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A novel 2-D method for computing the convex hull of a sufficiently dense set of n integer points is introduced. The approach employs a ranking function that avoids sorting the points directly thus reducing the overall time complexity. The…

Computational Geometry · Computer Science 2013-01-22 G. M. Megson , J. Cadenas

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…

Optimization and Control · Mathematics 2022-09-20 Francesco Micheli , Tyler Summers , John Lygeros

In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…

Statistics Theory · Mathematics 2018-04-16 Anatoli Juditsky , Arkadi Nemirovski

Stochastic gradient descent (SGD) is the workhorse of modern machine learning. Sometimes, there are many different potential gradient estimators that can be used. When so, choosing the one with the best tradeoff between cost and variance is…

Machine Learning · Computer Science 2020-10-23 Tomas Geffner , Justin Domke

We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…

Statistics Theory · Mathematics 2022-03-03 Bernard Bercu , Jérémie Bigot , Sébastien Gadat , Emilia Siviero

Statistical Shape Modeling (SSM) is a valuable tool for investigating and quantifying anatomical variations within populations of anatomies. However, traditional correspondence-based SSM generation methods have a prohibitive inference…

Computer Vision and Pattern Recognition · Computer Science 2023-07-21 Jadie Adams , Shireen Elhabian

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of…

Computational Geometry · Computer Science 2017-05-02 Jie Xue , Yuan Li , Ravi Janardan

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…

Machine Learning · Statistics 2022-06-08 Michał Dereziński , Manfred K. Warmuth , Daniel Hsu

We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…

Statistics Theory · Mathematics 2021-03-16 Darinka Dentcheva , Yang Lin

Recently, direct data-driven prediction has found important applications for controlling unknown systems, particularly in predictive control. Such an approach provides exact prediction using behavioral system theory when noise-free data are…

Systems and Control · Electrical Eng. & Systems 2023-03-20 Mingzhou Yin , Andrea Iannelli , Roy S. Smith

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…

Applications · Statistics 2022-02-01 George V. Moustakides

In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In…

Machine Learning · Statistics 2021-05-17 Yueqi Cao , Didong Li , Huafei Sun , Amir H Assadi , Shiqiang Zhang

This article presents a novel method to sampling on manifolds based on the Dirichlet distribution. The proposed strategy allows to completely respect the underlying manifold around which data is observed, and to do massive samplings with…

Machine Learning · Statistics 2021-08-13 Luan S Prado , Thiago G Ritto

In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a…

Statistics Theory · Mathematics 2021-01-27 Vincent Margot , Jean-Patrick Baudry , Frédéric Guilloux , Olivier Wintenberger

We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…

Optimization and Control · Mathematics 2023-07-24 Émiland Garrabé , Hozefa Jesawada , Carmen Del Vecchio , Giovanni Russo

Traditional synthetic data generation methods rely on model-based approaches that tune the parameters of a model rather than focusing on the structure of the data itself. In contrast, Scagnostics is an exploratory graphical method that…

Computation · Statistics 2023-03-28 Janith C. Wanniarachchi , Thiyanga S. Talagala

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…

Machine Learning · Statistics 2020-07-27 Tengyuan Liang , Weijie Su

We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to…

Optimization and Control · Mathematics 2022-07-28 Rohit Kannan , Güzin Bayraksan , James R. Luedtke

The convex hull of a set of points, $C$, serves to expose extremal properties of $C$ and can help identify elements in $C$ of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be…

Computational Geometry · Computer Science 2016-11-07 Lori Ziegelmeier , Michael Kirby , Chris Peterson

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

Statistics Theory · Mathematics 2020-06-22 Christophe Gaillac , Eric Gautier