Related papers: AR and MA representation of partial autocorrelatio…
This is a "spatial autocorrelation analysis" of spatial autocorrelation. I use the 1-dimension spatial autocorrelation function (ACF) and partial autocorrelation function (PACF) to analyze four kinds of weight function in common use for the…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
We study continual learning in the large scale setting where tasks in the input sequence are not limited to classification, and the outputs can be of high dimension. Among multiple state-of-the-art methods, we found vanilla experience…
In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile…
We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation…
The paper proposes an identification procedure for autoregressive gaussian stationary stochastic processes wherein the manifest (or observed) variables are mostly related through a limited number of latent (or hidden) variables. The method…
Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the…
We study the asymptotic convergence of the partial averaging method, a technique used in conjunction with the random series implementation of the Feynman-Kac formula. We prove asymptotic bounds valid for most series representations in the…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic…
We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…
The paper considers high frequency sampled multivariate continuous-time ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior…
In this work we introduce the class of unit-Weibull Autoregressive Moving Average models for continuous random variables taking values in $(0,1)$. The proposed model is an observation driven one, for which, conditionally on a set of…
Activation functions (AF) are necessary components of neural networks that allow approximation of functions, but AFs in current use are usually simple monotonically increasing functions. In this paper, we propose trainable compound AF (TCA)…
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…
An integral function of fully autonomous robots and humans is the ability to focus attention on a few relevant percepts to reach a certain goal while disregarding irrelevant percepts. Humans and animals rely on the interactions between the…
An integral function of fully autonomous robots and humans is the ability to focus attention on a few relevant percepts to reach a certain goal while disregarding irrelevant percepts. Humans and animals rely on the interactions between the…
Intelligent agents can cope with sensory-rich environments by learning task-agnostic state abstractions. In this paper, we propose an algorithm to approximate causal states, which are the coarsest partition of the joint history of actions…
We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functions. We leverage this perspective to provide formal evidence regarding the usefulness of value…
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and…