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Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose…
Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions.…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
Zhang et al. (ICML 2021, PLMR 139, pp. 12447-1245) introduced probabilistic generating circuits (PGCs) as a probabilistic model to unify probabilistic circuits (PCs) and determinantal point processes (DPPs). At a first glance, PGCs store a…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
In many real-world scenarios, it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data. Probabilistic circuits (PCs), a prominent family of tractable probabilistic models,…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of…
Deep generative models (DGMs) have recently demonstrated remarkable success in capturing complex probability distributions over graphs. Although their excellent performance is attributed to powerful and scalable deep neural networks, it is,…
A fundamental challenge in probabilistic modeling is to balance expressivity and inference efficiency. Tractable probabilistic models (TPMs) aim to directly address this tradeoff by imposing constraints that guarantee efficient inference of…
We present a comprehensive survey of the advancements and techniques in the field of tractable probabilistic generative modeling, primarily focusing on Probabilistic Circuits (PCs). We provide a unified perspective on the inherent…
The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
Designing expressive generative models that support exact and efficient inference is a core question in probabilistic ML. Probabilistic circuits (PCs) offer a framework where this tractability-vs-expressiveness trade-off can be analyzed…
Probabilistic circuits (PCs) are a family of generative models which allows for the computation of exact likelihoods and marginals of its probability distributions. PCs are both expressive and tractable, and serve as popular choices for…
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…
Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…