Related papers: Yet Another Analysis of Dice Problems
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Bayesian optimization (BO) is a popular, sample-efficient technique for expensive, black-box optimization. One such problem arising in manufacturing is that of maximizing the reliability, or equivalently minimizing the probability of a…
Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
We provide a decision theoretic analysis of bandit experiments under local asymptotics. Working within the framework of diffusion processes, we define suitable notions of asymptotic Bayes and minimax risk for these experiments. For normally…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
Policy inference plays an essential role in the contextual bandit problem. In this paper, we use empirical likelihood to develop a Bayesian inference method for the joint analysis of multiple contextual bandit policies in finite sample…
Mixture models are an expressive hypothesis class that can approximate a rich set of policies. However, using mixture policies in the Maximum Entropy (MaxEnt) framework is not straightforward. The entropy of a mixture model is not equal to…
For a wide range of entropy measures, easy calculation of equilibria is possible using a principle of Game Theoretical Equilibrium related to Jaynes Maximum Entropy Principle. This follows previous work of the author and relates to works of…
In this paper we present a data-driven approach for uncertainty propagation. In particular, we consider stochastic differential equations with parametric uncertainty. Solution of the differential equation is approximated using maximum…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
The computational costs of inference and planning have confined Bayesian model-based reinforcement learning to one of two dismal fates: powerful Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian non-parametric…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
Within a framework of utmost generality, we show that the entropy maximization procedure with linear constraints uniquely leads to the Shannon-Boltzmann-Gibbs entropy. Therefore, the use of this procedure with linear constraints should not…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0,1\}^n$, given sample access to $P$. We show that the sample complexity of the problem is…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…