Related papers: Conditional probability calculations for the nonli…

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…

The discrete Schr\"odinger equation on a half-line lattice with the Dirichlet boundary condition is considered when the potential is real valued, is summable, and has a finite first moment. The Darboux transformation formulas are derived…

This paper is concerned with the numerical analysis of linear and nonlinear Schr{\"o}dinger equations with analytic potentials. While the regularity of the potential (and the source term when there is one) automatically conveys to the…

Learning a distribution conditional on a set of discrete-valued features is a commonly encountered task. This becomes more challenging with a high-dimensional feature set when there is the possibility of interaction between the features. In…

Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…

Motivated by the need to analyze continuously updated data sets in the context of time-to-event modeling, we propose a novel nonparametric approach to estimate the conditional hazard function given a set of continuous and discrete…

We construct a martingale solution of the stochastic nonlinear Schr\"odinger equation with a multiplicative noise of jump type in the Marcus canonical form. The problem is formulated in a general framework that covers the subcritical…

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

Conditional density estimation generalizes regression by modeling a full density f(yjx) rather than only the expected value E(yjx). This is important for many tasks, including handling multi-modality and generating prediction intervals.…

This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in a multivariate setting. We first demonstrate that conditional density estimation is impossible if one only…

The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…

Conditional copulas are flexible statistical tools that couple joint conditional and marginal conditional distributions. In a linear regression setting with more than one covariate and two dependent outcomes, we propose the use of additive…

We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

We present an analytical study of a nonlinear oscillator subject to an additive Ornstein-Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or…

We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…

We present a novel implementation of conditional Long Short-Term Memory Recurrent Neural Networks that successfully predict the spectral evolution of a pulse in nonlinear periodically-poled waveguides. The developed networks offer large…

In this paper the one-dimensional nonparaxial nonlinear Schr\"odinger equation is considered. This was proposed as an alternative to the classical nonlinear Schr\"odinger equation in those situations where the assumption of paraxiality may…

The effect of noise on the nonlinear photoionization of an atom due to a femtosecond pulse is investigated in the framework of the stochastic Schr\"odinger equation. A modest amount of white noise results in an enhancement of the net…

We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high…