Related papers: An algorithm for quantifying dependence in multiva…
In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
Estimating the dependency of variables is a fundamental task in data analysis. Identifying the relevant attributes in databases leads to better data understanding and also improves the performance of learning algorithms, both in terms of…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, many of the common approaches were borrowed from other fields. We clarify what the goal of a multivariate algorithm should be for the search…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned…
In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…
Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…
In many scientific tasks we are interested in discovering whether there exist any correlations in our data. This raises many questions, such as how to reliably and interpretably measure correlation between a multivariate set of attributes,…
Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the…