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Probabilistic forecasting relies on past observations to provide a probability distribution for a future outcome, which is often evaluated against the realization using a scoring rule. Here, we perform probabilistic forecasting with…

Machine Learning · Statistics 2024-03-06 Lorenzo Pacchiardi , Rilwan Adewoyin , Peter Dueben , Ritabrata Dutta

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

Machine Learning · Statistics 2016-06-03 Jinghui Chen , Quanquan Gu

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…

Machine Learning · Statistics 2019-11-01 Jayaraman J. Thiagarajan , Bindya Venkatesh , Deepta Rajan

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

Methodology · Statistics 2021-08-27 Ioannis Kalogridis , Stefan Van Aelst

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…

Numerical Analysis · Mathematics 2025-04-03 Nir Sharon , Vinesha Peiris , Nadia Sukhorukova , Julien Ugon

We introduce the dispersion models with a regression structure to extend the generalized linear models, the exponential family nonlinear models (Cordeiro and Paula, 1989) and the proper dispersion models (J{\o}rgensen, 1997a). We provide a…

Methodology · Statistics 2010-03-23 Alexandre B. Simas , Gauss M. Cordeiro , Andréa V. Rocha

This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…

Statistics Theory · Mathematics 2015-05-21 Shota Katayama , Hironori Fujisawa

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…

Statistics Theory · Mathematics 2014-05-06 Piero Barone , Isabella Lari

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…

Statistics Theory · Mathematics 2016-11-21 Ashwini Maurya

Consider the problem of simultaneous estimation of location and variance matrix under Huber's contaminated Gaussian model. First, we study minimum $f$-divergence estimation at the population level, corresponding to a generative adversarial…

Statistics Theory · Mathematics 2022-08-09 Ziyue Wang , Zhiqiang Tan

This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems $Bx = b$ with positive definite $B$ for $x$. The goal is to replace the point estimates returned by existing methods with…

Optimization and Control · Mathematics 2014-10-16 Philipp Hennig

Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable…

Social and Information Networks · Computer Science 2023-08-16 Zheng Zhai , Hengchao Chen , Qiang Sun

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

Machine Learning · Statistics 2016-09-27 Ethan X. Fang , Han Liu , Kim-Chuan Toh , Wen-Xin Zhou

Accurate prediction of user consumption is a key part not only in understanding consumer flexibility and behavior patterns, but in the design of robust and efficient energy saving programs as well. Existing prediction methods usually have…

Machine Learning · Statistics 2017-02-22 Pan Li , Baosen Zhang , Yang Weng , Ram Rajagopal

We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the…

Machine Learning · Statistics 2016-06-20 Boram Yoon

We consider estimation of undirected Gaussian graphical models and inverse covariances in high-dimensional scenarios by penalizing the corresponding precision matrix. While single $L_1$ (Graphical Lasso) and $L_2$ (Graphical Ridge)…

Methodology · Statistics 2021-01-07 Solt Kovács , Tobias Ruckstuhl , Helena Obrist , Peter Bühlmann

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…

Statistics Theory · Mathematics 2013-11-11 Li Zhang

Estimator algorithms in learning automata are useful tools for adaptive, real-time optimization in computer science and engineering applications. This paper investigates theoretical convergence properties for a special case of estimator…

Machine Learning · Computer Science 2012-09-28 Ryan Martin , Omkar Tilak

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao