Related papers: Statistical physics of independent component analy…
Statistical modeling is often used to measure the strength of evidence for or against hypotheses on given data. We have previously proposed an information-dynamic framework in support of a properly calibrated measurement scale for…
Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very…
Two separate statistical tests are described and developed in order to test un-binned data sets for adherence to the power-law form. The first test employs the TP-statistic, a function defined to deviate from zero when the sample deviates…
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most of existing methods are based on the minimization of the function of…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
Measurement system analysis aims to quantify the variability in data attributable to the measurement system and evaluate its contribution to overall data variability. This paper conducts a rigorous theoretical investigation of the…
In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both…
The problem of statistical learning is to construct a predictor of a random variable $Y$ as a function of a related random variable $X$ on the basis of an i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable predictors…
Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…