The Experts below are selected from a list of 1815 Experts worldwide ranked by ideXlab platform
Bezirgen Veliyev - One of the best experts on this subject based on the ideXlab platform.
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functional sequential treatment allocation with Covariates
arXiv: Machine Learning, 2020Co-Authors: Anders Bredahl Kock, David Preinerstorfer, Bezirgen VeliyevAbstract:We consider a multi-armed bandit problem with Covariates. Given a realization of the Covariate Vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socio-economic functional such as an inequality, welfare or poverty measure. We develop expected regret lower bounds for this problem, and construct a near minimax optimal assignment policy.
Anders Bredahl Kock - One of the best experts on this subject based on the ideXlab platform.
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functional sequential treatment allocation with Covariates
arXiv: Machine Learning, 2020Co-Authors: Anders Bredahl Kock, David Preinerstorfer, Bezirgen VeliyevAbstract:We consider a multi-armed bandit problem with Covariates. Given a realization of the Covariate Vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socio-economic functional such as an inequality, welfare or poverty measure. We develop expected regret lower bounds for this problem, and construct a near minimax optimal assignment policy.
David Ruppert - One of the best experts on this subject based on the ideXlab platform.
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Pivotal bootstrap for quantile-based modal regression
arXiv: Statistics Theory, 2020Co-Authors: Tao Zhang, Kengo Kato, David RuppertAbstract:In this paper, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop a novel bootstrap method, which we call the pivotal bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the pivotal bootstrap for the conditional mode. We also extend the preceding analysis to the case where the dimension of the Covariate Vector is increasing with the sample size. Finally, we conduct simulation experiments and a real data analysis using U.S. wage data to demonstrate the finite sample performance of our inference method.
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Penalized Spline Estimation for Partially Linear Single-Index Models
Journal of the American Statistical Association, 2002Co-Authors: David RuppertAbstract:Single-index models are potentially important tools for multivariate nonparametric regression. They generalize linear regression by replacing the linear combination α0Tx with a nonparametric component, η0(α0Tx), where η0(·) is an unknown univariate link function. By reducing the dimensionality from that of a general Covariate Vector x to a univariate index α0Tx, single-index models avoid the so-called “curse of dimensionality.” We propose penalized spline (P-spline) estimation of η0(·) in partially linear single-index models, where the mean function has the form η0(α0Tx) + β 0Tz. The P-spline approach offers a number of advantages over other fitting methods for single-index models. All parameters in the P-spline single-index model can be estimated simultaneously by penalized nonlinear least squares. As a direct least squares fitting method, our approach is rapid and computationally stable. Standard nonlinear least squares software can be used. Moreover, joint inference for η0(·), α0, and β0 is possible by...
Kottas Athanasios - One of the best experts on this subject based on the ideXlab platform.
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Bayesian nonparametric modeling for mean residual life regression
2018Co-Authors: Poynor Valerie, Kottas AthanasiosAbstract:The mean residual life function is a key functional for a survival distribution. It has practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the survival distribution. However, it has received limited attention in terms of inference methods under a probabilistic modeling framework. In this paper, we seek to provide general inference methodology for mean residual life regression. Survival data often include a set of predictor variables for the survival response distribution, and in many cases it is natural to include the Covariates as random variables into the modeling. We thus propose a Dirichlet process mixture modeling approach for the joint stochastic mechanism of the Covariates and survival responses. This approach implies a flexible model structure for the mean residual life of the conditional response distribution, allowing general shapes for mean residual life as a function of Covariates given a specific time point, as well as a function of time given particular values of the Covariate Vector. To expand the scope of the modeling framework, we extend the mixture model to incorporate dependence across experimental groups, such as treatment and control groups. This extension is built from a dependent Dirichlet process prior for the group-specific mixing distributions, with common locations and weights that vary across groups through latent bivariate beta distributed random variables. We develop properties of the proposed regression models, and discuss methods for prior specification and posterior inference. The different components of the methodology are illustrated with simulated data sets. Moreover, the modeling approach is applied to a data set comprising right censored survival times of patients with small cell lung cancer.Comment: arXiv admin note: text overlap with arXiv:1411.748
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Nonparametric Bayesian Inference for Mean Residual Life Functions in Survival Analysis
2018Co-Authors: Poynor Valerie, Kottas AthanasiosAbstract:The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the survival distribution. However, it has received limited attention in terms of inference methods under a probabilistic modeling framework. We seek to provide general inference methodology for mean residual life regression. Survival data often include a set of predictor variables for the survival response distribution, and in many cases it is natural to include the Covariates as random variables into the modeling. We thus employ Dirichlet process mixture modeling for the joint stochastic mechanism of the Covariates and survival responses. This approach implies a flexible model structure for the mean residual life of the conditional response distribution, allowing general shapes for mean residual life as a function of Covariates given a specific time point, as well as a function of time given particular values of the Covariate Vector. To expand the scope of the modeling framework, we extend the mixture model to incorporate dependence across experimental groups, such as treatment and control groups. This extension is built from a dependent Dirichlet process prior for the group-specific mixing distributions, with common locations and weights that vary across groups through latent bivariate Beta distributed random variables. We develop properties of the regression models, and discuss methods for prior specification and posterior inference. The different components of the methodology are illustrated with simulated data examples, and the model is also applied to a data set comprising right censored survival times
David Preinerstorfer - One of the best experts on this subject based on the ideXlab platform.
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functional sequential treatment allocation with Covariates
arXiv: Machine Learning, 2020Co-Authors: Anders Bredahl Kock, David Preinerstorfer, Bezirgen VeliyevAbstract:We consider a multi-armed bandit problem with Covariates. Given a realization of the Covariate Vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socio-economic functional such as an inequality, welfare or poverty measure. We develop expected regret lower bounds for this problem, and construct a near minimax optimal assignment policy.
