Related papers: On Relaxing Determinism in Arithmetic Circuits

Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function.…

In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are usually solved in each iteration. This is true both for Active Set (AS) methods as well as for Interior Point (IP) methods, and for…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

The Abstraction and Reasoning Corpus (ARC) provides a compact laboratory for studying abstract reasoning, an ability central to human intelligence. Modern AI systems, including LLMs and ViTs, largely operate as sequence-of-behavior…

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,…

Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…

In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional…

Probabilistic circuits (PCs) have emerged as a powerful framework to compactly represent probability distributions for efficient and exact probabilistic inference. It has been shown that PCs with a general directed acyclic graph (DAG)…

In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…

Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and artificial intelligence. Forbidding patterns (generic sub-instances) provides a means of defining…

Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…

In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…

Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not…

With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

Performance measurement is an essential task once a statistical model is created. The Area Under the receiving operating characteristics Curve (AUC) is the most popular measure for evaluating the quality of a binary classifier. In this…

With the increased use of machine learning systems for decision making, questions about the fairness properties of such systems start to take center stage. Most existing work on algorithmic fairness assume complete observation of features…

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…

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…

We initiate the study of counting Markov Equivalence Classes (MEC) under logical constraints. MECs are equivalence classes of Directed Acyclic Graphs (DAGs) that encode the same conditional independence structure among the random variables…