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Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
Statistical models for networks with complex dependencies pose particular challenges for model selection and evaluation. In particular, many well-established statistical tools for selecting between models assume conditional independence of…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…
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…
Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…
We propose a nonparametric procedure to achieve fast inference in generative graphical models when the number of latent states is very large. The approach is based on iterative latent variable preselection, where we alternate between…
Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…
We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by…
This paper is concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider $M= \frac{1}{m} YY^*$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with…
Learning the distribution of a continuous or categorical response variable $\boldsymbol y$ given its covariates $\boldsymbol x$ is a fundamental problem in statistics and machine learning. Deep neural network-based supervised learning…
This paper explores the extension of the classical two-parameter Weibull distribution to a four-parameter Harris extended Weibull (HEW) distribution. The flexibility of this probability distribution is illustrated by the varying shapes of…
Distributional regression aims to estimate the full conditional distribution of a target variable, given covariates. Popular methods include linear and tree-ensemble based quantile regression. We propose a neural network-based…
To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…