Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to approximate posterior distributions. When we obtain samples from a posterior distribution, Hamiltonian Monte Carlo (HMC) has been widely used for the continuous variable part and Markov chain Monte Carlo (MCMC) for the discrete variable part. Another sampling method, the bouncy particle sampler (BPS), has been proposed, which combines uniform linear motion and stochastic reflection to perform sampling. BPS was reported to have the advantage of being easier to set simulation parameters than HMC. To accelerate the convergence to a posterior distribution, we introduced parallel tempering (PT) to BPS, and then proposed an algorithm when the inverse temperature exchange rate is set to infinity. We performed numerical simulations and demonstrated its effectiveness for multimodal distribution.

Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic differential equations in the probability literature, we propose and study regime-switching Langevin dynamics (RS-LD) and regime-switching kinetic Langevin dynamics (RS-KLD). Based on their discretizations, we introduce regime-switching Langevin Monte Carlo (RS-LMC) and regime-switching kinetic Langevin Monte Carlo (RS-KLMC) algorithms, which can also be viewed as LMC and KLMC algorithms with random stepsizes. We also propose frictional-regime-switching kinetic Langevin dynamics (FRS-KLD) and its associated algorithm frictional-regime-switching kinetic Langevin Monte Carlo (FRS-KLMC), which can also be viewed as the KLMC algorithm with random frictional coefficients. We provide their 2-Wasserstein non-asymptotic convergence guarantees to the target distribution, and analyze the iteration complexities. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of our proposed algorithms.

This work proposes and studies the distributed resource allocation problem in asynchronous and stochastic settings. We consider a distributed system with multiple workers and a coordinating server with heterogeneous computation and communication times. We explore an approximate stochastic primal-dual approach with the aim of 1) adhering to the resource budget constraints, 2) allowing for the asynchronicity between the workers and the server, and 3) relying on the locally available stochastic gradients. We analyze our Asynchronous stochastic Primal-Dual (Asyn-PD) algorithm and prove its convergence in the second moment to the saddle point solution of the approximate problem at the rate of $O(1/t)$, where $t$ is the iteration number. Furthermore, we verify our algorithm numerically to validate the analytically derived convergence results, and demonstrate the advantages of utilizing our asynchronous algorithm rather than deploying a synchronous algorithm where the server must wait until it gets update from all workers.

We study the problem of learning the optimal control policy for fine-tuning a given diffusion process, using general value function approximation. We develop a new class of algorithms by solving a variational inequality problem based on the Hamilton-Jacobi-Bellman (HJB) equations. We prove sharp statistical rates for the learned value function and control policy, depending on the complexity and approximation errors of the function class. In contrast to generic reinforcement learning problems, our approach shows that fine-tuning can be achieved via supervised regression, with faster statistical rate guarantees.

Scientists are often interested in estimating an association between a covariate and a binary- or count-valued response. For instance, public health officials are interested in how much disease presence (a binary response per individual) varies as temperature or pollution (covariates) increases. Many existing methods can be used to estimate associations, and corresponding uncertainty intervals, but make unrealistic assumptions in the spatial domain. For instance, they incorrectly assume models are well-specified. Or they assume the training and target locations are i.i.d. -- whereas in practice, these locations are often not even randomly sampled. Some recent work avoids these assumptions but works only for continuous responses with spatially constant noise. In the present work, we provide the first confidence intervals with guaranteed asymptotic nominal coverage for spatial associations given discrete responses, even under simultaneous model misspecification and nonrandom sampling of spatial locations. To do so, we demonstrate how to handle spatially varying noise, provide a novel proof of consistency for our proposed estimator, and use a delta method argument with a Lyapunov central limit theorem. We show empirically that standard approaches can produce unreliable confidence intervals and can even get the sign of an association wrong, while our method reliably provides correct coverage.

In federated learning, communication cost can be significantly reduced by transmitting the information over the air through physical channels. In this paper, we propose a new class of adaptive federated stochastic gradient descent (SGD) algorithms that can be implemented over physical channels, taking into account both channel noise and hardware constraints. We establish theoretical guarantees for the proposed algorithms, demonstrating convergence rates that are adaptive to the stochastic gradient noise level. We also demonstrate the practical effectiveness of our algorithms through simulation studies with deep learning models.

The success of Federated Learning depends on the actions that participants take out of sight. We model Federated Learning not as a mere optimization task but as a strategic system entangled with rules and incentives. From this perspective, we present an analytical framework that makes it possible to clearly identify where behaviors that genuinely improve performance diverge from those that merely target metrics. We introduce two indices that respectively quantify behavioral incentives and collective performance loss, and we use them as the basis for consistently interpreting the impact of operational choices such as rule design, the level of information disclosure, evaluation methods, and aggregator switching. We further summarize thresholds, auto-switch rules, and early warning signals into a checklist that can be applied directly in practice, and we provide both a practical algorithm for allocating limited audit resources and a performance guarantee. Simulations conducted across diverse environments consistently validate the patterns predicted by our framework, and we release all procedures for full reproducibility. While our approach operates most strongly under several assumptions, combining periodic recalibration, randomization, and connectivity-based alarms enables robust application under the variability of real-world operations. We present both design principles and operational guidelines that lower the incentives for metric gaming while sustaining and expanding stable cooperation.

Legal documents pose unique challenges for text classification due to their domain-specific language and often limited labeled data. This paper proposes a hybrid approach for classifying legal texts by combining unsupervised topic and graph embeddings with a supervised model. We employ Top2Vec to learn semantic document embeddings and automatically discover latent topics, and Node2Vec to capture structural relationships via a bipartite graph of legal documents. The embeddings are combined and clustered using KMeans, yielding coherent groupings of documents. Our computations on a legal document dataset demonstrate that the combined Top2Vec+Node2Vec approach improves clustering quality over text-only or graph-only embeddings. We conduct a sensitivity analysis of hyperparameters, such as the number of clusters and the dimensionality of the embeddings, and demonstrate that our method achieves competitive performance against baseline Latent Dirichlet Allocation (LDA) and Non-Negative Matrix Factorization (NMF) models. Key findings indicate that while the pipeline presents an innovative approach to unsupervised legal document analysis by combining semantic topic modeling with graph embedding techniques, its efficacy is contingent upon the quality of initial topic generation and the representational power of the chosen embedding models for specialized legal language. Strategic recommendations include the exploration of domain-specific embeddings, more comprehensive hyperparameter tuning for Node2Vec, dynamic determination of cluster numbers, and robust human-in-the-loop validation processes to enhance legal relevance and trustworthiness. The pipeline demonstrates potential for exploratory legal data analysis and as a precursor to supervised learning tasks but requires further refinement and domain-specific adaptation for practical legal applications.

Bayesian Additive Regression Trees (BART) of Chipman et al. (2010) has proven to be a powerful tool for nonparametric modeling and prediction. Monotone BART (Chipman et al., 2022) is a recent development that allows BART to be more precise in estimating monotonic functions. We further these developments by proposing probit monotone BART, which allows the monotone BART framework to estimate conditional mean functions when the outcome variable is binary.

Actuarial ratemaking depends on high-quality data, yet access to such data is often limited by the cost of obtaining new data, privacy concerns, etc. In this paper, we explore synthetic-data generation as a potential solution to these issues. In addition to discussing generative methods previously studied in the actuarial literature, we introduce to the insurance community another approach based on Multiple Imputation by Chained Equations (MICE). We present a comparative study using an open-source dataset and evaluating MICE-based models against other generative models like Variational Autoencoders and Conditional Tabular Generative Adversarial Networks. We assess how well synthetic data preserves the original marginal distributions of variables as well as the multivariate relationships among covariates. We also investigate the consistency between Generalized Linear Models (GLMs) trained on synthetic data with GLMs trained on the original data. Furthermore, we assess the ease of use of each generative approach and study the impact of augmenting original data with synthetic data on the performance of GLMs for predicting claim counts. Our results highlight the potential of MICE-based methods in creating high-quality tabular data while being more user-friendly than the other methods.