相关论文: On recovering the Radon-Nikodym derivative under t…
We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability…
Radon--Nikodym approach to relaxation dynamics, where probability density is built first and then used to calculate observable dynamic characteristic is developed and applied to relaxation type signals study. In contrast with $L^2$ norm…
Which principle underpins the design of an effective anomaly detection loss function? The answer lies in the concept of Radon-Nikod\'ym theorem, a fundamental concept in measure theory. The key insight from this article is: Multiplying the…
With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…
For distribution regression problem, where a bag of $x$--observations is mapped to a single $y$ value, a one--step solution is proposed. The problem of random distribution to random value is transformed to random vector to random value by…
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a unit cubic domain…
The functional linear regression model has been widely studied and utilized for dealing with functional predictors. In this paper, we study the Nystr\"om subsampling method, a strategy used to tackle the computational complexities inherent…
We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym…
Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\langle f(\mathbf{x})\psi^2 \rangle / \langle\psi^2\rangle$, where the $\psi(\mathbf{x})$ is a linear function on input…
This paper deals with the problem of reconstructing a band-limited signal when a finite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for…
This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one…
A novel algorithm was recently presented to utilize emerging time dependent probability density data to extract molecular potential energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the…
In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations $\gdag = F(\udag)$ where $\gdag$ is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density $t\gdag$…
We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
The paper proves generalization results for a class of stochastic learning algorithms. The method applies whenever the algorithm generates an absolutely continuous distribution relative to some a-priori measure and the Radon Nikodym…