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Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
In this article, we investigate the problem of estimating a spatially inhomogeneous function and its derivatives in the white noise model using Besov-Laplace priors. We show that smoothness-matching priors attains minimax optimal posterior…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
Hybrid Monte-Carlo (HMC) sampling smoother is a fully non-Gaussian four-dimensional data assimilation algorithm that works by directly sampling the posterior distribution formulated in the Bayesian framework. The smoother in its original…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss…
In this paper, we study the asymptotic properties of regularized least squares with indefinite kernels in reproducing kernel Krein spaces (RKKS). By introducing a bounded hyper-sphere constraint to such non-convex regularized risk…
The mathematical theory of reproducing kernel Hilbert spaces (RKHS) provides powerful tools for minimum variance estimation (MVE) problems. Here, we extend the classical RKHS based analysis of MVE in several directions. We develop a…
The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating…
Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
Probabilistic predictions are probability distributions over the set of possible outcomes. Such predictions quantify the uncertainty in the outcome, making them essential for effective decision making. By combining multiple predictions, the…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…
We obtain rates of contraction of posterior distributions in inverse problems defined by scales of smoothness classes. We derive abstract results for general priors, with contraction rates determined by Galerkin approximation. The rate…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
Weak lensing mass-mapping is a useful tool to access the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies and finite fields/missing data, the recovery of dark matter maps constitutes a challenging…