相关论文: Minimax convergence rates of a binary classificati…

The study of minimax convergence rates for classification procedures adapted to SDE paths is rarely addressed in the literature. Only one paper established optimal convergence rates for a binary classifier for SDE paths constructed from the…

We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all…

We address the multiclass classification problem for stochastic diffusion paths, assuming that the classes are distinguished by their drift functions, while the diffusion coefficient remains common across all classes. In this setting, we…

We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then…

Consider a diffusion process X, solution of a time-homogeneous stochastic differential equation. We assume that the diffusion process X is observed at discrete times, at high frequency, which means that the time step tends toward zero. In…

In massive data analysis, training and testing data often come from very different sources, and their probability distributions are not necessarily identical. A feature example is nonparametric classification in posterior drift model where…

The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers. This paper studies…

It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than $n^{-1/2}$. The work on this subject has suggested…

It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, i.e., the rates faster than $n^{-1/2}$. The works on this subject suggested…

We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…

We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…

In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time…

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

In this work we consider a problem of multi-label classification, where each instance is associated with some binary vector. Our focus is to find a classifier which minimizes false negative discoveries under constraints. Depending on the…

Incorporating boundary conditions into stochastic models of passive or active particle motion is usually implemented at the level of the associated forward or backward Kolmogorov equation, whose solution determines the probability…

A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the…

This paper presents a minimum flow approach applicable to a wide range of doubly nonlinear diffusion problems. We introduce a minimum flow steepest descent algorithm that seeks an optimal traffic flow by minimizing an internal energy…

In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as…

We study stochastic differential equations(SDEs) with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence…

Driven by diverse applications, several recent models impose randomly switching boundary conditions on either a PDE or SDE. The purpose of this paper is to provide tools for calculating statistics of these models and to establish a…