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Tag: mean

  • Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data

    Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data arXiv:2602.23602v1 Announce Type: new Abstract: Heteroscedasticity — where the variance of a variable changes with other variables — is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and decision-making. However,…

  • On the Effect of Regularization on Nonparametric Mean-Variance Regression

    On the Effect of Regularization on Nonparametric Mean-Variance Regression arXiv:2511.22004v1 Announce Type: new Abstract: Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty quantification. However, overparameterized mean-variance models struggle with signal-to-noise…

  • Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games

    Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games arXiv:2505.22781v1 Announce Type: new Abstract: We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established performance of TRPO in the reinforcement learning (RL) setting,…

  • A Dictionary of Closed-Form Kernel Mean Embeddings

    A Dictionary of Closed-Form Kernel Mean Embeddings arXiv:2504.18830v1 Announce Type: new Abstract: Kernel mean embeddings — integrals of a kernel with respect to a probability distribution — are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference based on the maximum mean discrepancy. These methods…

  • Learning Enhanced Ensemble Filters

    Learning Enhanced Ensemble Filters arXiv:2504.17836v1 Announce Type: new Abstract: The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state–observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting particles, employing a Gaussian ansatz for the joint distribution of the state and…

  • Propagation of Chaos in One-hidden-layer Neural Networks beyond Logarithmic Time

    Propagation of Chaos in One-hidden-layer Neural Networks beyond Logarithmic Time arXiv:2504.13110v1 Announce Type: new Abstract: We study the approximation gap between the dynamics of a polynomial-width neural network and its infinite-width counterpart, both trained using projected gradient descent in the mean-field scaling regime. We demonstrate how to tightly bound this approximation gap through a differential…

  • Weighted quantization using MMD: From mean field to mean shift via gradient flows

    Weighted quantization using MMD: From mean field to mean shift via gradient flows arXiv:2502.10600v1 Announce Type: new Abstract: Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a finite weighted mixture of Dirac measures that best approximates…

  • Testing Conditional Mean Independence Using Generative Neural Networks

    Testing Conditional Mean Independence Using Generative Neural Networks arXiv:2501.17345v1 Announce Type: new Abstract: Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure that utilizes deep generative neural networks to estimate the conditional…

  • Deep Generalized Schr”odinger Bridges: From Image Generation to Solving Mean-Field Games

    Deep Generalized Schr”odinger Bridges: From Image Generation to Solving Mean-Field Games arXiv:2412.20279v1 Announce Type: new Abstract: Generalized Schr”odinger Bridges (GSBs) are a fundamental mathematical framework used to analyze the most likely particle evolution based on the principle of least action including kinetic and potential energy. In parallel to their well-established presence in the theoretical realms…