Related papers: Neural Likelihoods via Cumulative Distribution Fun…

We derive a fully analytical, one-line closed-form expression for the cumulative distribution function (CDF) of the product of two correlated zero-mean normal random variables, avoiding any series representation. This result complements the…

Conditional Neural Processes~(CNPs) bridge neural networks with probabilistic inference to approximate functions of Stochastic Processes under meta-learning settings. Given a batch of non-{\it i.i.d} function instantiations, CNPs are…

The randomized distributed function computation (RDFC) framework, which unifies many cutting-edge distributed computation and learning applications, is considered. An autoencoder (AE) architecture is proposed to minimize the total variation…

Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted…

This paper proposes a deep convolutional neural network model for ordinal regression by considering a family of probabilistic ordinal link functions in the output layer. The link functions are those used for cumulative link models, which…

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…

This paper proposes a new method to combine several densities such that each density dominates a separate part of a joint distribution. The method is fully unsupervised, i.e. the parameters in the densities and the thresholds are…

A sum of lognormal random variables (RVs) appears in many problems of science and engineering. For example, it is invloved in computing the distribution of recevied signal and interference powers for radio channels subject to lognormal…

Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…

We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…

Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on…

We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum…

We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…

Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function…

Probabilistic load forecasting (PLF) is a key component in the extended tool-chain required for efficient management of smart energy grids. Neural networks are widely considered to achieve improved prediction performances, supporting highly…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

The process of aggregation is ubiquitous in almost all deep nets models. It functions as an important mechanism for consolidating deep features into a more compact representation, whilst increasing robustness to overfitting and providing…

The estimation of cumulative distribution functions (CDF) and probability density functions (PDF) is a fundamental practice in applied statistics. However, challenges often arise when dealing with data arranged in grouped intervals. In this…

In this paper, we illustrate a novel method for solving optimization problems when derivatives are not explicitly available. We show that combining implicit filtering (IF), an existing derivative free optimization (DFO) method, with a deep…

Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature.…