Related papers: Approximate Discrete Probability Distribution Repr…

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…

We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the…

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…

Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…

This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…

We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to…

When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…

Deep neural networks are highly effective at a range of computational tasks. However, they tend to be computationally expensive, especially in vision-related problems, and also have large memory requirements. One of the most effective…

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…

Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large…

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is…

We consider a minimax problem motivated by distributionally robust optimization (DRO) when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization…

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…

Stochastic and (distributionally) robust optimization problems often become computationally challenging as the number of scenarios or data points increases. Scenario reduction is therefore a key technique for improving tractability. We…

Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…