Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the high computational complexity of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose the Bayesian Optimization by Kernel regression and density-based Exploration (BOKE) algorithm. BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and the improved kernel regression upper confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE and ensures its robustness. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.

Reverberant speech, denoting the speech signal degraded by the process of reverberation, contains crucial knowledge of both anechoic source speech and room impulse response (RIR). This work proposes a variational Bayesian inference (VBI) framework with neural speech prior (VINP) for joint speech dereverberation and blind RIR identification. In VINP, a probabilistic signal model is constructed in the time-frequency (T-F) domain based on convolution transfer function (CTF) approximation. For the first time, we propose using an arbitrary discriminative dereverberation deep neural network (DNN) to predict the prior distribution of anechoic speech within a probabilistic model. By integrating both reverberant speech and the anechoic speech prior, VINP yields the maximum a posteriori (MAP) and maximum likelihood (ML) estimations of the anechoic speech spectrum and CTF filter, respectively. After simple transformations, the waveforms of anechoic speech and RIR are estimated. Moreover, VINP is effective for automatic speech recognition (ASR) systems, which sets it apart from most deep learning (DL)-based single-channel dereverberation approaches. Experiments on single-channel speech dereverberation demonstrate that VINP reaches an advanced level in most metrics related to human perception and displays unquestionable state-of-the-art (SOTA) performance in ASR-related metrics. For blind RIR identification, experiments indicate that VINP attains the SOTA level in blind estimation of reverberation time at 60 dB (RT60) and direct-to-reverberation ratio (DRR). Codes and audio samples are available online.

Model-based offline reinforcement learning (MORL) aims to learn a policy by exploiting a dynamics model derived from an existing dataset. Applying conservative quantification to the dynamics model, most existing works on MORL generate trajectories that approximate the real data distribution to facilitate policy learning by using current information (e.g., the state and action at time step $t$). However, these works neglect the impact of historical information on environmental dynamics, leading to the generation of unreliable trajectories that may not align with the real data distribution. In this paper, we propose a new MORL algorithm \textbf{R}eliability-guaranteed \textbf{T}ransformer (RT), which can eliminate unreliable trajectories by calculating the cumulative reliability of the generated trajectory (i.e., using a weighted variational distance away from the real data). Moreover, by sampling candidate actions with high rewards, RT can efficiently generate high-return trajectories from the existing offline data. We theoretically prove the performance guarantees of RT in policy learning, and empirically demonstrate its effectiveness against state-of-the-art model-based methods on several benchmark tasks.

Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by vulnerabilities such as single-point failures and communication bottlenecks. This paper presents a decentralized framework tailored for parameter inference in spatial low-rank models to address these challenges. A key obstacle arises from the spatial dependence among observations, which prevents the log-likelihood from being expressed as a summation-a critical requirement for decentralized optimization approaches. To overcome this challenge, we propose a novel objective function leveraging the evidence lower bound, which facilitates the use of decentralized optimization techniques. Our approach employs a block descent method integrated with multi-consensus and dynamic consensus averaging for effective parameter optimization. We prove the convexity of the new objective function in the vicinity of the true parameters, ensuring the convergence of the proposed method. Additionally, we present the first theoretical results establishing the consistency and asymptotic normality of the estimator within the context of spatial low-rank models. Extensive simulations and real-world data experiments corroborate these theoretical findings, showcasing the robustness and scalability of the framework.

We introduce Social Bayesian Optimization (SBO), a vote-efficient algorithm for consensus-building in collective decision-making. In contrast to single-agent scenarios, collective decision-making encompasses group dynamics that may distort agents' preference feedback, thereby impeding their capacity to achieve a social-influence-free consensus -- the most preferable decision based on the aggregated agent utilities. We demonstrate that under mild rationality axioms, reaching social-influence-free consensus using noisy feedback alone is impossible. To address this, SBO employs a dual voting system: cheap but noisy public votes (e.g., show of hands in a meeting), and more accurate, though expensive, private votes (e.g., one-to-one interview). We model social influence using an unknown social graph and leverage the dual voting system to efficiently learn this graph. Our theoretical findigns show that social graph estimation converges faster than the black-box estimation of agents' utilities, allowing us to reduce reliance on costly private votes early in the process. This enables efficient consensus-building primarily through noisy public votes, which are debiased based on the estimated social graph to infer social-influence-free feedback. We validate the efficacy of SBO across multiple real-world applications, including thermal comfort, team building, travel negotiation, and energy trading collaboration.

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption, current state-of-the-art samplers still struggle to navigate the complex and highly multimodal posteriors of BNNs. As a consequence, sampling still requires considerably longer inference times than non-Bayesian methods even for small neural networks, despite recent advances in making software implementations more efficient. Besides the difficulty of finding high-probability regions, the time until samplers provide sufficient exploration of these areas remains unpredictable. To tackle these challenges, we introduce an ensembling approach that leverages strategies from optimization and a recently proposed sampler called Microcanonical Langevin Monte Carlo (MCLMC) for efficient, robust and predictable sampling performance. Compared to approaches based on the state-of-the-art No-U-Turn Sampler, our approach delivers substantial speedups up to an order of magnitude, while maintaining or improving predictive performance and uncertainty quantification across diverse tasks and data modalities. The suggested Microcanonical Langevin Ensembles and modifications to MCLMC additionally enhance the method's predictability in resource requirements, facilitating easier parallelization. All in all, the proposed method offers a promising direction for practical, scalable inference for BNNs.

Identification of protein-protein interactions (PPIs) helps derive cellular mechanistic understanding, particularly in the context of complex conditions such as neurodegenerative disorders, metabolic syndromes, and cancer. Large Language Models (LLMs) have demonstrated remarkable potential in predicting protein structures and interactions via automated mining of vast biomedical literature; yet their inherent uncertainty remains a key challenge for deriving reproducible findings, critical for biomedical applications. In this study, we present an uncertainty-aware adaptation of LLMs for PPI analysis, leveraging fine-tuned LLaMA-3 and BioMedGPT models. To enhance prediction reliability, we integrate LoRA ensembles and Bayesian LoRA models for uncertainty quantification (UQ), ensuring confidence-calibrated insights into protein behavior. Our approach achieves competitive performance in PPI identification across diverse disease contexts while addressing model uncertainty, thereby enhancing trustworthiness and reproducibility in computational biology. These findings underscore the potential of uncertainty-aware LLM adaptation for advancing precision medicine and biomedical research.

Conformal prediction methods create prediction bands with distribution-free guarantees but do not explicitly capture epistemic uncertainty, which can lead to overconfident predictions in data-sparse regions. Although recent conformal scores have been developed to address this limitation, they are typically designed for specific tasks, such as regression or quantile regression. Moreover, they rely on particular modeling choices for epistemic uncertainty, restricting their applicability. We introduce $\texttt{EPICSCORE}$, a model-agnostic approach that enhances any conformal score by explicitly integrating epistemic uncertainty. Leveraging Bayesian techniques such as Gaussian Processes, Monte Carlo Dropout, or Bayesian Additive Regression Trees, $\texttt{EPICSCORE}$ adaptively expands predictive intervals in regions with limited data while maintaining compact intervals where data is abundant. As with any conformal method, it preserves finite-sample marginal coverage. Additionally, it also achieves asymptotic conditional coverage. Experiments demonstrate its good performance compared to existing methods. Designed for compatibility with any Bayesian model, but equipped with distribution-free guarantees, $\texttt{EPICSCORE}$ provides a general-purpose framework for uncertainty quantification in prediction problems.

This paper addresses the problem of mixed-membership estimation in networks, where the goal is to efficiently estimate the latent mixed-membership structure from the observed network. Recognizing the widespread availability and valuable information carried by node covariates, we propose a novel network model that incorporates both community information, as represented by the Degree-Corrected Mixed Membership (DCMM) model, and node covariate similarities to determine connections. We investigate the regularized maximum likelihood estimation (MLE) for this model and demonstrate that our approach achieves optimal estimation accuracy for both the similarity matrix and the mixed-membership, in terms of both the Frobenius norm and the entrywise loss. Since directly analyzing the original convex optimization problem is intractable, we employ nonconvex optimization to facilitate the analysis. A key contribution of our work is identifying a crucial assumption that bridges the gap between convex and nonconvex solutions, enabling the transfer of statistical guarantees from the nonconvex approach to its convex counterpart. Importantly, our analysis extends beyond the MLE loss and the mean squared error (MSE) used in matrix completion problems, generalizing to all the convex loss functions. Consequently, our analysis techniques extend to a broader set of applications, including ranking problems based on pairwise comparisons. Finally, simulation experiments validate our theoretical findings, and real-world data analyses confirm the practical relevance of our model.