Related papers: ISDE : Independence Structure Density Estimation
We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…
We derive independence tests by means of dependence measures thresholding in a semiparametric context. Precisely, estimates of phi-mutual informations, associated to phi-divergences between a joint distribution and the product distribution…
Based on $X \sim N_d(\theta, \sigma^2_X I_d)$, we study the efficiency of predictive densities under $\alpha-$divergence loss $L_{\alpha}$ for estimating the density of $Y \sim N_d(\theta, \sigma^2_Y I_d)$. We identify a large number of…
This paper develops a conditional independence (CI) test from a conditional density ratio (CDR) for weakly dependent data. The main contribution is presenting a closed-form expression for the estimated conditional density ratio function…
The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters…
The autodependogram is a graphical device recently proposed in the literature to analyze autodependencies. It is defined computing the classical Pearson chi-square statistics of independence at various lags in order to point out the…
The state-of-the-art dimensionality reduction approaches largely rely on complicated optimization procedures. On the other hand, closed-form approaches requiring merely eigen-decomposition do not have enough sophistication and nonlinearity.…
The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have…
The goal of quantitative elastography is to identify biomechanical parameters from interior displacement data, which are provided by other modalities, such as ultrasound or magnetic resonance imaging. In this paper, we analyze the stability…
For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the…
With the rise of the Internet of Things, strategies for effectively processing big data are essential for discovering meaningul insights. The time series datasets produced by groups of interconnected devices contain valuable underlying…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
Due to its efficiency and reasonable accuracy, density functional theory is one of the most widely used electronic structure theories in condensed matter physics, materials physics, and quantum chemistry. The accuracy and efficiency of a…
In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to…
Independent component analysis (ICA) is linked up with the problem of estimating a non linear functional of a density, for which optimal estimators are well known. The precision of ICA is analyzed from the viewpoint of functional spaces in…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
The aim of this paper is to analyze from a mathematical perspective some existing schemes to partition a molecular density into several atomic contributions, with a specific focus on Iterative Stockholder Atom (ISA) methods. We provide a…
We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution…
Intrinsic image decomposition (IID) is the task of separating an image into albedo and shade. In real-world scenes, it is difficult to quantitatively assess IID quality due to the unavailability of ground truth. The existing method provides…
Numerical data imputation algorithms replace missing values by estimates to leverage incomplete data sets. Current imputation methods seek to minimize the error between the unobserved ground truth and the imputed values. But this strategy…