Related papers: Influence and interaction indexes for pseudo-Boole…
The current state-of-the-art Scrabble agents are not learning-based but depend on truncated Monte Carlo simulations and the quality of such agents is contingent upon the time available for running the simulations. This thesis takes steps…
A statistical, data-driven method is presented that quantifies influences between variables of a dynamical system. The method is based on finding a suitable representation of points by fuzzy affiliations with respect to landmark points…
Within the domain of game theory, power indexes are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal [D. Felsenthal. A Well-Behaved Index of a Priori P-Power for…
Recent work has shown that it is possible to circumvent the calculation of the spectral density and directly calculate the coefficients of the discretized influence functionals using data from classical trajectory simulations. However, the…
Effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size. Existing effect size indices are developed for particular parametric models or…
Treatment effect heterogeneity with respect to covariates is common in instrumental variable (IV) analyses. An intuitive approach, which we call the interacted two-stage least squares (2sls), is to postulate a working linear model of the…
The goal of this paper is to critically evaluate a heuristic algorithm for the Inverse Banzhaf Index problem by Laruelle and Widgr\'en. Few qualitative results are known about the approximation quality of the heuristics for this problem.…
Decisions in a shareholder meeting or a legislative committee are often modeled as a weighted game. Influence of a member is then measured by a power index. A large variety of different indices has been introduced in the literature. This…
We study causal effect estimation from observational data under interference. The interference pattern is captured by an observed network. We adopt the chain graph framework of Tchetgen Tchetgen et. al. (2021), which allows (i) interaction…
In this paper we derive tight bounds on the expected value of products of {\em low influence} functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated…
Influence functions approximate the "influences" of training data-points for test predictions and have a wide variety of applications. Despite the popularity, their computational cost does not scale well with model and training data size.…
In the last few years, many works have tried to explain the predictions of deep learning models. Few methods, however, have been proposed to verify the accuracy or faithfulness of these explanations. Recently, influence functions, which is…
Composite indicators aggregate a set of variables using weights which are understood to reflect the variables' importance in the index. In this paper we propose to measure the importance of a given variable within existing composite…
A dataset has been classified by some unknown classifier into two types of points. What were the most important factors in determining the classification outcome? In this work, we employ an axiomatic approach in order to uniquely…
This series of papers has two broader aims: 1) Construct a theory for multi-partite open quantum systems comprising several layers of structure with self-consistent back-actions. Develop the graded influence action formalism…
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…
A symmetric pseudo-Boolean function is a map from Boolean tuples to real numbers which is invariant under input variable interchange. We prove that any such function can be equivalently expressed as a power series or factorized. The kernel…
Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights,…
Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of the different agents for that function. This generalizes…
The entropy/influence conjecture, raised by Friedgut and Kalai in 1996, seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is…