We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common distribution with an unknown parameter (vector). This parameter belongs to either a normal or abnormal space depending on the current state of the process. Before the change point, all processes, including the anomalous one, are in a normal state; after the change point, the anomalous process transitions to an abnormal state. Our goal is to design a sequential search strategy that minimizes the Bayes risk by balancing sample complexity and detection accuracy. We propose a deterministic search algorithm with the following notable properties. First, we analytically demonstrate that when the distributions of both normal and abnormal processes are unknown, the algorithm is asymptotically optimal in minimizing the Bayes risk as the error probability approaches zero. In the second setting, where the parameter under the null hypothesis is known, the algorithm achieves asymptotic optimality with improved detection time based on the true normal state. Simulation results are presented to validate the theoretical findings.

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have proposed such decompositions, they lack the type of formal guarantees we provide. Our method is based on the new notion of higher-order calibration, which generalizes ordinary calibration to the setting of higher-order predictors that predict mixtures over label distributions at every point. We show how to measure as well as achieve higher-order calibration using access to $k$-snapshots, namely examples where each point has $k$ independent conditional labels. Under higher-order calibration, the estimated aleatoric uncertainty at a point is guaranteed to match the real-world aleatoric uncertainty averaged over all points where the prediction is made. To our knowledge, this is the first formal guarantee of this type that places no assumptions whatsoever on the real-world data distribution. Importantly, higher-order calibration is also applicable to existing higher-order predictors such as Bayesian and ensemble models and provides a natural evaluation metric for such models. We demonstrate through experiments that our method produces meaningful uncertainty decompositions for image classification.

Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov Chain Monte Carlo methods face slow convergence and computational burdens. Existing Variational Inference methods, which require pre-generated topologies and typically treat tree structures and branch lengths independently, may overlook critical sequence features, limiting their accuracy and flexibility. We propose PhyloGen, a novel method leveraging a pre-trained genomic language model to generate and optimize phylogenetic trees without dependence on evolutionary models or aligned sequence constraints. PhyloGen views phylogenetic inference as a conditionally constrained tree structure generation problem, jointly optimizing tree topology and branch lengths through three core modules: (i) Feature Extraction, (ii) PhyloTree Construction, and (iii) PhyloTree Structure Modeling. Meanwhile, we introduce a Scoring Function to guide the model towards a more stable gradient descent. We demonstrate the effectiveness and robustness of PhyloGen on eight real-world benchmark datasets. Visualization results confirm PhyloGen provides deeper insights into phylogenetic relationships.

Adaptive Traffic Signal Control (ATSC) system is a critical component of intelligent transportation, with the capability to significantly alleviate urban traffic congestion. Although reinforcement learning (RL)-based methods have demonstrated promising performance in achieving ATSC, existing methods are still prone to making unreasonable policies. Therefore, this paper proposes a novel Bayesian Critique-Tune-Based Reinforcement Learning with Adaptive Pressure for multi-intersection signal control (BCT-APLight). In BCT-APLight, the Critique-Tune (CT) framework, a two-layer Bayesian structure is designed to refine the excessive trust of RL policies. Specifically, the Bayesian inference-based Critique Layer provides effective evaluations of the credibility of policies; the Bayesian decision-based Tune Layer fine-tunes policies by minimizing the posterior risks when the evaluations are negative. Meanwhile, an attention-based Adaptive Pressure (AP) mechanism is designed to effectively weight the vehicle queues in each lane, thereby enhancing the rationality of traffic movement representation within the network. Equipped with the CT framework and AP mechanism, BCT-APLight effectively enhances the reasonableness of RL policies. Extensive experiments conducted with a simulator across a range of intersection layouts demonstrate that BCT-APLight is superior to other state-of-the-art (SOTA) methods on seven real-world datasets. Specifically, BCT-APLight decreases average queue length by \textbf{\(\boldsymbol{9.60\%}\)} and average waiting time by \textbf{\(\boldsymbol{15.28\%}\)}.

This work addresses a key limitation in current federated learning approaches, which predominantly focus on homogeneous tasks, neglecting the task diversity on local devices. We propose a principled integration of multi-task learning using multi-output Gaussian processes (MOGP) at the local level and federated learning at the global level. MOGP handles correlated classification and regression tasks, offering a Bayesian non-parametric approach that naturally quantifies uncertainty. The central server aggregates the posteriors from local devices, updating a global MOGP prior redistributed for training local models until convergence. Challenges in performing posterior inference on local devices are addressed through the P\'{o}lya-Gamma augmentation technique and mean-field variational inference, enhancing computational efficiency and convergence rate. Experimental results on both synthetic and real data demonstrate superior predictive performance, OOD detection, uncertainty calibration and convergence rate, highlighting the method's potential in diverse applications. Our code is publicly available at https://github.com/JunliangLv/task_diversity_BFL.

Score identity Distillation (SiD) is a data-free method that has achieved state-ofthe-art performance in image generation by leveraging only a pretrained diffusion model, without requiring any training data. However, the ultimate performance of SiD is constrained by the accuracy with which the pretrained model captures the true data scores at different stages of the diffusion process. In this paper, we introduce SiDA (SiD with Adversarial Loss), which not only enhances generation quality but also improves distillation efficiency by incorporating real images and adversarial loss. SiDA utilizes the encoder from the generator's score network as a discriminator, allowing it to distinguish between real images and those generated by SiD. The adversarial loss is batch-normalized within each GPU and then combined with the original SiD loss. This integration effectively incorporates the average "fakeness" per GPU batch into the pixel-based SiD loss, enabling SiDA to distill a single-step generator. SiDA converges significantly faster than its predecessor when distilled from scratch, and swiftly improves upon the original model's performance during fine-tuning from a pre-distilled SiD generator. This one-step adversarial distillation method establishes new benchmarks in generation performance when distilling EDM diffusion models, achieving FID scores of 1.499 on CIFAR-10 unconditional, 1.396 on CIFAR-10 conditional, and 1.110 on ImageNet 64x64. When distilling EDM2 models trained on ImageNet 512x512, our SiDA method surpasses even the largest teacher model, EDM2-XXL, which achieved an FID of 1.81 using classifier-free guidance (CFG) and 63 generation steps. In contrast, SiDA achieves FID scores of 2.156 for size XS, 1.669 for S, 1.488 for M, 1.413 for L, 1.379 for XL, and 1.366 for XXL, all without CFG and in a single generation step.

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable terms. To tackle this issue, state-of-the-art approaches formulate the problem as that of sampling from a surrogate diffusion model targeting the posterior and decompose its scores into two terms: the prior score and an intractable guidance term. While the former is replaced by the pre-trained score of the considered diffusion model, the guidance term has to be estimated. In this paper, we propose a novel approach that utilises a decomposition of the transitions which, in contrast to previous methods, allows a trade-off between the complexity of the intractable guidance term and that of the prior transitions. We validate the proposed approach through extensive experiments on linear and nonlinear inverse problems, including challenging cases with latent diffusion models as priors. We then demonstrate its applicability to various modalities and its promising impact on public health by tackling cardiovascular disease diagnosis through the reconstruction of incomplete electrocardiograms. The code is publicly available at https://github.com/ Inverse problems aim to reconstruct signals from incomplete and noisy observations and are prevalent across various fields. In signal and image processing, common examples include signal deconvolution, image restoration, and tomographic image reconstruction (Stuart, 2010; Idier, 2013). Other applications extend to protein backbone motif scaffolding (Watson et al., 2023) and urban mobility modeling (Jiang et al., 2023).

Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for statistical models. The derived bound has wide-ranging applications in statistical inference. It yields improved contraction rates for fractional posteriors in Bayesian nonparametrics. It can also be used to study a wide range of estimation methods, such as variational inference or Maximum Likelihood Estimation (MLE). By bridging these diverse areas, this work advances our understanding of the fundamental limits of statistical inference and the role of information in learning from data. We hope that these results will not only clarify connections between statistical inference and information theory but also help to develop a new toolbox to study a wide range of estimators.

Gaussian graphical model selection is an important paradigm with numerous applications, including biological network modeling, financial network modeling, and social network analysis. Traditional approaches assume access to independent and identically distributed (i.i.d) samples, which is often impractical in real-world scenarios. In this paper, we address Gaussian graphical model selection under observations from a more realistic dependent stochastic process known as Glauber dynamics. Glauber dynamics, also called the Gibbs sampler, is a Markov chain that sequentially updates the variables of the underlying model based on the statistics of the remaining model. Such models, aside from frequently being employed to generate samples from complex multivariate distributions, naturally arise in various settings, such as opinion consensus in social networks and clearing/stock-price dynamics in financial networks. In contrast to the extensive body of existing work, we present the first algorithm for Gaussian graphical model selection when data are sampled according to the Glauber dynamics. We provide theoretical guarantees on the computational and statistical complexity of the proposed algorithm's structure learning performance. Additionally, we provide information-theoretic lower bounds on the statistical complexity and show that our algorithm is nearly minimax optimal for a broad class of problems.

This paper presents a Multi-Agent Norm Perception and Induction Learning Model aimed at facilitating the integration of autonomous agent systems into distributed healthcare environments through dynamic interaction processes. The nature of the medical norm system and its sharing channels necessitates distinct approaches for Multi-Agent Systems to learn two types of norms. Building on this foundation, the model enables agents to simultaneously learn descriptive norms, which capture collective tendencies, and prescriptive norms, which dictate ideal behaviors. Through parameterized mixed probability density models and practice-enhanced Markov games, the multi-agent system perceives descriptive norms in dynamic interactions and captures emergent prescriptive norms. We conducted experiments using a dataset from a neurological medical center spanning from 2016 to 2020.