Related papers: On approximating the $f$-divergence between two Is…
We study the convergence rate of stochastic optimization of exact (NP-hard) objectives, for which only biased estimates of the gradient are available. We motivate this problem in the context of learning the structure and parameters of Ising…
A time series is a sequence of data items; typical examples are videos, stock ticker data, or streams of temperature measurements. Quite some research has been devoted to comparing and indexing simple time series, i.e., time series where…
The study of mixture models constitutes a large domain of research in statistics. In the first part of this work, we present phi-divergences and the existing methods which produce robust estimators. We are more particularly interested in…
It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between…
Fairness-aware learning is a novel framework for classification tasks. Like regular empirical risk minimization (ERM), it aims to learn a classifier with a low error rate, and at the same time, for the predictions of the classifier to be…
This paper introduces the $f$-EI$(\phi)$ algorithm, a novel iterative algorithm which operates on measures and performs $f$-divergence minimisation in a Bayesian framework. We prove that for a rich family of values of $(f,\phi)$ this…
In this technical report we describe some properties of f-divergences and f-GAN training. We present an elementary derivation of the f-divergence lower bounds which form the basis of f-GAN training. We derive informative but perhaps…
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
We study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate. The prediction task considered in this paper is that of predicting the values of a subset of variables…
We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $\mu$.…
The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a feasible point does not exist. However,…
Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…
We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL…
The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate…
Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne a well posed problem when applied to the model; secondly the…
In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key…
A function $f : \mathbb{F}_2^n \to \mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $\mathbb{F}_2^n$, we study efficient algorithms for the…
Providing various machine learning (ML) applications in the real world, concerns about discrimination hidden in ML models are growing, particularly in high-stakes domains. Existing techniques for assessing the discrimination level of ML…