Related papers: Copula Representations and Error Surface Projectio…

There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated)…

Interpretability of machine learning is defined as the extent to which humans can comprehend the reason of a decision. However, a neural network is not considered interpretable due to the ambiguity in its decision-making process. Therefore,…

Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to…

Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

We derive an approximation error bound that holds simultaneously for a function and all its derivatives up to any prescribed order. The bounds apply to elementary functions, including multivariate polynomials, the exponential function, and…

Graph-structured data are ubiquitous. However, graphs encode diverse types of information and thus play different roles in data representation. In this paper, we distinguish the \textit{representational} and the \textit{correlational} roles…

We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…

The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on…

Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…

A new non-linear variant of a quantitative extension of the uniform boundedness principle is used to show sharpness of error bounds for univariate approximation by sums of sigmoid and ReLU functions. Single hidden layer feedforward neural…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…

We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical…

We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques…

We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…

Higher order artificial neurons whose outputs are computed by applying an activation function to a higher order multinomial function of the inputs have been considered in the past, but did not gain acceptance due to the extra parameters and…

Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of…

Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on…