This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine learning$\unicode{x2014}$which includes black-box variational inference, adaptive MCMC, normalizing flow construction and transport-assisted MCMC, surrogate-likelihood MCMC, coreset construction for MCMC with big data, Markov chain gradient descent, Markovian score climbing, and more$\unicode{x2014}$within one common framework. By doing so, the theory and methods developed for each may be translated and generalized.

Model-based planners for partially observable problems must accommodate both model uncertainty during planning and goal uncertainty during objective inference. However, model-based planners may be brittle under these types of uncertainty because they rely on an exact model and tend to commit to a single optimal behavior. Inspired by results in the model-free setting, we propose an entropy-regularized model-based planner for partially observable problems. Entropy regularization promotes policy robustness for planning and objective inference by encouraging policies to be no more committed to a single action than necessary. We evaluate the robustness and objective inference performance of entropy-regularized policies in three problem domains. Our results show that entropy-regularized policies outperform non-entropy-regularized baselines in terms of higher expected returns under modeling errors and higher accuracy during objective inference.

Mussel farming is one of the most important aquaculture industries. The main risk to mussel farming is harmful algal blooms (HABs), which pose a risk to human consumption. In Galicia, the Spanish main producer of cultivated mussels, the opening and closing of the production areas is controlled by a monitoring program. In addition to the closures resulting from the presence of toxicity exceeding the legal threshold, in the absence of a confirmatory sampling and the existence of risk factors, precautionary closures may be applied. These decisions are made by experts without the support or formalisation of the experience on which they are based. Therefore, this work proposes a predictive model capable of supporting the application of precautionary closures. Achieving sensitivity, accuracy and kappa index values of 97.34%, 91.83% and 0.75 respectively, the kNN algorithm has provided the best results. This allows the creation of a system capable of helping in complex situations where forecast errors are more common.

A novel online clustering algorithm is presented where an Evolving Restricted Boltzmann Machine (ERBM) is embedded with a Kohonen Network called ERBM-KNet. The proposed ERBM-KNet efficiently handles streaming data in a single-pass mode using the ERBM, employing a bias-variance strategy for neuron growing and pruning, as well as online clustering based on a cluster update strategy for cluster prediction and cluster center update using KNet. Initially, ERBM evolves its architecture while processing unlabeled image data, effectively disentangling the data distribution in the latent space. Subsequently, the KNet utilizes the feature extracted from ERBM to predict the number of clusters and updates the cluster centers. By overcoming the common challenges associated with clustering algorithms, such as prior initialization of the number of clusters and subpar clustering accuracy, the proposed ERBM-KNet offers significant improvements. Extensive experimental evaluations on four benchmarks and one industry dataset demonstrate the superiority of ERBM-KNet compared to state-of-the-art approaches.

In this paper, we propose a new deinterleaving method for mixtures of discrete renewal Markov chains. This method relies on the maximization of a penalized likelihood score. It exploits all available information about both the sequence of the different symbols and their arrival times. A theoretical analysis is carried out to prove that minimizing this score allows to recover the true partition of symbols in the large sample limit, under mild conditions on the component processes. This theoretical analysis is then validated by experiments on synthetic data. Finally, the method is applied to deinterleave pulse trains received from different emitters in a RESM (Radar Electronic Support Measurements) context and we show that the proposed method competes favorably with state-of-the-art methods on simulated warfare datasets.

Inspired by Bayesian approaches to brain function in neuroscience, we give a simple theory of probabilistic inference for a unified account of reasoning and learning. We simply model how data cause symbolic knowledge in terms of its satisfiability in formal logic. The underlying idea is that reasoning is a process of deriving symbolic knowledge from data via abstraction, i.e., selective ignorance. The logical consequence relation is discussed for its proof-based theoretical correctness. The MNIST dataset is discussed for its experiment-based empirical correctness.

This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) to incorporate the case where each data point comprises the weighted sum of a known number of pure component signals, observed across several input locations. Our framework allows the use of a range of priors for the weights of each observation. This flexibility enables us to represent use cases including sum-to-one constraints for estimating fractional makeup, and binary weights for classification. Our contributions are particularly relevant to spectroscopy, where changing conditions may cause the underlying pure component signals to vary from sample to sample. To demonstrate the applicability to both spectroscopy and other domains, we consider several applications: a near-infrared spectroscopy data set with varying temperatures, a simulated data set for identifying flow configuration through a pipe, and a data set for determining the type of rock from its reflectance.

We study the Stochastic Shortest Path (SSP) problem with a linear mixture transition kernel, where an agent repeatedly interacts with a stochastic environment and seeks to reach certain goal state while minimizing the cumulative cost. Existing works often assume a strictly positive lower bound of the cost function or an upper bound of the expected length for the optimal policy. In this paper, we propose a new algorithm to eliminate these restrictive assumptions. Our algorithm is based on extended value iteration with a fine-grained variance-aware confidence set, where the variance is estimated recursively from high-order moments. Our algorithm achieves an $\tilde{\mathcal O}(dB_*\sqrt{K})$ regret bound, where $d$ is the dimension of the feature mapping in the linear transition kernel, $B_*$ is the upper bound of the total cumulative cost for the optimal policy, and $K$ is the number of episodes. Our regret upper bound matches the $\Omega(dB_*\sqrt{K})$ lower bound of linear mixture SSPs in Min et al. (2022), which suggests that our algorithm is nearly minimax optimal.

This study tackles the challenges of adversarial corruption in model-based reinforcement learning (RL), where the transition dynamics can be corrupted by an adversary. Existing studies on corruption-robust RL mostly focus on the setting of model-free RL, where robust least-square regression is often employed for value function estimation. However, these techniques cannot be directly applied to model-based RL. In this paper, we focus on model-based RL and take the maximum likelihood estimation (MLE) approach to learn transition model. Our work encompasses both online and offline settings. In the online setting, we introduce an algorithm called corruption-robust optimistic MLE (CR-OMLE), which leverages total-variation (TV)-based information ratios as uncertainty weights for MLE. We prove that CR-OMLE achieves a regret of $\tilde{\mathcal{O}}(\sqrt{T} + C)$, where $C$ denotes the cumulative corruption level after $T$ episodes. We also prove a lower bound to show that the additive dependence on $C$ is optimal. We extend our weighting technique to the offline setting, and propose an algorithm named corruption-robust pessimistic MLE (CR-PMLE). Under a uniform coverage condition, CR-PMLE exhibits suboptimality worsened by $\mathcal{O}(C/n)$, nearly matching the lower bound. To the best of our knowledge, this is the first work on corruption-robust model-based RL algorithms with provable guarantees.

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling intrinsically discrete data, such as language and graphs. This is achieved by formulating both the forward noising process and the corresponding reversed process as Continuous Time Markov Chains (CTMCs). In this paper, we investigate the theoretical properties of the discrete diffusion model. Specifically, we introduce an algorithm leveraging the uniformization of continuous Markov chains, implementing transitions on random time points. Under reasonable assumptions on the learning of the discrete score function, we derive Total Variation distance and KL divergence guarantees for sampling from any distribution on a hypercube. Our results align with state-of-the-art achievements for diffusion models in $\mathbb{R}^d$ and further underscore the advantages of discrete diffusion models in comparison to the $\mathbb{R}^d$ setting.