Related papers: Nonparametric plug-in classifier for multiclass cl…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

We propose a nonparametric estimation for a class of fractional stochastic differential equations (FSDE) with random effects. We precisely consider general linear fractional stochastic differential equations with drift depending on random…

Machine learning algorithms have been used to determine probabilistic classifications of unassociated sources. Often classification into two large classes, such as Galactic and extra-galactic, is considered. However, there are many more…

We introduce a class of jump-diffusions, called holomorphic, of which the well-known classes of affine and polynomial processes are particular instances. The defining property concerns the extended generator, which is required to map a…

This paper uses Lie symmetry methods to calculate certain expectations for a large class of It\^{o} diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form $E_x(e^{-\lambda…

Fusion learning refers to synthesizing inferences from multiple sources or studies to provide more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on…

We study nonclassical features of multiphoton light emitted by clusters of single-photon emitters. As signatures of nonclassicality, we use violation of inequalities for normalized correlation functions of different orders or the…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

Road user trajectory prediction in dynamic environments is a challenging but crucial task for various applications, such as autonomous driving. One of the main challenges in this domain is the multimodal nature of future trajectories…

This paper extends the design-based framework to settings with multi-way cluster dependence, and shows how multi-way clustering can be justified when clustered assignment and clustered sampling occurs on different dimensions, or when either…

The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a…

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…

In this paper, we address the problem of classifying data within the radar reference window in terms of statistical properties. Specifically, we partition these data into statistically homogeneous subsets by identifying possible clutter…

This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with…

We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not…

This paper studies point identification of the distribution of the coefficients in some random coefficients models with exogenous regressors when their support is a proper subset, possibly discrete but countable. We exhibit trade-offs…

We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is…

We study a class of fourth order nonlinear parabolic equations which include the thin-film equation and the quantum drift-diffusion model as special cases. We investigate these equations by first developing functional inequalities of the…

We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…

We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient.…