Related papers: Fluctuation-dissipation theorem and models of lear…
It is shown that the quantum fluctuation dissipation theorem can be considered as a mathematical formulation in the spectral representation of Onsager hypothesis on the regression of fluctuations in physical systems. It is shown that the…
In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective}…
We all are fascinated by the phenomena of intelligent behavior, as generated both by our own brains and by the brains of other animals. As physicists we would like to understand if there are some general principles that govern the structure…
Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for…
Uncertainty-aware machine learners, such as Bayesian neural networks, output a quantification of uncertainty instead of a point prediction. We provide uncertainty-aware learners with a principled framework to characterize, and identify ways…
Bayesian network structure learning algorithms with limited data are being used in domains such as systems biology and neuroscience to gain insight into the underlying processes that produce observed data. Learning reliable networks from…
Recent works have reported on the collective behavior of multiphase systems under fractional flow. Such behavior has been linked to pressure and/or flux fluctuations under stationary flow conditions that occur over a broad range of…
We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a…
In this chapter, we consider probabilistic drift-diffusion models and Bayesian inference frameworks to address this issue, assisting better social human decision-making. We provide details of the models, as well as representative numerical…
The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the…
In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e. the maximisation algorithms…
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…
This is a set of lecture notes of a course on statistical physics and thermodynamics, which is oriented, to a certain extent, towards electrical engineering students. The main body of the lectures is devoted to statistical physics, whereas…
Recent results on the stationary state Fluctuation Theorems for work and heat fluctuations of Langevin systems are presented. The relevance of finite time corrections in understanding experimental and simulation results is explained in the…
Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical…
Data is scaling exponentially in fields ranging from genomics to neuroscience to economics. A central question is: can modern machine learning methods be applied to construct predictive models of natural systems like cells and brains based…
We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…
The brain constantly turns large flows of sensory information into selective representations of the environment. It, therefore, needs to learn to process those sensory inputs that are most relevant for behaviour. It is not well understood…
Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic…
We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given…