Related papers: Non-Parametric Inference of Relational Dependence
For years, independence has been considered as an important concept in many disciplines. Nevertheless, we present the first research that investigates the discovery problem of independence in data. In its arguably simplest form,…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…
In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing…
In this paper we develop a novel nonparametric framework to test the independence of two random variables $\mathbf{X}$ and $\mathbf{Y}$ with unknown respective marginals $H(dx)$ and $G(dy)$ and joint distribution $F(dx dy)$, based on {\it…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Control charts for process monitoring are widely used in practice. Most control charts require the monitored (residuals) process to be serially independent (and to satisfy specified distributional assumptions), whereas undetected dependence…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
This work investigates the problem of testing whether $d$ functional random variables are jointly independent using a modified estimator of the $d$-variable Hilbert Schmidt Indepedence Criterion ($d$HSIC) which generalizes HSIC for the case…
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…
We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of…
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
We propose a kernel-based nonparametric test of relative goodness of fit, where the goal is to compare two models, both of which may have unobserved latent variables, such that the marginal distribution of the observed variables is…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
Distributions over rankings are used to model data in a multitude of real world settings such as preference analysis and political elections. Modeling such distributions presents several computational challenges, however, due to the…
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…