Related papers: Neural Likelihoods via Cumulative Distribution Fun…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…
Learning the cumulative distribution function (CDF) of an outcome variable conditional on a set of features remains challenging, especially in high-dimensional settings. Conditional transformation models provide a semi-parametric approach…
We introduce conditional push-forward neural networks (CPFN), a generative framework for conditional distribution estimation. Instead of directly modeling the conditional density $f_{Y|X}$, CPFN learns a stochastic map…
Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
Conditional density estimation (CDE) is the task of estimating the probability of an event conditioned on some inputs. A neural network (NN) can also be used to compute the output distribution for continuous-domain, which can be viewed as…
We introduce a new type of graphical model called a "cumulative distribution network" (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…
We derive exact upper and lower bounds for the cumulative distribution function (cdf) of the output of a neural network (NN) over its entire support subject to noisy (stochastic) inputs. The upper and lower bounds converge to the true cdf…
We propose a method for finding a cumulative distribution function (cdf) that minimizes the distance to a given cdf, while belonging to an ambiguity set constructed relative to another cdf and, possibly, incorporating soft information. Our…
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…
Randomized neural networks (NNs) are an interesting alternative to conventional NNs that are more used for data modeling. The random vector functional-link (RVFL) network is an established and theoretically well-grounded randomized learning…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of…
Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density function (pdf) or the characteristic function (chf) of the state…
Probabilistic forecasting is not only a way to add more information to a prediction of the future, but it also builds on weaknesses in point prediction. Sudden changes in a time series can still be captured by a cumulative distribution…
The noncentral $t$-distribution is a generalization of the Student's $t$-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral $t$-distribution which is…