Related papers: Statistical Analysis from the Fourier Integral The…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…
We present in this paper a novel non-parametric approach useful for clustering Markov processes. We introduce a pre-processing step consisting in mapping multivariate independent and identically distributed samples from random variables to…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
We tackle the natural question of whether it is possible to estimate conditional distributions via Sklar's theorem by separately estimating the conditional distributions of the underlying copula and the marginals. Working with so-called…
The multivariate extended skew-normal distribution allows for accommodating raw data which are skewed and heavy tailed, and has at least three appealing statistical properties, namely closure under conditioning, affine transformations, and…
We develop a finite-sample, design-based theory for random forests in which each tree is a randomized conditional predictor acting on fixed covariates and the forest is their Monte Carlo average. An exact variance identity separates Monte…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
The freedom associated with the definition of parton distribution functions is analyzed and formulae governing the dependence of parton distribution functions and hard scattering cross-sections on unphysical quantities associated with the…
Weconsider Markov decision processes arising from a Markov model of an underlying natural phenomenon. Such phenomena are usually periodic (e.g. annual) in time, and so the Markov processes modelling them must be time-inhomogeneous, with…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
An introduction to the basics of Monte Carlo is given. The topics covered include, sample space, events, probabilities, random variables, mean, variance, covariance, characteristic function, chebyshev inequality, law of large numbers,…
Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Several tasks in information retrieval (IR) rely on assumptions regarding the distribution of some property (such as term frequency) in the data being processed. This thesis argues that such distributional assumptions can lead to incorrect…
The use of Fermat-Torricelli points can be an effective mathematical tool for analyzing numerical series that have a large variance, a pronounced nonlinear trend, or do not have a normal distribution of a random variable. Linear…
In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…