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Tag: nonlinear

  • Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions

    Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions arXiv:2512.06615v1 Announce Type: new Abstract: We present latent nonlinear denoising score matching (LNDSM), a novel training objective for score-based generative models that integrates nonlinear forward dynamics with the VAE-based latent SGM framework. This combination is achieved by reformulating the cross-entropy term using the approximate…

  • Decoding Nonlinear Signals In Large Observational Datasets

    Decoding Nonlinear Signals In Large Observational Datasets Rain, snow, or something In between? The post Decoding Nonlinear Signals In Large Observational Datasets appeared first on Towards Data Science. Fraser King Go to original source

  • Optimal High-probability Convergence of Nonlinear SGD under Heavy-tailed Noise via Symmetrization

    Optimal High-probability Convergence of Nonlinear SGD under Heavy-tailed Noise via Symmetrization arXiv:2507.09093v1 Announce Type: new Abstract: We study convergence in high-probability of SGD-type methods in non-convex optimization and the presence of heavy-tailed noise. To combat the heavy-tailed noise, a general black-box nonlinear framework is considered, subsuming nonlinearities like sign, clipping, normalization and their smooth counterparts.…

  • Nonlinear Causal Discovery through a Sequential Edge Orientation Approach

    Nonlinear Causal Discovery through a Sequential Edge Orientation Approach arXiv:2506.05590v1 Announce Type: new Abstract: Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model assumptions, rely heavily on general independence tests, or require…

  • Nonlinear Causal Discovery for Grouped Data

    Nonlinear Causal Discovery for Grouped Data arXiv:2506.05120v1 Announce Type: new Abstract: Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social science, and industrial manufacturing, the causal units of interest are groups of variables rather…

  • Optimal Nonlinear Online Learning under Sequential Price Competition via s-Concavity

    Optimal Nonlinear Online Learning under Sequential Price Competition via s-Concavity arXiv:2503.16737v1 Announce Type: new Abstract: We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices and subsequently observe their respective demand that is unobservable to competitors. The demand function for each seller depends…

  • Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling

    Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling arXiv:2503.15160v1 Announce Type: new Abstract: Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is first denoised via a standard Kalman update,…

  • Nonlinear Principal Component Analysis with Random Bernoulli Features for Process Monitoring

    Nonlinear Principal Component Analysis with Random Bernoulli Features for Process Monitoring arXiv:2503.12456v1 Announce Type: new Abstract: The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel matrices. This dependence poses significant challenges in…

  • LNUCB-TA: Linear-nonlinear Hybrid Bandit Learning with Temporal Attention

    LNUCB-TA: Linear-nonlinear Hybrid Bandit Learning with Temporal Attention arXiv:2503.00387v1 Announce Type: new Abstract: Existing contextual multi-armed bandit (MAB) algorithms fail to effectively capture both long-term trends and local patterns across all arms, leading to suboptimal performance in environments with rapidly changing reward structures. They also rely on static exploration rates, which do not dynamically adjust…

  • Fr’echet Cumulative Covariance Net for Deep Nonlinear Sufficient Dimension Reduction with Random Objects

    Fr’echet Cumulative Covariance Net for Deep Nonlinear Sufficient Dimension Reduction with Random Objects arXiv:2502.15374v1 Announce Type: new Abstract: Nonlinear sufficient dimension reductioncitep{libing_generalSDR}, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning. However, most existing methods are not applicable when the response variables are complex non-Euclidean…

  • Proximal Iteration for Nonlinear Adaptive Lasso

    Proximal Iteration for Nonlinear Adaptive Lasso arXiv:2412.05726v1 Announce Type: new Abstract: Augmenting a smooth cost function with an $ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods. However, one drawback of the $ell_1$ penalty is bias: nonzero parameters are underestimated…