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Truncated Linear Regression in High Dimensions [article]

Constantinos Daskalakis, Dhruv Rohatgi, Manolis Zampetakis
2020 arXiv   pre-print
As in standard linear regression, in truncated linear regression, we are given access to observations (A_i, y_i)_i whose dependent variable equals y_i= A_i^ T· x^* + η_i, where x^* is some fixed unknown  ...  In order to deal with both truncation and high-dimensionality at the same time, we develop new techniques that not only generalize the existing ones but we believe are of independent interest.  ...  Truncated Linear Regression in High Dimensions Constantinos Daskalakis Dhruv Rohatgi  ... 
arXiv:2007.14539v1 fatcat:hnftqn46dfg4tfnfz6bqhn5ni4

Analyzing rating distributions with heaps and censoring points using the generalized Craggit model

Volker Lang, Martin Groß
2020 MethodsX  
Our generalized Craggit model fits the data of this experiment much better than a hierarchical linear model, which is the method that is usually implemented to analyze factorial survey experiments.  ...  In this experiment, a three-step rating instrument was used, which resulted in a rating distribution with heaps and censoring.  ...  the Craggit truncated regression components-ε i tl in Eq. (4) and ε i th in Eq  ... 
doi:10.1016/j.mex.2020.100868 pmid:32309151 pmcid:PMC7155229 fatcat:x5uxb3o77zggxeexgyi66maf6y

Statistical Prediction [chapter]

2007 Inference and Prediction in Large Dimensions  
V LINEAR PROCESSES IN HIGH DIMENSIONS 215 3.6 Rate in uniform norm . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.7 Adaptive projection . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.7.1  ...  6.3.2 Almost sure convergence . . . . . . . . . . . . . . . . . . . 132 6.4 Regression estimation in the dependent case . . . . . . . . . . . . . 140 Optimal and superoptimal rates for density estimation  ... 
doi:10.1002/9780470724033.ch1 fatcat:oliurfgpvrc4horei6en5jxale

QR-PLSR: Reduced-rank regression for high-speed hardware implementation

Frank Westad, Klaus Diepold, Harald Martens
1996 Journal of Chemometrics  
high-speed full rank linear regression (corresponding statistically to multiple linear regression (MLR)) is based on the QR decomposition algorithm.  ...  INTRODUCTION In high-speed regression modelling of very high volumes of dynamic data in e.g. chemical process control, adaptive instrument recalibration or medical monitoring, the computational speed and  ... 
doi:10.1002/(sici)1099-128x(199609)10:5/6<439::aid-cem443>3.0.co;2-c fatcat:mgff37pdmrdsnj23icew4lojsy

Sensitivity Prewarping for Local Surrogate Modeling [article]

Nathan Wycoff, Mickaël Binois, Robert B. Gramacy
2021 arXiv   pre-print
We discuss the relationship between several sensitivity analysis methods based on kernel regression before describing how they give rise to a transformation of the input variables.  ...  Numerical experiments on observational data and benchmark test functions, including a high-dimensional computer simulator from the automotive industry, provide empirical validation.  ...  As before, vecc ran into numerical issues in high dimension and is only deployed in truncated input spaces.  ... 
arXiv:2101.06296v2 fatcat:c6rd73mqobb6xgny4y5wucraa4

Page 376 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
The authors consider the standard linear regression model but allow the error term to be nonsymmetric. They give conditions  ...  Our approach allows the dimension to increase with sample size, so that the theoretical model may accurately reflect the situations encountered in practice, e.g., approximately 20 dimensions and 40 data  ... 

Partially functional linear regression in high dimensions

Dehan Kong, Kaijie Xue, Fang Yao, Hao H. Zhang
2016 Biometrika  
How to incorporate scalar predictors in functional linear regression and perform model selection/regularization is an important issue.  ...  REGULARIZED PARTIALLY FUNCTIONAL LINEAR REGRESSION 2·1.  ...  In addition, M j is a n × s n matrix with (i, k)th element ξ ijk , M = (M 1 , . . . , M d ), and N = (M, Z M ) = (N 1 , . . . , N n ) T  ... 
doi:10.1093/biomet/asv062 fatcat:5avi67bqb5cf7dpenjqvgttrfy

Convolutional Signature for Sequential Data [article]

Ming Min, Tomoyuki Ichiba
2022 arXiv   pre-print
In the high dimensional case, it suffers from exponential growth in the number of features in truncated signature transform.  ...  This object has been studied successfully for machine learning with mostly applications in low dimensional cases.  ...  Experiments -Regression Problem for Maximum-Call Payoff We investigate our model on a specific rainbow option, high-dimension European type maximum call option.  ... 
arXiv:2009.06719v2 fatcat:f4pmfxsmpzebzmfhm35o3pt42m

Global optimization using mixed integer quadratic programming on non-convex two-way interaction truncated linear multivariate adaptive regression splines [article]

Xinglong Ju, Jay M. Rosenberger, Victoria C. P. Chen, Feng Liu
2020 arXiv   pre-print
linear univariate functions (TITL-MARS).  ...  Multivariate adaptive regression splines (MARS) is a flexible statistical modeling method that has been popular for data mining applications.  ...  The index of the truncated linear term in B m (x) is denoted as k, and K m is the total number of truncated linear terms in B m (x).  ... 
arXiv:2006.15707v1 fatcat:ievyoe4evncdhobittblzfgg4q

Estimating Patient Dose from X-ray Tube Output Metrics: Automated Measurement of Patient Size from CT Images Enables Large-scale Size-specific Dose Estimates

Ichiro Ikuta, Graham I. Warden, Katherine P. Andriole, Ramin Khorasani, Aaron Sodickson
2014 Radiology  
Linear regression models relating reductions in measured D(W) to a metric of anatomy truncation were used to compensate for the effects of clinical image truncation.  ...  Linear regression models were created to compare D(W) with the effective diameter (D(eff)) used to select size-specific volume CT dose index (CTDI(vol)) conversion factors as defined in report 204 of the  ...  While our linear regression correction of Figure 6 does tend to overshoot for high degrees of anatomy truncation in the thorax, it nonetheless improves D W estimation substantially.  ... 
doi:10.1148/radiol.13122727 pmid:24086075 pmcid:PMC4228751 fatcat:gf64kck3ercytkz6zk76rmfsri

Computationally and Statistically Efficient Truncated Regression [article]

Constantinos Daskalakis, Themis Gouleakis, Christos Tzamos, Manolis Zampetakis
2020 arXiv   pre-print
While consistent estimators of the regression coefficients have been identified, the error rates are not well-understood, especially in high dimensions.  ...  We provide a computationally and statistically efficient estimator for the classical problem of truncated linear regression, where the dependent variable y = w^T x + ϵ and its corresponding vector of covariates  ...  Computationally efficient robust sparse estimation in high dimensions.  ... 
arXiv:2010.12000v1 fatcat:aehp7kka7rhatdnhfddokm2vxm

Discussions on Fernhead and Prangle (2012) [article]

D. J. Nott, Y. Fan, S. A. Sisson
2012 arXiv   pre-print
The links between regression methods in ABC and Bayes Linear Analysis are discussed further in Nott et al (2011) .  ...  Based on samples of (θ, s) in a truncated region of the prior (as per Section 3, point (a)), one fits a regression model e.g. θ = α+βF (s), where F (s) = (f (s), . . . , f (s)).  ... 
arXiv:1201.1893v1 fatcat:hlm5pgbgg5erdaafwkh7gezssm

Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results [article]

Niccolo' Anceschi, Augusto Fasano, Daniele Durante, Giacomo Zanella
2022 arXiv   pre-print
high dimensions.  ...  A broad class of models that routinely appear in several fields can be expressed as partially or fully discretized Gaussian linear regressions.  ...  predictor and induce increasing shrinkage in high dimensions.  ... 
arXiv:2206.08118v1 fatcat:xlekejxnvnefzjpsqnrjgchqvq

Page 2755 of Mathematical Reviews Vol. , Issue 91E [page]

1991 Mathematical Reviews  
S. (3-YORK); Lee, H.S. (3-TRNT-S); Reid, N. (3-TRNT-S) Nonnormal linear regression: an example of significance levels in high dimensions. Biometrika 77 (1990), no. 2, 333-341.  ...  Summary: “In this paper we examine some existing procedures for testing linear and log-linear regression models, especially with re- spect to the truncation of the disturbance term in the linear model.  ... 

Discovering Sociolinguistic Associations with Structured Sparsity

Jacob Eisenstein, Noah A. Smith, Eric P. Xing
2011 Annual Meeting of the Association for Computational Linguistics  
We perform two regression studies.  ...  Using aggregate demographic statistics about the authors' geographic communities, we solve a multi-output regression problem between demographics and lexical frequencies.  ...  http://www.lexicalist.com -ball for learning in high dimensions. In Proceedings of ICML.  ... 
dblp:conf/acl/EisensteinSX11 fatcat:zk3w2rybjvghzgsbwluukns2zi
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