Related papers: Adaptive joint distribution learning
We present neural mixture distributional regression (NMDR), a holistic framework to estimate complex finite mixtures of distributional regressions defined by flexible additive predictors. Our framework is able to handle a large number of…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
Theoretical analysis of the divide-and-conquer based distributed learning with least square loss in the reproducing kernel Hilbert space (RKHS) have recently been explored within the framework of learning theory. However, the studies on…
Suppose that $Y$ is a scalar and $X$ is a second-order stochastic process, where $Y$ and $X$ are conditionally independent given the random variables $\xi_1,...,\xi_p$ which belong to the closed span $L_X^2$ of $X$. This paper investigates…
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…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
In this paper we investigate the connection between supervised learning and linear inverse problems. We first show that a linear inverse problem can be view as a function approximation problem in a reproducing kernel Hilbert space (RKHS)…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an…
This paper combines vector-valued reproducing kernel Hilbert space (vRKHS) embedding with robust adaptive observation, yielding an algorithm that is both non-parametric and robust. The main contribution of this paper lies in the ability of…
We propose a decentralized online learning algorithm for distributed random inverse problems over network graphs with online measurements, and unifies the distributed parameter estimation in Hilbert spaces and the least mean square problem…
Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS). The solution describes the observed data and has a small RKHS norm.…
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…
The H\'ajek-Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon-Nikodym density for each measure with respect to the other one) or…
Data loss is a critical problem in structural health monitoring (SHM). Probability distributions play a highly important role in many applications. Improving the quality of distribution estimations made using incomplete samples is highly…
Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…
Metric learning from a set of triplet comparisons in the form of "Do you think item h is more similar to item i or item j?", indicating similarity and differences between items, plays a key role in various applications including image…