scholarly journals A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

2022 ◽  
Author(s):  
Katerina Papagiannouli
Keyword(s):  
Numerical Experiments ◽  
Selection Rule ◽  
Stopping Rule ◽  
Data Driven ◽  
Adaptive Procedure ◽  
Continuous Part ◽  
Parameter Choice ◽  
Adaptive Estimator ◽  
Time Points ◽  
Balancing Principle

AbstractWe suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepskiĭ-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.

scholarly journals Data-Driven Parameter Choice for Illumination Artifact Correction of Digital Images

2020 ◽  
pp. 1-1
Author(s):  
Hong-Phuong Dang ◽  
Myriam Vimond ◽  
Segolen Geffray
Keyword(s):  
Digital Images ◽  
Data Driven ◽  
Parameter Choice ◽  
Artifact Correction

Optimal Stopping of a Random Sequence with Unknown Distribution

2021 ◽  
Author(s):  
Alexander Goldenshluger ◽  
Assaf Zeevi
Keyword(s):  
Optimal Stopping ◽  
Numerical Experiments ◽  
Random Sequence ◽  
Stopping Rule ◽  
Asymptotically Optimal ◽  
First Order ◽  
Unknown Distribution ◽  
Distributional Information ◽  
The Subject ◽  
General Method

The subject of this paper is the problem of optimal stopping of a sequence of independent and identically distributed random variables with unknown distribution. We propose a stopping rule that is based on relative ranks and study its performance as measured by the maximal relative regret over suitable nonparametric classes of distributions. It is shown that the proposed rule is first-order asymptotically optimal and nearly rate optimal in terms of the rate at which the relative regret converges to zero. We also develop a general method for numerical solution of sequential stopping problems with no distributional information and use it in order to implement the proposed stopping rule. Some numerical experiments illustrating performance of the rule are presented as well.

A parameter choice strategy for a multilevel augmentation method in iterated Lavrentiev regularization

2018 ◽  
Vol 26 (2) ◽  
pp. 153-170 ◽  
Author(s):  
Chunmei Zeng ◽  
Xingjun Luo ◽  
Suhua Yang ◽  
Fanchun Li
Keyword(s):  
Integral Equation ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Parameter Choice ◽  
Lavrentiev Regularization ◽  
Choice Strategy ◽  
Ill Posed ◽  
Parameter Choice Strategy

AbstractIn this paper we apply the multilevel augmentation method to solve an ill-posed integral equation via the iterated Lavrentiev regularization. This method leads to fast solutions of discrete iterated Lavrentiev regularization. The convergence rates of the iterated Lavrentiev regularization are achieved by using a certain parameter choice strategy. Finally, numerical experiments are given to illustrate the efficiency of the method.

On the Parameter Choice in the Multilevel Augmentation Method

2020 ◽  
Vol 20 (3) ◽  
pp. 555-571
Author(s):  
Suhua Yang ◽  
Xingjun Luo ◽  
Chunmei Zeng ◽  
Zhihai Xu ◽  
Wenyu Hu
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Tikhonov Regularization Method ◽  
Fredholm Integral Equations ◽  
Parameter Choice ◽  
Choice Strategy ◽  
Ill Posed ◽  
Parameter Choice Strategy

AbstractIn this paper, we apply the multilevel augmentation method for solving ill-posed Fredholm integral equations of the first kind via iterated Tikhonov regularization method. The method leads to fast solutions of the discrete regularization methods for the equations. The convergence rates of iterated Tikhonov regularization are achieved by using a modified parameter choice strategy. Finally, numerical experiments are given to illustrate the efficiency of the method.

scholarly journals Semi-heuristic parameter choice rules for Tikhonov regularisation with operator perturbations

2019 ◽  
Vol 27 (1) ◽  
pp. 117-131 ◽  
Author(s):  
Uno Hämarik ◽  
Urve Kangro ◽  
Stefan Kindermann ◽  
Kemal Raik
Keyword(s):  
Noise Level ◽  
Numerical Experiments ◽  
Heuristic Rules ◽  
Parameter Choice ◽  
Data Noise ◽  
Operator Error ◽  
New Family ◽  
Ill Posed ◽  
Tikhonov Regularisation ◽  
Parameter Choice Rules

Abstract We study the choice of the regularisation parameter for linear ill-posed problems in the presence of data noise and operator perturbations, for which a bound on the operator error is known but the data noise level is unknown. We introduce a new family of semi-heuristic parameter choice rules that can be used in the stated scenario. We prove convergence of the new rules and provide numerical experiments that indicate an improvement compared to standard heuristic rules.

scholarly journals The Analog Data Assimilation

2017 ◽  
Vol 145 (10) ◽  
pp. 4093-4107 ◽  
Author(s):  
Redouane Lguensat ◽  
Pierre Tandeo ◽  
Pierre Ailliot ◽  
Manuel Pulido ◽  
Ronan Fablet
Keyword(s):  
Data Assimilation ◽  
Particle Filtering ◽  
Numerical Experiments ◽  
Explicit Knowledge ◽  
Classical Model ◽  
Data Driven ◽  
Matlab Toolbox ◽  
Model Driven ◽  
Forecasting Methods ◽  
Lorenz 96

In light of growing interest in data-driven methods for oceanic, atmospheric, and climate sciences, this work focuses on the field of data assimilation and presents the analog data assimilation (AnDA). The proposed framework produces a reconstruction of the system dynamics in a fully data-driven manner where no explicit knowledge of the dynamical model is required. Instead, a representative catalog of trajectories of the system is assumed to be available. Based on this catalog, the analog data assimilation combines the nonparametric sampling of the dynamics using analog forecasting methods with ensemble-based assimilation techniques. This study explores different analog forecasting strategies and derives both ensemble Kalman and particle filtering versions of the proposed analog data assimilation approach. Numerical experiments are examined for two chaotic dynamical systems: the Lorenz-63 and Lorenz-96 systems. The performance of the analog data assimilation is discussed with respect to classical model-driven assimilation. A Matlab toolbox and Python library of the AnDA are provided to help further research building upon the present findings.

scholarly journals Optimization-Based Calibration of Simulation Input Models

2019 ◽  
Vol 67 (5) ◽  
pp. 1362-1382 ◽  
Author(s):  
Aleksandrina Goeva ◽  
Henry Lam ◽  
Huajie Qian ◽  
Bo Zhang
Keyword(s):  
Performance Measures ◽  
Iterative Procedure ◽  
Numerical Experiments ◽  
Penalty Method ◽  
Input Data ◽  
Statistical Information ◽  
Data Driven ◽  
Output Data ◽  
Simulation Input ◽  
Distributionally Robust

Studies on simulation input uncertainty are often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and other related performance measures of interest. We propose an optimization-based framework to compute statistically valid bounds on input quantities. The framework utilizes constraints that connect the statistical information of the real-world outputs with the input–output relation via a simulable map. We analyze the statistical guarantees of this approach from the view of data-driven distributionally robust optimization, and show how they relate to the function complexity of the constraints arising in our framework. We investigate an iterative procedure based on a stochastic quadratic penalty method to approximately solve the resulting optimization. We conduct numerical experiments to demonstrate our performances in bounding the input models and related quantities.

Application of Adaptive Cluster Sampling with a Data-Driven Stopping Rule to Plant Disease Incidence

2013 ◽  
Vol 161 (9) ◽  
pp. 632-641 ◽  
Author(s):  
Stefano Antonio Gattone ◽  
Mohamed Esha ◽  
Jesse Wachira Mwangi
Keyword(s):  
Plant Disease ◽  
Disease Incidence ◽  
Stopping Rule ◽  
Data Driven ◽  
Cluster Sampling ◽  
Adaptive Cluster Sampling

scholarly journals Meta Dynamic Pricing: Transfer Learning Across Experiments

2021 ◽  
Author(s):  
Hamsa Bastani ◽  
David Simchi-Levi ◽  
Ruihao Zhu
Keyword(s):  
Transfer Learning ◽  
Dynamic Pricing ◽  
Numerical Experiments ◽  
Estimation Error ◽  
Data Driven ◽  
Special Issue ◽  
Thompson Sampling ◽  
Large N ◽  
Alignment Technique ◽  
Shared Structure

We study the problem of learning shared structure across a sequence of dynamic pricing experiments for related products. We consider a practical formulation in which the unknown demand parameters for each product come from an unknown distribution (prior) that is shared across products. We then propose a meta dynamic pricing algorithm that learns this prior online while solving a sequence of Thompson sampling pricing experiments (each with horizon T) for N different products. Our algorithm addresses two challenges: (i) balancing the need to learn the prior (meta-exploration) with the need to leverage the estimated prior to achieve good performance (meta-exploitation) and (ii) accounting for uncertainty in the estimated prior by appropriately “widening” the estimated prior as a function of its estimation error. We introduce a novel prior alignment technique to analyze the regret of Thompson sampling with a misspecified prior, which may be of independent interest. Unlike prior-independent approaches, our algorithm’s meta regret grows sublinearly in N, demonstrating that the price of an unknown prior in Thompson sampling can be negligible in experiment-rich environments (large N). Numerical experiments on synthetic and real auto loan data demonstrate that our algorithm significantly speeds up learning compared with prior-independent algorithms. This paper was accepted by George J. Shanthikumar for the Management Science Special Issue on Data-Driven Analytics.

Adaptive cluster sampling with a data driven stopping rule

2010 ◽  
Vol 20 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Stefano A. Gattone ◽  
Tonio Di Battista
Keyword(s):  
Stopping Rule ◽  
Data Driven ◽  
Cluster Sampling ◽  
Adaptive Cluster Sampling
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