Related papers: An Improved Solution to the Two Normal Means Probl…

In this paper, we address the problem of approximating solutions of ill-posed problems using mollification. We quickly review existing mollification regularization methods and provide two new approximate solutions to a general ill-posed…

We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix…

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…

We consider Empirical Bayes (EB) estimation in the normal means problem, when the standard deviations of the observations are not known precisely, but estimated with error -- which is almost always the case in practical applications. In…

Variational inference with a factorized Gaussian posterior estimate is a widely used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…

We study the normal mean inference problem, which involves simultaneous testing of the means of many normal distributions. This problem has been extensively studied within the empirical Bayes (EB) framework. However, the reliability of most…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…

In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

We introduce "noninvertible" generalization of statistics - semistatistics replacing condition when double exchanging gives identity to "regularity" condition. Then in categorical language we correspondingly generalize braidings and the…

Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…

We study the problem of learning causal models from observational data through the lens of interpolation and its counterpart -- regularization. A large volume of recent theoretical, as well as empirical work, suggests that, in highly…

Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…

As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…

We study a regularized variant of the Bayesian Persuasion problem, where the receiver's decision process includes a divergence-based penalty that accounts for deviations from perfect rationality. This modification smooths the underlying…