Related papers: On the Universality of the Logistic Loss Function
We study the gradient flow for a relaxed approximation to the Kullback-Leibler (KL) divergence between a moving source and a fixed target distribution. This approximation, termed the KALE (KL approximate lower-bound estimator), solves a…
Causal machine-learning is about predicting the net-effect (true-lift) of treatments. Given the data of a treatment group and a control group, it is similar to a standard supervised-learning problem. Unfortunately, there is no similarly…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
In statistical classification and machine learning, classification error is an important performance measure, which is minimized by the Bayes decision rule. In practice, the unknown true distribution is usually replaced with a model…
Kullback-Leibler (KL) control enables efficient numerical methods for nonlinear optimal control problems. The crucial assumption of KL control is the full controllability of the transition distribution. However, this assumption is often…
Data processing inequalities for $f$-divergences can be sharpened using constants called "contraction coefficients" to produce strong data processing inequalities. For any discrete source-channel pair, the contraction coefficients for…
Huber loss, its asymmetric variants and their associated functionals (here named Huber functionals) are studied in the context of point forecasting and forecast evaluation. The Huber functional of a distribution is the set of minimizers of…
Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with…
Loss functions are error metrics that quantify the difference between a prediction and its corresponding ground truth. Fundamentally, they define a functional landscape for traversal by gradient descent. Although numerous loss functions…
Generating a Boltzmann distribution in high dimension has recently been achieved with Normalizing Flows, which enable fast and exact computation of the generated density, and thus unbiased estimation of expectations. However, current…
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…
Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…
Motivated by the computation of the non-parametric maximum likelihood estimator (NPMLE) and the Bayesian posterior in statistics, this paper explores the problem of convex optimization over the space of all probability distributions. We…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper…
Consider the supervised learning setting where the goal is to learn to predict labels $\mathbf y$ given points $\mathbf x$ from a distribution. An \textit{omnipredictor} for a class $\mathcal L$ of loss functions and a class $\mathcal C$ of…
The use of deep neural networks in real-world applications require well-calibrated networks with confidence scores that accurately reflect the actual probability. However, it has been found that these networks often provide over-confident…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different probability distributions. In this work, we give an information-theoretic analysis of the…
The problem of estimating the Kullback-Leibler divergence $D(P\|Q)$ between two unknown distributions $P$ and $Q$ is studied, under the assumption that the alphabet size $k$ of the distributions can scale to infinity. The estimation is…
Kullback-Leibler (KL) divergence is one of the most important divergence measures between probability distributions. In this paper, we prove several properties of KL divergence between multivariate Gaussian distributions. First, for any two…