Related papers: Influence and interaction indexes for pseudo-Boole…

In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust…

Influence functions offer a principled way to trace model predictions back to training data, but their use in deep learning is hampered by the need to invert a large, ill-conditioned Hessian matrix. Approximations such as Generalised…

Data cohesion, a recently introduced measure inspired by social interactions, uses distance comparisons to assess relative proximity. In this work, we provide a collection of results which can guide the development of cohesion-based methods…

Empowerment quantifies the influence an agent has on its environment. This is formally achieved by the maximum of the expected KL-divergence between the distribution of the successor state conditioned on a specific action and a distribution…

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove new bounds on the number of relevant variables for boolean functions in terms of a variety of complexity measures. Our approach unifies and refines…

The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…

The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…

We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…

We develop a new technique for proving concentration inequalities which relate between the variance and influences of Boolean functions. Using this technique, we 1. Settle a conjecture of Talagrand [Tal97] proving that $$\int_{\left\{…

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…

Influence functions provide a principled method to assess the contribution of individual training samples to a specific target. Yet, their high computational costs limit their applications on large-scale models and datasets. Existing…

Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the…

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of…

One of the most pressing issues in AI in recent years has been the need to address the lack of explainability of many of its models. We focus on explanations for discrete Bayesian network classifiers (BCs), targeting greater transparency of…

Recently, influence functions present an apparatus for achieving explainability for deep neural models by quantifying the perturbation of individual train instances that might impact a test prediction. Our objectives in this paper are…

We introduce the Banach-Butterfly Invariant (BBT), an influence-adaptive Banach geometry on the Walsh-Hadamard butterfly factorization. For a Boolean function $f:\{-1,+1\}^n\to\{-1,+1\}$ with coordinate influences $\mathrm{Inf}_\ell(f)$,…

This manuscript includes some classical results we select apart from the new results we've found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of this work so that…

Many reinforcement learning (RL) environments consist of independent entities that interact sparsely. In such environments, RL agents have only limited influence over other entities in any particular situation. Our idea in this work is that…