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Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
Factor analysis (FA) is a statistical tool for studying how observed variables with some mutual dependences can be expressed as functions of mutually independent unobserved factors, and it is widely applied throughout the psychological,…
The black box problem in machine learning has led to the introduction of an ever-increasing set of explanation methods for complex models. These explanations have different properties, which in turn has led to the problem of method…
Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata…
This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to…
An interpretable model or method has several appealing features, such as reliability to adversarial examples, transparency of decision-making, and communication facilitator. However, interpretability is a subjective concept, and even its…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
Forest automata (FA) have recently been proposed as a tool for shape analysis of complex heap structures. FA encode sets of tree decompositions of heap graphs in the form of tuples of tree automata. In order to allow for representing…
Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis.…
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
Interpretability allows the domain-expert to directly evaluate the model's relevance and reliability, a practice that offers assurance and builds trust. In the healthcare setting, interpretable models should implicate relevant biological…
Denoising diffusion models enable conditional generation and density modeling of complex relationships like images and text. However, the nature of the learned relationships is opaque making it difficult to understand precisely what…
While deep neural networks (DNN) have become an effective computational tool, the prediction results are often criticized by the lack of interpretability, which is essential in many real-world applications such as health informatics.…
Hierarchical feature learning based on convolutional neural networks (CNN) has recently shown significant potential in various computer vision tasks. While allowing high-quality discriminative feature learning, the downside of CNNs is the…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is…
Formal Concept Analysis (FCA) is a mathematical theory based on the formalization of the notions of concept and concept hierarchies. It has been successfully applied to several Computer Science fields such as data mining,software…