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Tag: gaussian

  • Quantifying Normality: Convergence Rate to Gaussian Limit for Stochastic Approximation and Unadjusted OU Algorithm

    Quantifying Normality: Convergence Rate to Gaussian Limit for Stochastic Approximation and Unadjusted OU Algorithm arXiv:2602.13906v1 Announce Type: new Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these asymptotic…

  • Gaussian Process Assisted Meta-learning for Image Classification and Object Detection Models

    Gaussian Process Assisted Meta-learning for Image Classification and Object Detection Models arXiv:2512.20021v1 Announce Type: new Abstract: Collecting operationally realistic data to inform machine learning models can be costly. Before collecting new data, it is helpful to understand where a model is deficient. For example, object detectors trained on images of rare objects may not be…

  • Feature Detection, Part 2: Laplace & Gaussian Operators

    Feature Detection, Part 2: Laplace & Gaussian Operators Laplace meets Gaussian — the story of two operators in edge detection The post Feature Detection, Part 2: Laplace & Gaussian Operators appeared first on Towards Data Science. Vyacheslav Efimov Go to original source

  • Simplicial Gaussian Models: Representation and Inference

    Simplicial Gaussian Models: Representation and Inference arXiv:2510.12983v1 Announce Type: new Abstract: Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial Gaussian model (SGM), which extends Gaussian PGM to simplicial complexes. SGM jointly models random…

  • Gaussian Certified Unlearning in High Dimensions: A Hypothesis Testing Approach

    Gaussian Certified Unlearning in High Dimensions: A Hypothesis Testing Approach arXiv:2510.13094v1 Announce Type: new Abstract: Machine unlearning seeks to efficiently remove the influence of selected data while preserving generalization. Significant progress has been made in low dimensions $(p ll n)$, but high dimensions pose serious theoretical challenges as standard optimization assumptions of $Omega(1)$ strong convexity…

  • Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix

    Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix arXiv:2510.06685v1 Announce Type: new Abstract: Self-attention layers have become fundamental building blocks of modern deep neural networks, yet their theoretical understanding remains limited, particularly from the perspective of random matrix theory. In this work, we provide a rigorous analysis of the singular value spectrum of…

  • On the Rate of Gaussian Approximation for Linear Regression Problems

    On the Rate of Gaussian Approximation for Linear Regression Problems arXiv:2509.14039v1 Announce Type: new Abstract: In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the…

  • Implementing the Gaussian Challenge in Python

    Implementing the Gaussian Challenge in Python Beginner-friendly tutorial to understand range function and Python loops The post Implementing the Gaussian Challenge in Python appeared first on Towards Data Science. Mahnoor Javed Go to original source

  • Uniform convergence for Gaussian kernel ridge regression

    Uniform convergence for Gaussian kernel ridge regression arXiv:2508.11274v1 Announce Type: new Abstract: This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical understanding of KRR with the Gaussian kernel, where…

  • Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling

    Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling arXiv:2508.10782v1 Announce Type: new Abstract: We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms — including gradient-based optimization methods and approximate message passing (AMP) — with Gaussian data matrices and full-memory, non-separable nonlinearities. The central result constructs an explicit coupling between the…

  • LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process

    LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process arXiv:2507.22493v1 Announce Type: new Abstract: We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the input to a high-dimensional…

  • Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights

    Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights arXiv:2507.12686v1 Announce Type: new Abstract: We study the Finite-Dimensional Distributions (FDDs) of deep neural networks with randomly initialized weights that have finite-order moments. Specifically, we establish Gaussian approximation bounds in the Wasserstein-$1$ norm between the FDDs and their Gaussian limit assuming a Lipschitz activation…

  • Determination of Particle-Size Distributions from Light-Scattering Measurement Using Constrained Gaussian Process Regression

    Determination of Particle-Size Distributions from Light-Scattering Measurement Using Constrained Gaussian Process Regression arXiv:2507.03736v1 Announce Type: new Abstract: In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly formulated as a Fredholm integral equation of…

  • Gaussian Processes and Reproducing Kernels: Connections and Equivalences

    Gaussian Processes and Reproducing Kernels: Connections and Equivalences arXiv:2506.17366v1 Announce Type: new Abstract: This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences…

  • The Currents of Conflict: Decomposing Conflict Trends with Gaussian Processes

    The Currents of Conflict: Decomposing Conflict Trends with Gaussian Processes arXiv:2506.06828v1 Announce Type: new Abstract: I present a novel approach to estimating the temporal and spatial patterns of violent conflict. I show how we can use highly temporally and spatially disaggregated data on conflict events in tandem with Gaussian processes to estimate temporospatial conflict trends.…

  • Distributional encoding for Gaussian process regression with qualitative inputs

    Distributional encoding for Gaussian process regression with qualitative inputs arXiv:2506.04813v1 Announce Type: new Abstract: Gaussian Process (GP) regression is a popular and sample-efficient approach for many engineering applications, where observations are expensive to acquire, and is also a central ingredient of Bayesian optimization (BO), a highly prevailing method for the optimization of black-box functions. However,…

  • Sharp Gaussian approximations for Decentralized Federated Learning

    Sharp Gaussian approximations for Decentralized Federated Learning arXiv:2505.08125v1 Announce Type: new Abstract: Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation…

  • From Two Sample Testing to Singular Gaussian Discrimination

    From Two Sample Testing to Singular Gaussian Discrimination arXiv:2505.04613v1 Announce Type: new Abstract: We establish that testing for the equality of two probability measures on a general separable and compact metric space is equivalent to testing for the singularity between two corresponding Gaussian measures on a suitable Reproducing Kernel Hilbert Space. The corresponding Gaussians are…

  • Sparse Gaussian Neural Processes

    Sparse Gaussian Neural Processes arXiv:2504.01650v1 Announce Type: new Abstract: Despite significant recent advances in probabilistic meta-learning, it is common for practitioners to avoid using deep learning models due to a comparative lack of interpretability. Instead, many practitioners simply use non-meta-models such as Gaussian processes with interpretable priors, and conduct the tedious procedure of training their…

  • Feature learning from non-Gaussian inputs: the case of Independent Component Analysis in high dimensions

    Feature learning from non-Gaussian inputs: the case of Independent Component Analysis in high dimensions arXiv:2503.23896v1 Announce Type: new Abstract: Deep neural networks learn structured features from complex, non-Gaussian inputs, but the mechanisms behind this process remain poorly understood. Our work is motivated by the observation that the first-layer filters learnt by deep convolutional neural networks…

  • Rolled Gaussian process models for curves on manifolds

    Rolled Gaussian process models for curves on manifolds arXiv:2503.21980v1 Announce Type: cross Abstract: Given a planar curve, imagine rolling a sphere along that curve without slipping or twisting, and by this means tracing out a curve on the sphere. It is well known that such a rolling operation induces a local isometry between the sphere…

  • Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions

    Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions arXiv:2503.16580v1 Announce Type: new Abstract: We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This distance is defined by penalizing…

  • Support Collapse of Deep Gaussian Processes with Polynomial Kernels for a Wide Regime of Hyperparameters

    Support Collapse of Deep Gaussian Processes with Polynomial Kernels for a Wide Regime of Hyperparameters arXiv:2503.12266v1 Announce Type: new Abstract: We analyze the prior that a Deep Gaussian Process with polynomial kernels induces. We observe that, even for relatively small depths, averaging effects occur within such a Deep Gaussian Process and that the prior can…

  • Exploiting Concavity Information in Gaussian Process Contextual Bandit Optimization

    Exploiting Concavity Information in Gaussian Process Contextual Bandit Optimization arXiv:2503.10836v1 Announce Type: new Abstract: The contextual bandit framework is widely used to solve sequential optimization problems where the reward of each decision depends on auxiliary context variables. In settings such as medicine, business, and engineering, the decision maker often possesses additional structural information on the…

  • Near-Optimal Approximations for Bayesian Inference in Function Space

    Near-Optimal Approximations for Bayesian Inference in Function Space arXiv:2502.18279v1 Announce Type: new Abstract: We propose a scalable inference algorithm for Bayes posteriors defined on a reproducing kernel Hilbert space (RKHS). Given a likelihood function and a Gaussian random element representing the prior, the corresponding Bayes posterior measure $Pi_{text{B}}$ can be obtained as the stationary distribution…

  • LITE: Efficiently Estimating Gaussian Probability of Maximality

    LITE: Efficiently Estimating Gaussian Probability of Maximality arXiv:2501.13535v1 Announce Type: new Abstract: We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not…

  • Fast Multi-Group Gaussian Process Factor Models

    Fast Multi-Group Gaussian Process Factor Models arXiv:2412.16773v1 Announce Type: new Abstract: Gaussian processes are now commonly used in dimensionality reduction approaches tailored to neuroscience, especially to describe changes in high-dimensional neural activity over time. As recording capabilities expand to include neuronal populations across multiple brain areas, cortical layers, and cell types, interest in extending Gaussian…

  • Learning from Summarized Data: Gaussian Process Regression with Sample Quasi-Likelihood

    Learning from Summarized Data: Gaussian Process Regression with Sample Quasi-Likelihood arXiv:2412.17455v1 Announce Type: new Abstract: Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit from this development. Difficulties still arise…

  • Nonlinearity and Uncertainty Informed Moment-Matching Gaussian Mixture Splitting

    Nonlinearity and Uncertainty Informed Moment-Matching Gaussian Mixture Splitting arXiv:2412.00343v1 Announce Type: new Abstract: Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations offer distinct advantages over sampling based methods in their computational cost and continuous representation.…

  • Intrinsic Wrapped Gaussian Process Regression Modeling for Manifold-valued Response Variable

    Intrinsic Wrapped Gaussian Process Regression Modeling for Manifold-valued Response Variable arXiv:2411.18989v1 Announce Type: new Abstract: In this paper, we propose a novel intrinsic wrapped Gaussian process regression model for response variable measured on Riemannian manifold. We apply the parallel transport operator to define an intrinsic covariance structure addressing a critical aspect of constructing a well…