Related papers: Statistical Mechanics of Learning: A Variational A…

We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…

We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the…

Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…

Spurious association between X and Y may be due to a confounding variable W. Statisticians may adjust for W using a variety of techniques. This paper presents the results of simulations conducted to assess the performance of those…

Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…

Inverse reinforcement learning methods aim to retrieve the reward function of a Markov decision process based on a dataset of expert demonstrations. The commonplace scarcity and heterogeneous sources of such demonstrations can lead to the…

Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In…

These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.

Building invariance to non-meaningful transformations is essential to building efficient and generalizable machine learning models. In practice, the most common way to learn invariance is through data augmentation. There has been recent…

This document introduces basics in data preparation, feature selection and learning basics for high energy physics tasks. The emphasis is on feature selection by principal component analysis, information gain and significance measures for…

Traditional statistical estimation, or statistical inference in general, is static, in the sense that the estimate of the quantity of interest does not change the future evolution of the quantity. In some sequential estimation problems…

We present a variational method for online state estimation and parameter learning in state-space models (SSMs), a ubiquitous class of latent variable models for sequential data. As per standard batch variational techniques, we use…

Recently, variational quantum metrology was proposed for Hamiltonians with multiplicative parameters, wherein the estimation precision can be optimized via variational circuits. However, systems with generic Hamiltonians still lack these…

We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

We describe the application of tools from statistical mechanics to analyse the dynamics of various classes of supervised learning rules in perceptrons. The character of this paper is mostly that of a cross between a biased non-encyclopedic…

Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…

This paper extends the application of the stochastic variational method to noncentral interactions. Several examples are presented for three- and four-nucleon systems with realistic nuclear forces. The correlated Gaussians easily cope with…

Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…