1,131 research outputs found

    Exploiting Structural Properties in the Analysis of High-dimensional Dynamical Systems

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    The physical and cyber domains with which we interact are filled with high-dimensional dynamical systems. In machine learning, for instance, the evolution of overparametrized neural networks can be seen as a dynamical system. In networked systems, numerous agents or nodes dynamically interact with each other. A deep understanding of these systems can enable us to predict their behavior, identify potential pitfalls, and devise effective solutions for optimal outcomes. In this dissertation, we will discuss two classes of high-dimensional dynamical systems with specific structural properties that aid in understanding their dynamic behavior. In the first scenario, we consider the training dynamics of multi-layer neural networks. The high dimensionality comes from overparametrization: a typical network has a large depth and hidden layer width. We are interested in the following question regarding convergence: Do network weights converge to an equilibrium point corresponding to a global minimum of our training loss, and how fast is the convergence rate? The key to those questions is the symmetry of the weights, a critical property induced by the multi-layer architecture. Such symmetry leads to a set of time-invariant quantities, called weight imbalance, that restrict the training trajectory to a low-dimensional manifold defined by the weight initialization. A tailored convergence analysis is developed over this low-dimensional manifold, showing improved rate bounds for several multi-layer network models studied in the literature, leading to novel characterizations of the effect of weight imbalance on the convergence rate. In the second scenario, we consider large-scale networked systems with multiple weakly-connected groups. Such a multi-cluster structure leads to a time-scale separation between the fast intra-group interaction due to high intra-group connectivity, and the slow inter-group oscillation, due to the weak inter-group connection. We develop a novel frequency-domain network coherence analysis that captures both the coherent behavior within each group, and the dynamical interaction between groups, leading to a structure-preserving model-reduction methodology for large-scale dynamic networks with multiple clusters under general node dynamics assumptions

    Robustness, Heterogeneity and Structure Capturing for Graph Representation Learning and its Application

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    Graph neural networks (GNNs) are potent methods for graph representation learn- ing (GRL), which extract knowledge from complicated (graph) structured data in various real-world scenarios. However, GRL still faces many challenges. Firstly GNN-based node classification may deteriorate substantially by overlooking the pos- sibility of noisy data in graph structures, as models wrongly process the relation among nodes in the input graphs as the ground truth. Secondly, nodes and edges have different types in the real-world and it is essential to capture this heterogeneity in graph representation learning. Next, relations among nodes are not restricted to pairwise relations and it is necessary to capture the complex relations accordingly. Finally, the absence of structural encodings, such as positional information, deterio- rates the performance of GNNs. This thesis proposes novel methods to address the aforementioned problems: 1. Bayesian Graph Attention Network (BGAT): Developed for situations with scarce data, this method addresses the influence of spurious edges. Incor- porating Bayesian principles into the graph attention mechanism enhances robustness, leading to competitive performance against benchmarks (Chapter 3). 2. Neighbour Contrastive Heterogeneous Graph Attention Network (NC-HGAT): By enhancing a cutting-edge self-supervised heterogeneous graph neural net- work model (HGAT) with neighbour contrastive learning, this method ad- dresses heterogeneity and uncertainty simultaneously. Extra attention to edge relations in heterogeneous graphs also aids in subsequent classification tasks (Chapter 4). 3. A novel ensemble learning framework is introduced for predicting stock price movements. It adeptly captures both group-level and pairwise relations, lead- ing to notable advancements over the existing state-of-the-art. The integration of hypergraph and graph models, coupled with the utilisation of auxiliary data via GNNs before recurrent neural network (RNN), provides a deeper under- standing of long-term dependencies between similar entities in multivariate time series analysis (Chapter 5). 4. A novel framework for graph structure learning is introduced, segmenting graphs into distinct patches. By harnessing the capabilities of transformers and integrating other position encoding techniques, this approach robustly capture intricate structural information within a graph. This results in a more comprehensive understanding of its underlying patterns (Chapter 6)

    Algorithms and complexity for approximately counting hypergraph colourings and related problems

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    The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Δ, this problem falls into the regime of Lovász local lemma when Δ ≲ qᵏ. In prior, however, fast approximate counting algorithms exist when Δ ≲ qᵏ/³, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. • When q, k ≥ 4 are evens and Δ ≥ 5·qᵏ/², approximating the number of hypergraph colourings is NP-hard. • When the input hypergraph is linear and Δ ≲ qᵏ/², a fast approximate counting algorithm does exist

    Une méthode de mesure du mouvement humain pour la programmation par démonstration

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    Programming by demonstration (PbD) is an intuitive approach to impart a task to a robot from one or several demonstrations by the human teacher. The acquisition of the demonstrations involves the solution of the correspondence problem when the teacher and the learner differ in sensing and actuation. Kinesthetic guidance is widely used to perform demonstrations. With such a method, the robot is manipulated by the teacher and the demonstrations are recorded by the robot's encoders. In this way, the correspondence problem is trivial but the teacher dexterity is afflicted which may impact the PbD process. Methods that are more practical for the teacher usually require the identification of some mappings to solve the correspondence problem. The demonstration acquisition method is based on a compromise between the difficulty of identifying these mappings, the level of accuracy of the recorded elements and the user-friendliness and convenience for the teacher. This thesis proposes an inertial human motion tracking method based on inertial measurement units (IMUs) for PbD for pick-and-place tasks. Compared to kinesthetic guidance, IMUs are convenient and easy to use but can present a limited accuracy. Their potential for PbD applications is investigated. To estimate the trajectory of the teacher's hand, 3 IMUs are placed on her/his arm segments (arm, forearm and hand) to estimate their orientations. A specific method is proposed to partially compensate the well-known drift of the sensor orientation estimation around the gravity direction by exploiting the particular configuration of the demonstration. This method, called heading reset, is based on the assumption that the sensor passes through its original heading with stationary phases several times during the demonstration. The heading reset is implemented in an integration and vector observation algorithm. Several experiments illustrate the advantages of this heading reset. A comprehensive inertial human hand motion tracking (IHMT) method for PbD is then developed. It includes an initialization procedure to estimate the orientation of each sensor with respect to the human arm segment and the initial orientation of the sensor with respect to the teacher attached frame. The procedure involves a rotation and a static position of the extended arm. The measurement system is thus robust with respect to the positioning of the sensors on the segments. A procedure for estimating the position of the human teacher relative to the robot and a calibration procedure for the parameters of the method are also proposed. At the end, the error of the human hand trajectory is measured experimentally and is found in an interval between 28.528.5 mm and 61.861.8 mm. The mappings to solve the correspondence problem are identified. Unfortunately, the observed level of accuracy of this IHMT method is not sufficient for a PbD process. In order to reach the necessary level of accuracy, a method is proposed to correct the hand trajectory obtained by IHMT using vision data. A vision system presents a certain complementarity with inertial sensors. For the sake of simplicity and robustness, the vision system only tracks the objects but not the teacher. The correction is based on so-called Positions Of Interest (POIs) and involves 3 steps: the identification of the POIs in the inertial and vision data, the pairing of the hand POIs to objects POIs that correspond to the same action in the task, and finally, the correction of the hand trajectory based on the pairs of POIs. The complete method for demonstration acquisition is experimentally evaluated in a full PbD process. This experiment reveals the advantages of the proposed method over kinesthesy in the context of this work.La programmation par démonstration est une approche intuitive permettant de transmettre une tâche à un robot à partir d'une ou plusieurs démonstrations faites par un enseignant humain. L'acquisition des démonstrations nécessite cependant la résolution d'un problème de correspondance quand les systèmes sensitifs et moteurs de l'enseignant et de l'apprenant diffèrent. De nombreux travaux utilisent des démonstrations faites par kinesthésie, i.e., l'enseignant manipule directement le robot pour lui faire faire la tâche. Ce dernier enregistre ses mouvements grâce à ses propres encodeurs. De cette façon, le problème de correspondance est trivial. Lors de telles démonstrations, la dextérité de l'enseignant peut être altérée et impacter tout le processus de programmation par démonstration. Les méthodes d'acquisition de démonstration moins invalidantes pour l'enseignant nécessitent souvent des procédures spécifiques pour résoudre le problème de correspondance. Ainsi l'acquisition des démonstrations se base sur un compromis entre complexité de ces procédures, le niveau de précision des éléments enregistrés et la commodité pour l'enseignant. Cette thèse propose ainsi une méthode de mesure du mouvement humain par capteurs inertiels pour la programmation par démonstration de tâches de ``pick-and-place''. Les capteurs inertiels sont en effet pratiques et faciles à utiliser, mais sont d'une précision limitée. Nous étudions leur potentiel pour la programmation par démonstration. Pour estimer la trajectoire de la main de l'enseignant, des capteurs inertiels sont placés sur son bras, son avant-bras et sa main afin d'estimer leurs orientations. Une méthode est proposée afin de compenser partiellement la dérive de l'estimation de l'orientation des capteurs autour de la direction de la gravité. Cette méthode, appelée ``heading reset'', est basée sur l'hypothèse que le capteur passe plusieurs fois par son azimut initial avec des phases stationnaires lors d'une démonstration. Cette méthode est implémentée dans un algorithme d'intégration et d'observation de vecteur. Des expériences illustrent les avantages du ``heading reset''. Cette thèse développe ensuite une méthode complète de mesure des mouvements de la main humaine par capteurs inertiels (IHMT). Elle comprend une première procédure d'initialisation pour estimer l'orientation des capteurs par rapport aux segments du bras humain ainsi que l'orientation initiale des capteurs par rapport au repère de référence de l'humain. Cette procédure, consistant en une rotation et une position statique du bras tendu, est robuste au positionnement des capteurs. Une seconde procédure est proposée pour estimer la position de l'humain par rapport au robot et pour calibrer les paramètres de la méthode. Finalement, l'erreur moyenne sur la trajectoire de la main humaine est mesurée expérimentalement entre 28.5 mm et 61.8 mm, ce qui n'est cependant pas suffisant pour la programmation par démonstration. Afin d'atteindre le niveau de précision nécessaire, une nouvelle méthode est développée afin de corriger la trajectoire de la main par IHMT à partir de données issues d'un système de vision, complémentaire des capteurs inertiels. Pour maintenir une certaine simplicité et robustesse, le système de vision ne suit que les objets et pas l'enseignant. La méthode de correction, basée sur des ``Positions Of Interest (POIs)'', est constituée de 3 étapes: l'identification des POIs dans les données issues des capteurs inertiels et du système de vision, puis l'association de POIs liées à la main et de POIs liées aux objets correspondant à la même action, et enfin, la correction de la trajectoire de la main à partir des paires de POIs. Finalement, la méthode IHMT corrigée est expérimentalement évaluée dans un processus complet de programmation par démonstration. Cette expérience montre l'avantage de la méthode proposée sur la kinesthésie dans le contexte de ce travail

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction

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    Trajectory prediction is a crucial undertaking in understanding entity movement or human behavior from observed sequences. However, current methods often assume that the observed sequences are complete while ignoring the potential for missing values caused by object occlusion, scope limitation, sensor failure, etc. This limitation inevitably hinders the accuracy of trajectory prediction. To address this issue, our paper presents a unified framework, the Graph-based Conditional Variational Recurrent Neural Network (GC-VRNN), which can perform trajectory imputation and prediction simultaneously. Specifically, we introduce a novel Multi-Space Graph Neural Network (MS-GNN) that can extract spatial features from incomplete observations and leverage missing patterns. Additionally, we employ a Conditional VRNN with a specifically designed Temporal Decay (TD) module to capture temporal dependencies and temporal missing patterns in incomplete trajectories. The inclusion of the TD module allows for valuable information to be conveyed through the temporal flow. We also curate and benchmark three practical datasets for the joint problem of trajectory imputation and prediction. Extensive experiments verify the exceptional performance of our proposed method. As far as we know, this is the first work to address the lack of benchmarks and techniques for trajectory imputation and prediction in a unified manner.Comment: Accepted by CVPR 2023, Supplementary Material at https://github.com/colorfulfuture/GC-VRN

    Disentangled Graph Social Recommendation

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    Social recommender systems have drawn a lot of attention in many online web services, because of the incorporation of social information between users in improving recommendation results. Despite the significant progress made by existing solutions, we argue that current methods fall short in two limitations: (1) Existing social-aware recommendation models only consider collaborative similarity between items, how to incorporate item-wise semantic relatedness is less explored in current recommendation paradigms. (2) Current social recommender systems neglect the entanglement of the latent factors over heterogeneous relations (e.g., social connections, user-item interactions). Learning the disentangled representations with relation heterogeneity poses great challenge for social recommendation. In this work, we design a Disentangled Graph Neural Network (DGNN) with the integration of latent memory units, which empowers DGNN to maintain factorized representations for heterogeneous types of user and item connections. Additionally, we devise new memory-augmented message propagation and aggregation schemes under the graph neural architecture, allowing us to recursively distill semantic relatedness into the representations of users and items in a fully automatic manner. Extensive experiments on three benchmark datasets verify the effectiveness of our model by achieving great improvement over state-of-the-art recommendation techniques. The source code is publicly available at: https://github.com/HKUDS/DGNN.Comment: Accepted by IEEE ICDE 202

    Factor Graph Neural Networks

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    In recent years, we have witnessed a surge of Graph Neural Networks (GNNs), most of which can learn powerful representations in an end-to-end fashion with great success in many real-world applications. They have resemblance to Probabilistic Graphical Models (PGMs), but break free from some limitations of PGMs. By aiming to provide expressive methods for representation learning instead of computing marginals or most likely configurations, GNNs provide flexibility in the choice of information flowing rules while maintaining good performance. Despite their success and inspirations, they lack efficient ways to represent and learn higher-order relations among variables/nodes. More expressive higher-order GNNs which operate on k-tuples of nodes need increased computational resources in order to process higher-order tensors. We propose Factor Graph Neural Networks (FGNNs) to effectively capture higher-order relations for inference and learning. To do so, we first derive an efficient approximate Sum-Product loopy belief propagation inference algorithm for discrete higher-order PGMs. We then neuralize the novel message passing scheme into a Factor Graph Neural Network (FGNN) module by allowing richer representations of the message update rules; this facilitates both efficient inference and powerful end-to-end learning. We further show that with a suitable choice of message aggregation operators, our FGNN is also able to represent Max-Product belief propagation, providing a single family of architecture that can represent both Max and Sum-Product loopy belief propagation. Our extensive experimental evaluation on synthetic as well as real datasets demonstrates the potential of the proposed model.Comment: Accepted by JML

    Mining Butterflies in Streaming Graphs

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    This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection. sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals
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