Related papers: A Unifying Formal Approach to Importance Values in…
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified…
Influence diagrams have recently been used to analyse the safety and fairness properties of AI systems. A key building block for this analysis is a graphical criterion for value of information (VoI). This paper establishes the first…
The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional…
This paper illustrates the central role of loss functions in data-driven decision making, providing a comprehensive survey on their influence in cost-sensitive classification (CSC) and reinforcement learning (RL). We demonstrate how…
This paper develops computable metrics to assign priorities for information collection on network systems made up by binary components. Components are worth inspecting because their condition state is uncertain and the system functioning…
This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the…
The theory of influences in product measures has profound applications in theoretical computer science, combinatorics, and discrete probability. This deep theory is intimately connected to functional inequalities and to the Fourier analysis…
The enormous growth of the complexity of modern computer systems leads to an increasing demand for techniques that support the comprehensibility of systems. This has motivated the very active research field of formal methods that enhance…
We derive qualitative relationships about the informational relevance of variables in graphical decision models based on a consideration of the topology of the models. Specifically, we identify dominance relations for the expected value of…
In recent years, the black-box nature of deep learning models has limited their application in high-stakes domains such as medical diagnosis and finance, where interpretability is essential. To address this, we propose a novel approach…
This paper studies a difference between Binary Decision Diagrams (BDDs) and Zero-suppressed BDDs (ZDDs) from a conceptual point of view. It is commonly understood that a BDD is a representation of a Boolean function, whereas a ZDD is a…
We investigate the influences of variables on a Boolean function $f$ based on the quantum Bernstein-Vazirani algorithm. A previous paper (Floess et al. in Math. Struct. in Comp. Science 23: 386, 2013) has proved that if a $n$-variable…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
This paper deals with an important subject in classification problems addressed by machine learning techniques: the evaluation of the influence of each of the features on the classification of individuals. Specifically, a measure of that…
Recent work has shown that the input-output behavior of some machine learning systems can be captured symbolically using Boolean expressions or tractable Boolean circuits, which facilitates reasoning about the behavior of these systems.…
The influence of a variable is an important concept in the analysis of Boolean functions. The more general notion of influence of a set of variables on a Boolean function has four separate definitions in the literature. In the present work,…
Ordered binary decision diagrams (OBDDs) are a fundamental data structure for the manipulation of Boolean functions, with strong applications to finite-state symbolic model checking. OBDDs allow for efficient algorithms using top-down…
We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…
Concept Bottleneck Models (CBMs) first map raw input(s) to a vector of human-defined concepts, before using this vector to predict a final classification. We might therefore expect CBMs capable of predicting concepts based on distinct…
Decision Diagrams(DDs) are one of the most popular representations for boolean functions. They are widely used in the design and verification of circuits. Different types of DDs have been proven to represent important functions in…