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{\(\boldsymbol{15.28\%}\)}.

In many practical applications, decision-making processes must balance the costs of acquiring information with the benefits it provides. Traditional control systems often assume full observability, an unrealistic assumption when observations are expensive. We tackle the challenge of simultaneously learning observation and control strategies in such cost-sensitive environments by introducing the Observation-Constrained Markov Decision Process (OCMDP), where the policy influences the observability of the true state. To manage the complexity arising from the combined observation and control actions, we develop an iterative, model-free deep reinforcement learning algorithm that separates the sensing and control components of the policy. This decomposition enables efficient learning in the expanded action space by focusing on when and what to observe, as well as determining optimal control actions, without requiring knowledge of the environment's dynamics. We validate our approach on a simulated diagnostic task and a realistic healthcare environment using HeartPole. Given both scenarios, the experimental results demonstrate that our model achieves a substantial reduction in observation costs on average, significantly outperforming baseline methods by a notable margin in efficiency.

In multi-agent reinforcement learning (MARL), the centralized training with decentralized execution (CTDE) framework has gained widespread adoption due to its strong performance. However, the further development of CTDE faces two key challenges. First, agents struggle to autonomously assess the relevance of input information for cooperative tasks, impairing their decision-making abilities. Second, in communication-limited scenarios with partial observability, agents are unable to access global information, restricting their ability to collaborate effectively from a global perspective. To address these challenges, we introduce a novel cooperative MARL framework based on information selection and tacit learning. In this framework, agents gradually develop implicit coordination during training, enabling them to infer the cooperative behavior of others in a discrete space without communication, relying solely on local information. Moreover, we integrate gating and selection mechanisms, allowing agents to adaptively filter information based on environmental changes, thereby enhancing their decision-making capabilities. Experiments on popular MARL benchmarks show that our framework can be seamlessly integrated with state-of-the-art algorithms, leading to significant performance improvements.

In the paced realms of cybersecurity and digital forensics machine learning (ML) and deep learning (DL) have emerged as game changing technologies that introduce methods to identify stop and analyze cyber risks. This review presents an overview of the ML and DL approaches used in these fields showcasing their advantages drawbacks and possibilities. It covers a range of AI techniques used in spotting intrusions in systems and classifying malware to prevent cybersecurity attacks, detect anomalies and enhance resilience. This study concludes by highlighting areas where further research is needed and suggesting ways to create transparent and scalable ML and DL solutions that are suited to the evolving landscape of cybersecurity and digital forensics.

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 Dissertation is comprised of two main projects, addressing questions in neuroscience through applications of generative modeling. Project #1 (Chapter 4) explores how neurons encode features of the external world. I combine Helmholtz's "Perception as Unconscious Inference" -- paralleled by modern generative models like variational autoencoders (VAE) -- with the hierarchical structure of the visual cortex. This combination leads to the development of a hierarchical VAE model, which I test for its ability to mimic neurons from the primate visual cortex in response to motion stimuli. Results show that the hierarchical VAE perceives motion similar to the primate brain. Additionally, the model identifies causal factors of retinal motion inputs, such as object- and self-motion, in a completely unsupervised manner. Collectively, these results suggest that hierarchical inference underlines the brain's understanding of the world, and hierarchical VAEs can effectively model this understanding. Project #2 (Chapter 5) investigates the spatiotemporal structure of spontaneous brain activity and its reflection of brain states like rest. Using simultaneous fMRI and wide-field Ca2+ imaging data, this project demonstrates that the mouse cortex can be decomposed into overlapping communities, with around half of the cortical regions belonging to multiple communities. Comparisons reveal similarities and differences between networks inferred from fMRI and Ca2+ signals. The introduction (Chapter 1) is divided similarly to this abstract: sections 1.1 to 1.8 provide background information about Project #1, and sections 1.9 to 1.13 are related to Project #2. Chapter 2 includes historical background, Chapter 3 provides the necessary mathematical background, and finally, Chapter 6 contains concluding remarks and future directions.

Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and characterizing the sparse structures of noise. Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors and balancing the trade-off between low-rank and sparse components, especially in a mixed-noise scenario. To address these challenges, we introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. By embedding the proposed priors within the Bayesian framework, our method can automatically determine the optimal tensor nuclear norm and achieve a balance between the nuclear norm and sparse components. Furthermore, our method can be efficiently extended to the weighted tensor nuclear norm model. Experiments conducted on synthetic and real-world datasets demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches.