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Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard…

Optimization and Control · Mathematics 2024-03-26 Zifan Wang , Yulong Gao , Siyi Wang , Michael M. Zavlanos , Alessandro Abate , Karl H. Johansson

Random Matrix Theory (RMT) is applied to analyze weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5…

Machine Learning · Computer Science 2018-10-03 Charles H. Martin , Michael W. Mahoney

Richardson extrapolation is a classical technique from numerical analysis that can improve the approximation error of an estimation method by combining linearly several estimates obtained from different values of one of its hyperparameters,…

Machine Learning · Computer Science 2020-07-20 Francis Bach

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…

Machine Learning · Statistics 2018-10-29 Mikhail Belkin , Daniel Hsu , Partha Mitra

We introduce the concept of coverage risk as an error measure for density ridge estimation. The coverage risk generalizes the mean integrated square error to set estimation. We propose two risk estimators for the coverage risk and we show…

Methodology · Statistics 2015-06-09 Yen-Chi Chen , Christopher R. Genovese , Shirley Ho , Larry Wasserman

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted on account of the risk of `variational collapse' down to the…

We present a rigorous asymptotic analysis of Echo State Networks (ESNs) in a teacher student setting with a linear teacher with oracle weights. Leveraging random matrix theory, we derive closed form expressions for the asymptotic bias,…

Machine Learning · Statistics 2025-09-29 Yessin Moakher , Malik Tiomoko , Cosme Louart , Zhenyu Liao

Based on our \bl{\textbf{Random Duality Theory (RDT)}}, in a sequence of our recent papers \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19}, we introduced a powerful algorithmic mechanism (called \bl{\textbf{CLuP}}) that can be…

Information Theory · Computer Science 2020-11-24 Mihailo Stojnic

We study the econometric properties of so-called donut regression discontinuity (RD) designs, a robustness exercise which involves repeating estimation and inference without the data points in some area around the treatment threshold. This…

Econometrics · Economics 2023-08-29 Cladia Noack , Chistoph Rothe

General ridge estimators are widely used in the general linear model because they possess desirable properties such as linear sufficiency and linear admissibility. However, when the covariance matrix of the error term is partially unknown,…

Statistics Theory · Mathematics 2026-01-27 Hirai Mukasa

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

Statistics Theory · Mathematics 2024-10-11 Zifeng Zhang , Peng Ding , Wen Zhou , Haonan Wang

We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic…

Statistics Theory · Mathematics 2023-08-15 Zhichao Wang , Yizhe Zhu

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

Methodology · Statistics 2026-01-12 Kaiyuan Zhou , Xiaoyu Zhang , Wenyang Zhang , Di Wang

Tensor-on-tensor (TOT) regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard TOT regression is sensitive to outliers,…

Methodology · Statistics 2026-03-30 Mehdi Hirari , Fabio Centofanti , Mia Hubert , Stefan Van Aelst

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…

Statistics Theory · Mathematics 2016-10-24 Zoltan Szabo , Bharath Sriperumbudur , Barnabas Poczos , Arthur Gretton

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard RL. At the…

Optimization and Control · Mathematics 2023-03-27 Zifan Wang , Yulong Gao , Siyi Wang , Michael M. Zavlanos , Alessandro Abate , Karl H. Johansson

Inverse reinforcement learning (IRL) is typically formulated as maximizing entropy subject to matching the distribution of expert trajectories. Classical (dual-ascent) IRL guarantees monotonic performance improvement but requires fully…

Machine Learning · Computer Science 2026-05-13 Anish Diwan , Davide Tateo , Christopher E. Mower , Haitham Bou-Ammar , Jan Peters , Oleg Arenz

The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for…

Machine Learning · Computer Science 2021-06-22 Masahiro Kato , Shota Yasui , Kenichiro McAlinn

This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…

Probability · Mathematics 2018-12-21 Ruben G. Ascoli

The probabilistic diffusion model (DM), generating content by inferencing through a recursive chain structure, has emerged as a powerful framework for visual generation. After pre-training on enormous data, the model needs to be properly…

Computer Vision and Pattern Recognition · Computer Science 2025-09-30 Tao Ren , Zishi Zhang , Jingyang Jiang , Zehao Li , Shentao Qin , Yi Zheng , Guanghao Li , Qianyou Sun , Yan Li , Jiafeng Liang , Xinping Li , Yijie Peng