Related papers: Fluctuation-dissipation theorem and models of lear…
A central question in computational neuroscience is how structure determines function in neural networks. The emerging high-quality large-scale connectomic datasets raise the question of what general functional principles can be gleaned…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady-states and obeying markovian dynamics. We discuss the interpretation of this result in terms of…
We derive detailed and integral quantum fluctuation theorems for heat exchange in a quantum correlated bipartite thermal system using the framework of dynamic Bayesian networks. Contrary to the usual two-projective-measurement scheme that…
The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium…
Bayesian interpretations of neural network have a long history, dating back to early work in the 1990's and have recently regained attention because of their desirable properties like uncertainty estimation, model robustness and…
This work studies the distributed learning process on a network of agents. Agents make partial observation about an unknown hypothesis and iteratively share their beliefs over a set of possible hypotheses with their neighbors to learn the…
There is a mismatch between the standard theoretical analyses of statistical machine learning and how learning is used in practice. The foundational assumption supporting the theory is that we can represent features and models using…
In this paper we re-examine the traditional problem of connecting the internal fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also nonlinear processes. With…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
his article extends the fluctuation-dissipation analysis to generic complex fluids in confined geometries and to all the cases the hydromechanic fluid-interaction kernels may depend on the particle position. This represents a completely new…
In the first part of these short lecture notes, we will present an introduction on (auto-)correlation functions and linear-response functions in the language of a physicist. In particular, the fluctuation-dissipation theorem in classical…
Bayesian adaptive experimental design is a form of active learning, which chooses samples to maximize the information they give about uncertain parameters. Prior work has shown that other forms of active learning can suffer from active…
The classical theory of Brownian motion rests on fundamental laws of statistical mechanics, such as the equipartition theorem and the fluctuation-dissipation theorem, which are not applicable in non-isothermal situations. We derive the…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
Fluctuations in the statistical model of heavy ion collisions are studied. The role of statistics, relativity, constraints, decaying resonances and branching processes are investigated using this model. Also studied are thermodynamic…
The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard…
The main goal of statistical learning theory is to provide a fundamental framework for the problem of decision making and model construction based on sets of data. Here, we present a brief introduction to the fundamentals of statistical…
Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that…
We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of…