Bayesian Physics Informed Neural Networks (BPINN) have received considerable attention for inferring differential equations' system states and physical parameters according to noisy observations. However, in practice, Hamiltonian Monte Carlo (HMC) used to estimate the internal parameters of BPINN often encounters troubles, including poor performance and awful convergence for a given step size used to adjust the momentum of those parameters. To improve the efficacy of HMC convergence for the BPINN method and extend its application scope to multi-scale partial differential equations (PDE), we developed a robust multi-scale Bayesian PINN (dubbed MBPINN) method by integrating multi-scale deep neural networks (MscaleDNN) and Bayesian inference. In this newly proposed MBPINN method, we reframe HMC with Stochastic Gradient Descent (SGD) to ensure the most ``likely'' estimation is always provided, and we configure its solver as a Fourier feature mapping-induced MscaleDNN. The MBPINN method offers several key advantages: (1) it is more robust than HMC, (2) it incurs less computational cost than HMC, and (3) it is more flexible for complex problems. We demonstrate the applicability and performance of the proposed method through general Poisson and multi-scale elliptic problems in one- to three-dimensional spaces. Our findings indicate that the proposed method can avoid HMC failures and provide valid results. Additionally, our method can handle complex PDE and produce comparable results for general PDE. These findings suggest that our proposed approach has excellent potential for physics-informed machine learning for parameter estimation and solution recovery in the case of ill-posed problems.

This study investigates the causal relationships between Clinical Dementia Ratings (CDR) and its six domain scores across two distinct aging datasets: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Longitudinal Aging Study of India (LASI). Using Directed Acyclic Graphs (DAGs) derived from Bayesian network models, we analyze the dependencies among domain scores and their influence on the global CDR. Our approach leverages the PC algorithm to estimate the DAG structures for both datasets, revealing notable differences in causal relationships and edge strengths between the Western and Indian populations. The analysis highlights a stronger dependency of CDR scores on memory functions in both datasets, but with significant variations in edge strengths and node degrees. By contrasting these findings, we aim to elucidate population-specific differences and similarities in dementia progression, providing insights that could inform targeted interventions and improve understanding of dementia across diverse demographic contexts.

Its crux lies in the optimization of a tradeoff between accuracy and fairness of resultant models on the selected feature subset. The technical challenge of our setting is twofold: 1) streaming feature inputs, such that an informative feature may become obsolete or redundant for prediction if its information has been covered by other similar features that arrived prior to it, and 2) non-associational feature correlation, such that bias may be leaked from those seemingly admissible, non-protected features. To overcome this, we propose Streaming Feature Selection with Causal Fairness (SFCF) that builds two causal graphs egocentric to prediction label and protected feature, respectively, striving to model the complex correlation structure among streaming features, labels, and protected information. As such, bias can be eradicated from predictive modeling by removing those features being causally correlated with the protected feature yet independent to the labels. We theorize that the originally redundant features for prediction can later become admissible, when the learning accuracy is compromised by the large number of removed features (non-protected but can be used to reconstruct bias information). We benchmark SFCF\ on five datasets widely used in streaming feature research, and the results substantiate its performance superiority over six rival models in terms of efficiency and sparsity of feature selection and equalized odds of the resultant predictive models.

In this paper, we study user association and wireless bandwidth allocation for a hierarchical federated learning system that consists of mobile users, edge servers, and a cloud server. To minimize the length of a global round in hierarchical federated learning with equal bandwidth allocation, we formulate a combinatorial optimization problem. We design the twin sorting dynamic programming (TSDP) algorithm that obtains a globally optimal solution in polynomial time when there are two edge servers. In addition, we put forward the TSDP-assisted algorithm for user association when there are three or more edge servers. Furthermore, given a user association matrix, we formulate and solve a convex optimization problem for optimal wireless bandwidth allocation. Simulation results show that the proposed approach outperforms a number of alternative schemes.

Robust partially observable Markov decision processes (robust POMDPs) extend classical POMDPs to handle additional uncertainty on the transition and observation probabilities via so-called uncertainty sets. Policies for robust POMDPs must not only be memory-based to account for partial observability but also robust against model uncertainty to account for the worst-case instances from the uncertainty sets. We propose the pessimistic iterative planning (PIP) framework, which finds robust memory-based policies for robust POMDPs. PIP alternates between two main steps: (1) selecting an adversarial (non-robust) POMDP via worst-case probability instances from the uncertainty sets; and (2) computing a finite-state controller (FSC) for this adversarial POMDP. We evaluate the performance of this FSC on the original robust POMDP and use this evaluation in step (1) to select the next adversarial POMDP. Within PIP, we propose the rFSCNet algorithm. In each iteration, rFSCNet finds an FSC through a recurrent neural network trained using supervision policies optimized for the adversarial POMDP. The empirical evaluation in four benchmark environments showcases improved robustness against a baseline method in an ablation study and competitive performance compared to a state-of-the-art robust POMDP solver.

PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, it typically focus on providing generalization bounds with respect to a chosen loss function. In classification tasks, due to the non-convex nature of the 0-1 loss, a convex surrogate loss is often used, and thus current PAC-Bayesian bounds are primarily specified for this convex surrogate. This work shifts its focus to providing misclassification excess risk bounds for PAC-Bayesian classification when using a convex surrogate loss. Our key ingredient here is to leverage PAC-Bayesian relative bounds in expectation rather than relying on PAC-Bayesian bounds in probability. We demonstrate our approach in several important applications.

By using an parametric value function to replace the Monte-Carlo rollouts for value estimation, the actor-critic (AC) algorithms can reduce the variance of stochastic policy gradient so that to improve the convergence rate. While existing works mainly focus on analyzing convergence rate of AC algorithms under Markovian noise, the impacts of momentum on AC algorithms remain largely unexplored. In this work, we first propose a heavy-ball momentum based advantage actor-critic (\mbox{HB-A2C}) algorithm by integrating the heavy-ball momentum into the critic recursion that is parameterized by a linear function. When the sample trajectory follows a Markov decision process, we quantitatively certify the acceleration capability of the proposed HB-A2C algorithm. Our theoretical results demonstrate that the proposed HB-A2C finds an $\epsilon$-approximate stationary point with $\oo{\epsilon^{-2}}$ iterations for reinforcement learning tasks with Markovian noise. Moreover, we also reveal the dependence of learning rates on the length of the sample trajectory. By carefully selecting the momentum factor of the critic recursion, the proposed HB-A2C can balance the errors introduced by the initialization and the stoschastic approximation.

Moving Target Defense (MTD) has emerged as a proactive and dynamic framework to counteract evolving cyber threats. Traditional MTD approaches often rely on assumptions about the attackers knowledge and behavior. However, real-world scenarios are inherently more complex, with adaptive attackers and limited prior knowledge of their payoffs and intentions. This paper introduces a novel approach to MTD using a Markov Decision Process (MDP) model that does not rely on predefined attacker payoffs. Our framework integrates the attackers real-time responses into the defenders MDP using a dynamic Bayesian Network. By employing a factored MDP model, we provide a comprehensive and realistic system representation. We also incorporate incremental updates to an attack response predictor as new data emerges. This ensures an adaptive and robust defense mechanism. Additionally, we consider the costs of switching configurations in MTD, integrating them into the reward structure to balance execution and defense costs. We first highlight the challenges of the problem through a theoretical negative result on regret. However, empirical evaluations demonstrate the frameworks effectiveness in scenarios marked by high uncertainty and dynamically changing attack landscapes.

Social evolutionary theory seeks to explain increases in the scale and complexity of human societies, from origins to present. Over the course of the twentieth century, social evolutionary theory largely fell out of favor as a way of investigating human history, just as advances in complex systems science and computer science saw the emergence of powerful new conceptions of complex systems, and in particular new methods of measuring complexity. We propose that these advances in our understanding of complex systems and computer science should be brought to bear on our investigations into human history. To that end, we present a new framework for modeling how human societies co-evolve with their biotic environments, recognizing that both a society and its environment are computers. This leads us to model the dynamics of each of those two systems using the same, new kind of computational machine, which we define here. For simplicity, we construe a society as a set of interacting occupations and technologies. Similarly, under such a model, a biotic environment is a set of interacting distinct ecological and climatic processes. This provides novel ways to characterize social complexity, which we hope will cast new light on the archaeological and historical records. Our framework also provides a natural way to formalize both the energetic (thermodynamic) costs required by a society as it runs, and the ways it can extract thermodynamic resources from the environment in order to pay for those costs -- and perhaps to grow with any left-over resources.

A text stream is an ordered sequence of text documents generated over time. A massive amount of such text data is generated by online social platforms every day. Designing an algorithm for such text streams to extract useful information is a challenging task due to unique properties of the stream such as infinite length, data sparsity, and evolution. Thereby, learning useful information from such streaming data under the constraint of limited time and memory has gained increasing attention. During the past decade, although many text stream mining algorithms have proposed, there still exists some potential issues. First, high-dimensional text data heavily degrades the learning performance until the model either works on subspace or reduces the global feature space. The second issue is to extract semantic text representation of documents and capture evolving topics over time. Moreover, the problem of label scarcity exists, whereas existing approaches work on the full availability of labeled data. To deal with these issues, in this thesis, new learning models are proposed for clustering and multi-label learning on text streams.