Related papers: A compositional semantics for Repairable Fault Tre…
This paper introduces a novel supervised classification strategy that integrates functional data analysis (FDA) with tree-based methods, addressing the challenges of high-dimensional data and enhancing the classification performance of…
Recurrent Neural Networks (RNNs) have achieved tremendous success in processing sequential data, yet understanding and analyzing their behaviours remains a significant challenge. To this end, many efforts have been made to extract finite…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…
Factor analysis or sometimes referred to as variable analysis has been extensively used in classification problems for identifying specific factors that are significant to particular classes. This type of analysis has been widely used in…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
This paper integrates Fault Tree Analysis (FTA) and Bayesian Networks (BN) to assess collision risk and establish Automotive Safety Integrity Level (ASIL) B failure rate targets for critical autonomous vehicle (AV) components. The FTA-BN…
This paper offers a natural stochastic semantics of Networks of Priced Timed Automata (NPTA) based on races between components. The semantics provides the basis for satisfaction of probabilistic Weighted CTL properties (PWCTL),…
How to usefully encode compositional task structure has long been a core challenge in AI. Recent work in chain of thought prompting has shown that for very large neural language models (LMs), explicitly demonstrating the inferential steps…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
Foundation Models (FMs) have demonstrated unprecedented capabilities including zero-shot learning, high fidelity data synthesis, and out of domain generalization. However, as we show in this paper, FMs still have poor out-of-the-box…
In the maintenance of complex systems, fault trees are used to locate problems and provide targeted solutions. To enable fault trees stored as images to be directly processed by large language models, which can assist in tracking and…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
The goal of automatic resource bound analysis is to statically infer symbolic bounds on the resource consumption of the evaluation of a program. A longstanding challenge for automatic resource analysis is the inference of bounds that are…
Search trees are fundamental data structures in computer science. We study functionals on random search trees that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal…
Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved…
We present an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata (DFTAs). Unlike string automata, tree automata operate over hierarchical structures, posing unique challenges for…
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is…
In today's industrial practice, safety, reliability or availability artifacts such as fault trees, Markov models or FMEAs are mainly created manually by experts, often distinctively decoupled from systems engineering activities. Significant…
Cognitive computation such as e.g. language processing, is conventionally regarded as Turing computation, and Turing machines can be uniquely implemented as nonlinear dynamical systems using generalized shifts and subsequent G\"odel…