Related papers: Measuring Approximate Functional Dependencies: a C…
Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…
It is shown that the DFT exchange and correlation functionals satisfy an expression that couples exchange and correlation functionals and functional derivatives evaluated at three different densities and for two particle numbers. This…
Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. We…
Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the…
Interpretation methods to reveal the internal reasoning processes behind machine learning models have attracted increasing attention in recent years. To quantify the extent to which the identified interpretations truly reflect the intrinsic…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
Approximate linear programs (ALPs) are well-known models based on value function approximations (VFAs) to obtain policies and lower bounds on the optimal policy cost of discounted-cost Markov decision processes (MDPs). Formulating an ALP…
The frequency response function (FRF) is an established way to describe the outcome of experiments in posture control literature. The FRF is an empirical transfer function between an input stimulus and the induced body segment sway profile,…
Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for…
Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…
Measuring similarity of neural networks to understand and improve their behavior has become an issue of great importance and research interest. In this survey, we provide a comprehensive overview of two complementary perspectives of…
Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…
In case of incomplete database tables, a possible world is obtained by replacing any missing value by a value from the corresponding attribute's domain that can be infinite. A possible key or possible functional dependency constraint is…
The median absolute deviation (MAD) is a robust measure of scale that is simple to implement and easy to interpret. Motivated by this, we introduce interval estimators of the MAD to make reliable inferences for dispersion for a single…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
Deep neural networks have frequently been used to directly learn representations useful for a given task from raw input data. In terms of overall performance metrics, machine learning solutions employing deep representations frequently have…
We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…
New energy-density functionals (EDFs) inspired by effective-field theories (EFTs) have been recently proposed. The present work focuses on three of such functionals which were developed to produce satisfactory equations of state for nuclear…
Unlike covalent two-dimensional (2D) materials like graphene, 2D metals have non-layered structures due to their non-directional, metallic bonding. While experiments on 2D metals are still scarce and challenging, density-functional theory…