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Estimation of the complete distribution of a random variable is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting…

This paper proposes a nonparametric multivariate density forecast model based on deep learning. It not only offers the whole marginal distribution of each random variable in forecasting targets, but also reveals the future correlation…

The cumulative distribution function (CDF) is fundamental for characterizing random variables, making it essential in applications that require privacy-preserving data analysis. This paper introduces a novel framework for constructing…

There has long been debates on how we could interpret neural networks and understand the decisions our models make. Specifically, why deep neural networks tend to be error-prone when dealing with samples that output low softmax scores. We…

Survival analysis aims at modeling the relationship between covariates and event occurrence with some untracked (censored) samples. In implementation, existing methods model the survival distribution with strong assumptions or in a discrete…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

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…

The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…

Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper bounds; however, unless the covariates…

The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…

In selective classification (SC), a classifier abstains from making predictions that are likely to be wrong to avoid excessive errors. To deploy imperfect classifiers -- either due to intrinsic statistical noise of data or for robustness…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

Causal inference from observational data plays critical role in many applications in trustworthy machine learning. While sound and complete algorithms exist to compute causal effects, many of them assume access to conditional likelihoods,…

The cumulative distribution network (CDN) is a recently developed class of probabilistic graphical models (PGMs) permitting a copula factorization, in which the CDF, rather than the density, is factored. Despite there being much recent…

A protocol for distributed estimation of discrete distributions is proposed. Each agent begins with a single sample from the distribution, and the goal is to learn the empirical distribution of the samples. The protocol is based on a simple…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

In this work, a novel approach for the construction and training of time series models is presented that deals with the problem of learning on large time series with non-equispaced observations, which at the same time may possess features…

This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…