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Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional…

Probability · Mathematics 2024-06-06 Yuan Fang , Zhongquan Tan

In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no…

Computation · Statistics 2017-07-26 Jorge Alberto Achcar , Pedro Luiz Ramos , Edson Zangiacomi Martinez

Since the pioneering work of Gerhard Gruss dating back to 1935, Gruss's inequality and, more generally, Gruss-type bounds for covariances have fascinated researchers and found numerous applications in areas such as economics, insurance,…

Probability · Mathematics 2010-10-28 Martin Egozcue , Luis Fuentes Garcia , Wing-Keung Wong , Ricardas Zitikis

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…

Machine Learning · Computer Science 2022-11-03 Dragana Bajovic , Dusan Jakovetic , Soummya Kar

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an ``optimal'' predicted outcome distribution according to some…

Econometrics · Economics 2025-05-29 Anders Bredahl Kock , David Preinerstorfer

In this work, we unify several expected generalization error bounds based on random subsets using the framework developed by Hellstr\"om and Durisi [1]. First, we recover the bounds based on the individual sample mutual information from Bu…

Information Theory · Computer Science 2021-07-27 Borja Rodríguez-Gálvez , Germán Bassi , Ragnar Thobaben , Mikael Skoglund

Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex…

Optimization and Control · Mathematics 2020-07-27 Ahmed Khaled , Peter Richtárik

We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the…

Machine Learning · Computer Science 2021-08-17 Gergely Neu , Gintare Karolina Dziugaite , Mahdi Haghifam , Daniel M. Roy

In this paper, we propose a distributed algorithm, called Directed-Distributed Gradient Descent (D-DGD), to solve multi-agent optimization problems over directed graphs. Existing algorithms mostly deal with similar problems under the…

Optimization and Control · Mathematics 2016-02-02 Chenguang Xi , Qiong Wu , Usman A. Khan

Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call---among others---for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to…

Optimization and Control · Mathematics 2018-08-24 Tillmann Mühlpfordt , Timm Faulwasser , Veit Hagenmeyer

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

Statistics Theory · Mathematics 2020-12-15 Banghua Zhu , Jiantao Jiao , Jacob Steinhardt

Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and…

Methodology · Statistics 2022-05-25 Lucas Kook , Beate Sick , Peter Bühlmann

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of…

Optimization and Control · Mathematics 2014-07-18 Domenico Quagliarella , Giovanni Petrone , Gianluca Iaccarino

Bayesian classification labels observations based on given prior information, namely class-a priori and class-conditional probabilities. Bayes' risk is the minimum expected classification cost that is achieved by the Bayes' test, the…

Computer Vision and Pattern Recognition · Computer Science 2023-03-07 Frank Nielsen

We establish matching upper and lower generalization error bounds for mini-batch Gradient Descent (GD) training with either deterministic or stochastic, data-independent, but otherwise arbitrary batch selection rules. We consider smooth…

Machine Learning · Computer Science 2023-10-24 Konstantinos E. Nikolakakis , Amin Karbasi , Dionysis Kalogerias

Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected…

Risk Management · Quantitative Finance 2017-02-12 Anulekha Dhara , Bikramjit Das , Karthik Natarajan

Deep generative models (DGMs) seem a natural fit for detecting out-of-distribution (OOD) inputs, but such models have been shown to assign higher probabilities or densities to OOD images than images from the training distribution. In this…

Machine Learning · Computer Science 2021-07-20 Lily H. Zhang , Mark Goldstein , Rajesh Ranganath

As the unification of various models of ordered quantities, generalized order statistics act as a simplistic approach introduced in \cite{kamps1995concept}. In this present study, results pertaining to the expressions of marginal and joint…

Methodology · Statistics 2025-02-04 Neetu Gupta , S. K. Neogy , Qazi J. Azhad , Bhagwati Devi

We consider the high order moments estimator of the frontier of a random pair introduced by Girard, S., Guillou, A., Stupfler, G. (2012). {\it Frontier estimation with kernel regression on high order moments}. In the present paper, we show…

Statistics Theory · Mathematics 2013-07-17 Stephane Girard , Armelle Guillou , Gilles Stupfler