Related papers: A Unifying Formal Approach to Importance Values in…

This paper aims to explain deep neural networks (DNNs) from the perspective of multivariate interactions. In this paper, we define and quantify the significance of interactions among multiple input variables of the DNN. Input variables with…

The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown…

We introduce the prediction value (PV) as a measure of players' informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player $i$'s prediction…

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…

In this paper we consider the influences of variables on Boolean functions in general product spaces. Unlike the case of functions on the discrete cube where there is a clear definition of influence, in the general case at least three…

Feature attribution methods based on game theory are ubiquitous in the field of eXplainable Artificial Intelligence (XAI). Recent works proposed rigorous feature attribution using logic-based explanations, specifically targeting high-stakes…

Variable importance is central to scientific studies, including the social sciences and causal inference, healthcare, and other domains. However, current notions of variable importance are often tied to a specific predictive model. This is…

Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying…

Value-based methods play a fundamental role in Markov decision processes (MDPs) and reinforcement learning (RL). In this paper, we present a unified control-theoretic framework for analyzing valued-based methods such as value computation…

Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so…

Items in a test are often used as a basis for making decisions and such tests are therefore required to have good psychometric properties, like unidimensionality. In many cases the sum score is used in combination with a threshold to decide…

Traditional off-policy actor-critic Reinforcement Learning (RL) algorithms learn value functions of a single target policy. However, when value functions are updated to track the learned policy, they forget potentially useful information…

In this paper we investigate the problem of quantifying the contribution of each variable to the satisfying assignments of a Boolean function based on the Shapley value. Our main result is a polynomial-time equivalence between computing…

M\"obius inversion and Shapley values are two mathematical tools for characterizing and decomposing higher-order structure in complex systems. The former defines higher-order interactions as discrete derivatives over a partial order; the…

We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call case-factor diagrams (CFDs). CFDs…

We introduce a foundational sheaf theoretical scheme for the comprehension of quantum event structures, in terms of localization systems consisting of Boolean coordinatization coverings induced by measurement. The scheme is based on the…

Suppose that $n$ computer devices are to be connected to a network via inhomogeneous Bernoulli trials. The Shapley value of a device quantifies how much the network's value increases due to the participation of that device. Characteristic…

We aim to construct a class of learning algorithms that are of practical value to applied researchers in fields such as biostatistics, epidemiology and econometrics, where the need to learn from incompletely observed information is…

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification…