Related papers: Monte Carlo Dependency Estimation
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…
Operations is a key challenge in the domain of machine learning pipeline deployments involving monitoring and management of real-time prediction quality. Typically, metrics like accuracy, RMSE etc., are used to track the performance of…
We consider the $\mathcal{H}^2$-formatted compression and computational estimation of covariance functions on a compact set in $\mathbb{R}^d$. The classical sample covariance or Monte Carlo estimator is prohibitively expensive for many…
This paper proposes different methods to consistently detect multiple breaks in copula-based dependence measures, mainly focusing on Spearman's $\rho$. The leading model is a factor copula model due to its usefulness for analyzing data in…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
Classical analysis of variance requires that model terms be labeled as fixed or random and typically culminate by comparing variability from each batch (factor) to variability from errors; without a standard methodology to assess the…
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…
We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…
Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
Given a database and a target attribute of interest, how can we tell whether there exists a functional, or approximately functional dependence of the target on any set of other attributes in the data? How can we reliably, without bias to…