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Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
We develop two Regression Monte Carlo algorithms (value and performance iteration) to solve general problems of optimal stochastic control of discrete-time Markov processes. We formulate our method within an innovative framework that allow…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in…
Modern computational advances have enabled easy parallel implementations of Markov chain Monte Carlo (MCMC). However, almost all work in estimating the variance of Monte Carlo averages, including the efficient batch means (BM) estimator,…
Multi-label classification is a type of supervised machine learning that can simultaneously assign multiple labels to an instance. To solve this task, some methods divide the original problem into several sub-problems (local approach),…
Dependency parsing research, which has made significant gains in recent years, typically focuses on improving the accuracy of single-tree predictions. However, ambiguity is inherent to natural language syntax, and communicating such…
Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…
Machine-learning classifiers provide high quality of service in classification tasks. Research now targets cost reduction measured in terms of average processing time or energy per solution. Revisiting the concept of cascaded classifiers,…
Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
The term ``sequential Monte Carlo methods'' or, equivalently, ``particle filters,'' refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (\pi_t). We…
We propose a new family of regression models for analyzing categorical responses, called multinomial link models. It consists of four classes, namely, mixed-link models that generalize existing multinomial logistic models and their…
Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC) and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on…
Understanding degradation is crucial for ensuring the longevity and performance of materials, systems, and organisms. To illustrate the similarities across applications, this article provides a review of data-based method in materials…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
This paper considers clustered multi-task compressive sensing, a hierarchical model that solves multiple compressive sensing tasks by finding clusters of tasks that leverage shared information to mutually improve signal reconstruction. The…
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…
The aim of this work is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods. Most of the mathematical results related to the convergence are not found in most of the…