Related papers: Generalized Prediction Intervals for Arbitrary Dis…
We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…
In recent years the ultrahigh dimensional linear regression problem has attracted enormous attentions from the research community. Under the sparsity assumption most of the published work is devoted to the selection and estimation of the…
A class of discrete probability distributions contains distributions with limited support, i.e. possible argument values are limited to a set of numbers (typically consecutive). Examples of such data are results from subjective experiments…
There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
Conformal prediction, and split conformal prediction as a specific implementation, offer a distribution-free approach to estimating prediction intervals with statistical guarantees. Recent work has shown that split conformal prediction can…
Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the distribution or uncertainty of the response variable, traditional methods either assume that the posterior distribution of samples…
By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…
Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
Traditional neural network regression models provide only point estimates, failing to capture predictive uncertainty. Probabilistic neural networks (PNNs) address this limitation by producing output distributions, enabling the construction…