Federated Learning (FL), a distributed learning paradigm that scales on-device learning collaboratively, has emerged as a promising approach for decentralized AI applications. Local optimization methods such as Federated Averaging (FedAvg) are the most prominent methods for FL applications. Despite their simplicity and popularity, the theoretical understanding of local optimization methods is far from clear. This dissertation aims to advance the theoretical foundation of local methods in the following three directions. First, we establish sharp bounds for FedAvg, the most popular algorithm in Federated Learning. We demonstrate how FedAvg may suffer from a notion we call iterate bias, and how an additional third-order smoothness assumption may mitigate this effect and lead to better convergence rates. We explain this phenomenon from a Stochastic Differential Equation (SDE) perspective. Second, we propose Federated Accelerated Stochastic Gradient Descent (FedAc), the first principled acceleration of FedAvg, which provably improves the convergence rate and communication efficiency. Our technique uses on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability. Third, we study the Federated Composite Optimization problem, which extends the classic smooth setting by incorporating a shared non-smooth regularizer. We show that direct extensions of FedAvg may suffer from the "curse of primal averaging," resulting in slow convergence. As a solution, we propose a new primal-dual algorithm, Federated Dual Averaging, which overcomes the curse of primal averaging by employing a novel inter-client dual averaging procedure.

Memory replay based techniques have shown great success for continual learning with incrementally accumulated Euclidean data. Directly applying them to continually expanding graphs, however, leads to the potential memory explosion problem due to the need to buffer representative nodes and their associated topological neighborhood structures. To this end, we systematically analyze the key challenges in the memory explosion problem, and present a general framework, i.e., Parameter Decoupled Graph Neural Networks (PDGNNs) with Topology-aware Embedding Memory (TEM), to tackle this issue. The proposed framework not only reduces the memory space complexity from $\mathcal{O}(nd^L)$ to $\mathcal{O}(n)$~\footnote{$n$: memory budget, $d$: average node degree, $L$: the radius of the GNN receptive field}, but also fully utilizes the topological information for memory replay. Specifically, PDGNNs decouple trainable parameters from the computation ego-subgraph via \textit{Topology-aware Embeddings} (TEs), which compress ego-subgraphs into compact vectors (i.e., TEs) to reduce the memory consumption. Based on this framework, we discover a unique \textit{pseudo-training effect} in continual learning on expanding graphs and this effect motivates us to develop a novel \textit{coverage maximization sampling} strategy that can enhance the performance with a tight memory budget. Thorough empirical studies demonstrate that, by tackling the memory explosion problem and incorporating topological information into memory replay, PDGNNs with TEM significantly outperform state-of-the-art techniques, especially in the challenging class-incremental setting.

Visual sensing of environmental geometry allows robots to use artificial potential fields to avoid sparse obstacles. Yet robots must further traverse cluttered large obstacles for applications like search and rescue through rubble and planetary exploration across Martain rocks. Recent studies discovered that to traverse cluttered large obstacles, multi-legged insects and insect-inspired robots make strenuous transitions across locomotor modes with major changes in body orientation. When viewed on a potential energy landscape resulting from locomotor-obstacle physical interaction, these are barrier-crossing transitions across landscape basins. This potential energy landscape approach may provide a modeling framework for cluttered large obstacle traversal. Here, we take the next step toward this vision by testing whether force sensing allows the reconstruction of the potential energy landscape. We developed a cockroach-inspired, minimalistic robot capable of sensing obstacle contact forces and torques around its body as it propelled forward against a pair of cluttered grass-like beam obstacles. We performed measurements over many traverses with systematically varied body orientations. Despite the forces and torques not being fully conservative, they well-matched the potential energy landscape gradients and the landscape reconstructed from them well-matched ground truth. In addition, inspired by cockroach observations, we found that robot head oscillation during traversal further improved the accuracies of force sensing and landscape reconstruction. We still need to study how to reconstruct landscape during a single traverse, as in applications, robots have little chance to use multiple traverses to sample the environment systematically and how to find landscape saddles for least-effort transitions to traverse.

A hypergraph is a generalization of a graph that arises naturally when attribute-sharing among entities is considered. Although a hypergraph can be converted into a graph by expanding its hyperedges into fully connected subgraphs, going the reverse way is computationally complex and NP-complete. We therefore hypothesize that a hypergraph contains more information than a graph. In addition, it is more convenient to manipulate a hypergraph directly, rather than expand it into a graph. An open problem in hypergraphs is how to accurately and efficiently calculate their node distances. Estimating node distances enables us to find a node's nearest neighbors, and perform label propagation on hypergraphs using a K-nearest neighbors (KNN) approach. In this paper, we propose a novel approach based on random walks to achieve label propagation on hypergraphs. We estimate node distances as the expected hitting times of random walks. We note that simple random walks (SRW) cannot accurately describe highly complex real-world hypergraphs, which motivates us to introduce frustrated random walks (FRW) to better describe them. We further benchmark our method against DeepWalk, and show that while the latter can achieve comparable results, FRW has a distinct computational advantage in cases where the number of targets is fairly small. For such cases, we show that FRW runs in significantly shorter time than DeepWalk. Finally, we analyze the time complexity of our method, and show that for large and sparse hypergraphs, the complexity is approximately linear, rendering it superior to the DeepWalk alternative.

We define a distance between temporal graphs based on graph embeddings built using time-respecting random walks. We study both the case of matched graphs, when there exists a known relation between the nodes, and the unmatched case, when such a relation is unavailable and the graphs may be of different sizes. We illustrate the interest of our distance definition, using both real and synthetic temporal network data, by showing its ability to discriminate between graphs with different structural and temporal properties. Leveraging state-of-the-art machine learning techniques, we propose an efficient implementation of distance computation that is viable for large-scale temporal graphs.

Recent advancements in federated learning (FL) have greatly facilitated the development of decentralized collaborative applications, particularly in the domain of Artificial Intelligence of Things (AIoT). However, a critical aspect missing from the current research landscape is the ability to enable data-driven client models with symbolic reasoning capabilities. Specifically, the inherent heterogeneity of participating client devices poses a significant challenge, as each client exhibits unique logic reasoning properties. Failing to consider these device-specific specifications can result in critical properties being missed in the client predictions, leading to suboptimal performance. In this work, we propose a new training paradigm that leverages temporal logic reasoning to address this issue. Our approach involves enhancing the training process by incorporating mechanically generated logic expressions for each FL client. Additionally, we introduce the concept of aggregation clusters and develop a partitioning algorithm to effectively group clients based on the alignment of their temporal reasoning properties. We evaluate the proposed method on two tasks: a real-world traffic volume prediction task consisting of sensory data from fifteen states and a smart city multi-task prediction utilizing synthetic data. The evaluation results exhibit clear improvements, with performance accuracy improved by up to 54% across all sequential prediction models.

Globally, cardiovascular diseases (CVDs) are the leading cause of mortality, accounting for an estimated 17.9 million deaths annually. One critical clinical objective is the early detection of CVDs using electrocardiogram (ECG) data, an area that has received significant attention from the research community. Recent advancements based on machine learning and deep learning have achieved great progress in this domain. However, existing methodologies exhibit inherent limitations, including inappropriate model evaluations and instances of data leakage. In this study, we present a streamlined workflow paradigm for preprocessing ECG signals into consistent 10-second durations, eliminating the need for manual feature extraction/beat detection. We also propose a hybrid model of Long Short-Term Memory (LSTM) with Support Vector Machine (SVM) for fraud detection. This architecture consists of two LSTM layers and an SVM classifier, which achieves a SOTA results with an Average precision score of 0.9402 on the MIT-BIH arrhythmia dataset and 0.9563 on the MIT-BIH atrial fibrillation dataset. Based on the results, we believe our method can significantly benefit the early detection and management of CVDs.

Recently, the selection of machine learning model based on only the data distribution without concerning the noise of the data. This study aims to distinguish, which models perform well under noisy data, and establish whether stacking machine learning models actually provide robustness to otherwise weak-to-noise models. The electrochemical data were tested with 12 standalone models and stacking model. This includes XGB, LGBM, RF, GB, ADA, NN, ELAS, LASS, RIDGE, SVM, KNN, DT, and the stacking model. It is found that linear models handle noise well with the average error of (slope) to 1.75 F g-1 up to error per 100% percent noise added; but it suffers from prediction accuracy due to having an average of 60.19 F g-1 estimated at minimal error at 0% noise added. Tree-based models fail in terms of noise handling (average slope is 55.24 F g-1 at 100% percent noise), but it can provide higher prediction accuracy (lowest error of 23.9 F g-1) than that of linear. To address the controversial between prediction accuracy and error handling, the stacking model was constructed, which is not only show high accuracy (intercept of 25.03 F g-1), but it also exhibits good noise handling (slope of 43.58 F g-1), making stacking models a relatively low risk and viable choice for beginner and experienced machine learning research in electrochemistry. Even though neural networks (NN) are gaining popularity in the electrochemistry field. However, this study presents that NN is not suitable for electrochemical data, and improper tuning resulting in a model that is susceptible to noise. Thus, STACK models should provide better benefits in that even with untuned base models, they can achieve an accurate and noise-tolerant model. Overall, this work provides insight into machine learning model selection for electrochemical data, which should aid the understanding of data science in chemistry context.

In replay-based methods for continual learning, replaying input samples in episodic memory has shown its effectiveness in alleviating catastrophic forgetting. However, the potential key factor of cross-entropy loss with softmax in causing catastrophic forgetting has been underexplored. In this paper, we analyze the effect of softmax and revisit softmax masking with negative infinity to shed light on its ability to mitigate catastrophic forgetting. Based on the analyses, it is found that negative infinity masked softmax is not always compatible with dark knowledge. To improve the compatibility, we propose a general masked softmax that controls the stability by adjusting the gradient scale to old and new classes. We demonstrate that utilizing our method on other replay-based methods results in better performance, primarily by enhancing model stability in continual learning benchmarks, even when the buffer size is set to an extremely small value.

Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions between interactive entities. Revealing interaction laws is of fundamental importance but also particularly challenging due to underlying configurational complexities. The associated challenges become exacerbated for heterogeneous systems that are prevalent in reality, where multiple interaction types coexist simultaneously and relational inference is required. Here, we propose a novel probabilistic method for relational inference, which possesses two distinctive characteristics compared to existing methods. First, it infers the interaction types of different edges collectively by explicitly encoding the correlation among incoming interactions with a joint distribution, and second, it allows handling systems with variable topological structure over time. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it outperforms existing methods in accurately inferring interaction types. We further show that when combined with known constraints, it allows us, for example, to discover physics-consistent interaction laws of particle systems. Overall the proposed model is data-efficient and generalizable to large systems when trained on smaller ones. The developed methodology constitutes a key element for understanding interacting systems and may find application in graph structure learning.