Related papers: Solving Marginal MAP Exactly by Probabilistic Circ…
Probabilistic circuits (PCs) offer a promising avenue to perform embedded reasoning under uncertainty. They support efficient and exact computation of various probabilistic inference tasks by design. Hence, hardware-efficient computation of…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…
This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum…
Probabilistic circuits (PCs) are a prominent representation of probability distributions with tractable inference. While parameter learning in PCs is rigorously studied, structure learning is often more based on heuristics than on…
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…
In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete…
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…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
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…
Finding Minimal Unsatisfiable Subsets (MUSes) of binary constraints is a common problem in infeasibility analysis of over-constrained systems. However, because of the exponential search space of the problem, enumerating MUSes is extremely…
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…
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,…
This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…
Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we…