2,494 research outputs found

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

    Get PDF
    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

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Game-theoretic statistics and safe anytime-valid inference

    Full text link
    Safe anytime-valid inference (SAVI) provides measures of statistical evidence and certainty -- e-processes for testing and confidence sequences for estimation -- that remain valid at all stopping times, accommodating continuous monitoring and analysis of accumulating data and optional stopping or continuation for any reason. These measures crucially rely on test martingales, which are nonnegative martingales starting at one. Since a test martingale is the wealth process of a player in a betting game, SAVI centrally employs game-theoretic intuition, language and mathematics. We summarize the SAVI goals and philosophy, and report recent advances in testing composite hypotheses and estimating functionals in nonparametric settings.Comment: 25 pages. Under review. ArXiv does not compile/space some references properl

    Adaptive Robotic Information Gathering via Non-Stationary Gaussian Processes

    Full text link
    Robotic Information Gathering (RIG) is a foundational research topic that answers how a robot (team) collects informative data to efficiently build an accurate model of an unknown target function under robot embodiment constraints. RIG has many applications, including but not limited to autonomous exploration and mapping, 3D reconstruction or inspection, search and rescue, and environmental monitoring. A RIG system relies on a probabilistic model's prediction uncertainty to identify critical areas for informative data collection. Gaussian Processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data is typically non-stationary -- different locations do not have the same degree of variability. As a result, the prediction uncertainty does not accurately reveal prediction error, limiting the success of RIG algorithms. We propose a family of non-stationary kernels named Attentive Kernel (AK), which is simple, robust, and can extend any existing kernel to a non-stationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used stationary kernels and the leading non-stationary kernels. The improved uncertainty quantification guides the downstream informative planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features.Comment: International Journal of Robotics Research (IJRR). arXiv admin note: text overlap with arXiv:2205.0642

    Spatio-Temporal Wildfire Prediction using Multi-Modal Data

    Full text link
    Due to severe societal and environmental impacts, wildfire prediction using multi-modal sensing data has become a highly sought-after data-analytical tool by various stakeholders (such as state governments and power utility companies) to achieve a more informed understanding of wildfire activities and plan preventive measures. A desirable algorithm should precisely predict fire risk and magnitude for a location in real time. In this paper, we develop a flexible spatio-temporal wildfire prediction framework using multi-modal time series data. We first predict the wildfire risk (the chance of a wildfire event) in real-time, considering the historical events using discrete mutually exciting point process models. Then we further develop a wildfire magnitude prediction set method based on the flexible distribution-free time-series conformal prediction (CP) approach. Theoretically, we prove a risk model parameter recovery guarantee, as well as coverage and set size guarantees for the CP sets. Through extensive real-data experiments with wildfire data in California, we demonstrate the effectiveness of our methods, as well as their flexibility and scalability in large regions

    When Deep Learning Meets Polyhedral Theory: A Survey

    Full text link
    In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure of neural networks converged back to simpler representations based on piecewise constant and piecewise linear functions such as the Rectified Linear Unit (ReLU), which became the most commonly used type of activation function in neural networks. That made certain types of network structure \unicode{x2014}such as the typical fully-connected feedforward neural network\unicode{x2014} amenable to analysis through polyhedral theory and to the application of methodologies such as Linear Programming (LP) and Mixed-Integer Linear Programming (MILP) for a variety of purposes. In this paper, we survey the main topics emerging from this fast-paced area of work, which bring a fresh perspective to understanding neural networks in more detail as well as to applying linear optimization techniques to train, verify, and reduce the size of such networks

    AI: Limits and Prospects of Artificial Intelligence

    Get PDF
    The emergence of artificial intelligence has triggered enthusiasm and promise of boundless opportunities as much as uncertainty about its limits. The contributions to this volume explore the limits of AI, describe the necessary conditions for its functionality, reveal its attendant technical and social problems, and present some existing and potential solutions. At the same time, the contributors highlight the societal and attending economic hopes and fears, utopias and dystopias that are associated with the current and future development of artificial intelligence

    Adaptive novelty detection with false discovery rate guarantee

    Full text link
    This paper studies the semi-supervised novelty detection problem where a set of "typical" measurements is available to the researcher. Motivated by recent advances in multiple testing and conformal inference, we propose AdaDetect, a flexible method that is able to wrap around any probabilistic classification algorithm and control the false discovery rate (FDR) on detected novelties in finite samples without any distributional assumption other than exchangeability. In contrast to classical FDR-controlling procedures that are often committed to a pre-specified p-value function, AdaDetect learns the transformation in a data-adaptive manner to focus the power on the directions that distinguish between inliers and outliers. Inspired by the multiple testing literature, we further propose variants of AdaDetect that are adaptive to the proportion of nulls while maintaining the finite-sample FDR control. The methods are illustrated on synthetic datasets and real-world datasets, including an application in astrophysics

    On the View-and-Channel Aggregation Gain in Integrated Sensing and Edge AI

    Full text link
    Sensing and edge artificial intelligence (AI) are two key features of the sixth-generation (6G) mobile networks. Their natural integration, termed Integrated sensing and edge AI (ISEA), is envisioned to automate wide-ranging Internet-of-Tings (IoT) applications. To achieve a high sensing accuracy, multi-view features are uploaded to an edge server for aggregation and inference using an AI model. The view aggregation is realized efficiently using over-the-air computing (AirComp), which also aggregates channels to suppress channel noise. At its nascent stage, ISEA still lacks a characterization of the fundamental performance gains from view-and-channel aggregation, which motivates this work. Our framework leverages a well-established distribution model of multi-view sensing data where the classic Gaussian-mixture model is modified by adding sub-spaces matrices to represent individual sensor observation perspectives. Based on the model, we study the End-to-End sensing (inference) uncertainty, a popular measure of inference accuracy, of the said ISEA system by a novel approach involving designing a scaling-tight uncertainty surrogate function, global discriminant gain, distribution of receive Signal-to-Noise Ratio (SNR), and channel induced discriminant loss. We prove that the E2E sensing uncertainty diminishes at an exponential rate as the number of views/sensors grows, where the rate is proportional to global discriminant gain. Given channel distortion, we further show that the exponential scaling remains with a reduced decay rate related to the channel induced discriminant loss. Furthermore, we benchmark AirComp against equally fast, traditional analog orthogonal access, which reveals a sensing-accuracy crossing point between the schemes, leading to the proposal of adaptive access-mode switching. Last, the insights from our framework are validated by experiments using real-world dataset.Comment: 13 pages, 8 figure
    • …
    corecore