Related papers: Statistical physics of independent component analy…
Using methods of statistical mechanics, we analyse the effect of outliers on the supervised learning of a classification problem. The learning strategy aims at selecting informative examples and discarding outliers. We compare two…
A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…
Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by…
We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Independent component analysis is intended to recover the mutually independent components from their linear mixtures. This technique has been widely used in many fields, such as data analysis, signal processing, and machine learning. To…
Friction is one of the fundamental issues in physics, mechanics and material science with lots of practical applications. However, the understanding of macroscopic friction phenomena from microscopic aspect is still on the way. In this…
Independent component analysis (ICA) is a fundamental data processing technique to decompose the captured signals into as independent as possible components. Computing the contrast function, which serves as a measure of independence of…
The method of statistical differentials, which approximates the mean and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be…
In recent years, there has been growing interest in jointly analyzing a foreground dataset, representing an experimental group, and a background dataset, representing a control group. The goal of such contrastive investigations is to…
Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to…
The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the…
Self-consistent phonon (SCP) theory and its application in computing thermodynamic properties of materials are reviewed from a historical perspective. Various more recent implementations based on first-principles electronic structure…
A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…