and convolution kernel $g(\cdot,\cdot)$ unknown. We derive the minimax lower bounds…
Supremum norm loss is intuitively more meaningful to quantify function estimation error in statistics. In the context of multivariate nonparametric regression with unknown error, we propose a Bayesian procedure based on spike-and-slab prior…
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…
We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…
The aim of this paper is to describe a novel non-parametric noise reduction technique from the point of view of Bayesian inference that may automatically improve the signal-to-noise ratio of one- and two-dimensional data, such as e.g.…
Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated prediction sets with precise coverage guarantees for any classification model. However, its reliance…
In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…