An Introduction to Stochastic Deep Learning
The stochastic neural network, formulated as a composition of linear, logistic, and nonlinear regression modules, serves both as a deep learning model and as an analytical device for studying the properties of deep learning. It broadens deep learning beyond prediction‐oriented function approximation into a richer framework for statistical inference ...
Faming Liang
wiley +1 more source
Singularity in nonlinear systems: differential inclusion model for the standard and transformed fractional pantograph equation. [PDF]
Mobayen S +4 more
europepmc +1 more source
Detecting Relevant Deviations From the White Noise Assumption for Non‐Stationary Time Series
ABSTRACT We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non‐stationary time series. Second, we address the problem that a white noise test is usually not performed because one believes ...
Patrick Bastian
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Nonlinear fractional stochastic delay modeling and computational analysis of herpes simplex virus type II dynamics. [PDF]
Raza A +3 more
europepmc +1 more source
Adaptive Estimation for Weakly Dependent Functional Times Series
ABSTRACT We propose adaptive mean and autocovariance function estimators for stationary functional time series under 𝕃p−m‐approximability assumptions. These estimators are designed to adapt to the regularity of the curves and to accommodate both sparse and dense data designs.
Hassan Maissoro +2 more
wiley +1 more source
Large deviations of piecewise-deterministic Markov processes with application to stochastic calcium waves. [PDF]
Barbet G +3 more
europepmc +1 more source
Repelled Point Processes With Application to Numerical Integration
ABSTRACT We look at Monte Carlo numerical integration from a stochastic geometry point of view. While crude Monte Carlo estimators relate to linear statistics of a homogeneous Poisson point process (PPP), linear statistics of more regularly spread point processes can yield unbiased estimators with faster‐decaying variance, and thus lower integration ...
Diala Hawat +3 more
wiley +1 more source
Divergence and Model Adequacy, a Semiparametric Case Study. [PDF]
Broniatowski M, Moutsouka J.
europepmc +1 more source
Exponential convergence for ultrafast diffusion equations with log‐concave weights
Abstract We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log‐concave and log‐lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in Iacobelli [Discrete Contin. Dyn. Syst. 39 (2019), 4929–4943].
Max Fathi, Mikaela Iacobelli
wiley +1 more source
A neural network model for managing renewable resources with population growth. [PDF]
Ahmad S +3 more
europepmc +1 more source

