Related papers: The effect of round-off error on long memory proce…

We consider a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbations via an additive Gaussian noise. Our main study is the…

Environmental epidemiologists are often interested in estimating the effect of time-varying functions of the exposure history on health outcomes. However, the individual exposure measurements that constitute the history upon which an…

In this paper an easy to implement method of stochastically weighing short and long memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly…

Decoupling representation learning and classifier learning has been shown to be effective in classification with long-tailed data. There are two main ingredients in constructing a decoupled learning scheme; 1) how to train the feature…

Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests…

In solid-state physics, energies of molecular systems are usually computed with a plane-wave discretization of Kohn-Sham equations. A priori estimates of plane-wave convergence for periodic Kohn-Sham calculations with pseudopotentials have…

We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…

Contemporaneous aggregation of individual AR(1) random processes might lead to different properties of the limit aggregated time series, in particular, long memory (Granger, 1980). We provide a new characterization of the series of…

Local differential privacy is a differential privacy paradigm in which individuals first apply a privacy mechanism to their data (often by adding noise) before transmitting the result to a curator. The noise for privacy results in…

In modern optimization methods used in deep learning, each update depends on the history of previous iterations, often referred to as memory, and this dependence decays fast as the iterates go further into the past. For example, gradient…

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…

In recent years, adaptive identification methods that can achieve the true value convergence of parameters without requiring persistent excitation (PE) have been widely studied, and concurrent learning has been intensively studied. However,…

This paper proposes feasible asymptotically efficient estimators for a certain class of Gaussian noises with self-similar and stationary properties, which includes the fractional Gaussian noise, under high frequency observations. In this…

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…

We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…

We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $\tau$ rounds ago. First, we show that without stochastic…

The Ordered Weighted Averaging (OWA) operator is a traditional and commonly used criterion for aggregating discrete values of uncertain quantities. In this paper, it is shown that the discrete OWA naturally extends to the continuous case by…

We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of…

Differentially Private Stochastic Gradient Descent (DP-SGD) is a standard method for enforcing privacy in deep learning, typically using the Gaussian mechanism to perturb gradient updates. However, conventional mechanisms such as Gaussian…