Related papers: Neural Copula: A unified framework for estimating …
The goal of this paper is to develop a measure for characterizing complex dependence between stationary time series that cannot be captured by traditional measures such as correlation and coherence. Our approach is to use copula models of…
Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
We propose the extension of Fr\'{e}chet-Hoeffding copula bounds for circular data. The copula is a powerful tool for describing the dependency of random variables. In two dimensions, the Fr\'{e}chet-Hoeffding upper (lower) bound indicates…
Visualization and assessment of copula structures are crucial for accurately understanding and modeling the dependencies in multivariate data analysis. In this paper, we introduce an innovative method that employs functional boxplots and…
The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…
We propose an approach to construct a new family of generalized Farlie-Gumbel-Morgenstern (GFGM) copulas that naturally scales to high dimensions. A GFGM copula can model moderate positive and negative dependence, cover different types of…
This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…
A heterogeneous structure of social networks induces various intriguing phenomena. One of them is the friendship paradox, which states that on average your friends have more friends than you do. Its generalization, called the generalized…
A layered neural network is now one of the most common choices for the prediction of high-dimensional practical data sets, where the relationship between input and output data is complex and cannot be represented well by simple conventional…
One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…
This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
Nonparanormal models describe the joint distribution of multivariate responses via latent Gaussian, and thus parametric, copulae while allowing flexible nonparametric marginals. Some aspects of such distributions, for example conditional…
Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts…
Building higher-dimensional copulas is generally recognized as a difficult problem. Regular-vines using bivariate copulas provide a flexible class of high-dimensional dependency models. In large dimensions, the drawback of the model is the…