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Subset selection by Mallows' Cp: A mixed integer programming approach

Ryuhei Miyashiro, Yuichi Takano
2015 Expert systems with applications  
Employing Mallows' C p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem.  ...  This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model.  ...  Acknowledgments This work was partially supported by Grants-in-Aid for Scientific Research by the Ministry of Education, Culture, Sports, Science and Technology of Japan.  ... 
doi:10.1016/j.eswa.2014.07.056 fatcat:buyje3xkzvfonhizjwxsxw26fa

Optimal Model Averaging of Varying Coefficient Models

Cong Li, Qi Li, Jeffrey Racine
2017 Social Science Research Network  
We propose a Mallows model averaging procedure that is capable of delivering model averaging estimators with solid finite-sample performance.  ...  The approach is very simple to implement in practice and R code is provided in an appendix.  ...  For some integer N ≥ 1, (2014) ). Condition (12) imposes a finite moment bound and is satisfied by Gaussian noise.  ... 
doi:10.2139/ssrn.2905268 fatcat:zviagewggbbl7k4txl26j3pyjq

Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning [article]

Niclas Boehmer, Robert Bredereck, Edith Elkind, Piotr Faliszewski, Stanisław Szufa
2022 arXiv   pre-print
We use the "map of elections" approach of Szufa et al. (AAMAS 2020) to analyze several well-known vote distributions.  ...  For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled  ...  We also repeated the above experiment to measure the capabilities of our approach to estimate the parameters of a mixed Mallows distribution.  ... 
arXiv:2205.07831v1 fatcat:ituduiirtvaibkk4oqxqljrjfa

BayesMallows: An R Package for the Bayesian Mallows Model

Øystein Sørensen, Marta Crispino, Qinghua Liu, Valeria Vitelli
2020 The R Journal  
BayesMallows is an R package for analyzing preference data in the form of rankings with the Mallows rank model, and its finite mixture extension, in a Bayesian framework.  ...  Arjas, and A. Frigessi. Time-varying rankings with the Bayesian Mallows model. Stat, 6(1):14-30, 2017. URL https://doi.org/10.1002/sta4.132. [p20] G. Celeux, M. Hurn, and C. Robert.  ...  The following call finds the CP consensuses, and then uses select from dplyr and spread from tidyr to create one column for each cluster.  ... 
doi:10.32614/rj-2020-026 fatcat:tbfj774wcbdzrb7zqo6e3rffpe

Transfer Learning in Information Criteria-based Feature Selection [article]

Shaohan Chen, Nikolaos V. Sahinidis, Chuanhou Gao
2022 arXiv   pre-print
We propose a procedure that combines transfer learning with Mallows' Cp (TLCp) and prove that it outperforms the conventional Mallows' Cp criterion in terms of accuracy and stability.  ...  This paper investigates the effectiveness of transfer learning based on Mallows' Cp.  ...  Acknowledgments This project was supported by the National Natural Science Foundation of China under Grant No. 12071428 and 62111530247, and the Zhejiang Provincial Natural Science Foundation of China  ... 
arXiv:2107.02847v2 fatcat:kdsvh5czo5fn3glkchjfy6ykke

The ALAMO approach to machine learning

Zachary T. Wilson, Nikolaos V. Sahinidis
2017 Computers and Chemical Engineering  
Given a data set, the approach begins by building a low-complexity, linear model composed of explicit non-linear transformations of the independent variables.  ...  ALAMO is a computational methodology for leaning algebraic functions from data.  ...  would require mixed-integer nonlinear programming (MINLP).  ... 
doi:10.1016/j.compchemeng.2017.02.010 fatcat:crti5mbhjjfvzg6rt5tygoklcy

Frequentist Model Averaging for the Nonparametric Additive Model

Jun Liao, Alan Wan, Shuyuan He, Guohua Zou
2023 Statistica sinica  
Our weight choice criterion selects model weights by minimising a plug-in estimator of the risk of the model average estimator under a squared error loss function.  ...  mean squared error in a large part of the parameter space.  ...  Additive Model Mallows' Cp criterion.  ... 
doi:10.5705/ss.202020.0340 fatcat:3ckdz3zlm5hyrkncmc2qwbcqgm

Mitigating the Multicollinearity Problem and Its Machine Learning Approach: A Review

Jireh Yi-Le Chan, Steven Mun Hong Leow, Khean Thye Bea, Wai Khuen Cheng, Seuk Wai Phoong, Zeng-Wei Hong, Yen-Lin Chen
2022 Mathematics  
The two main approaches used to mitigate multicollinearity are variable selection methods and modified estimator methods.  ...  However, variable selection methods may negate efforts to collect more data as new data may eventually be dropped from modeling, while recent studies suggest that optimization approaches via machine learning  ...  Conflicts of Interest: No potential conflict of interest was reported by the authors.  ... 
doi:10.3390/math10081283 fatcat:ftggosq35fgkxduwhkqxoz7xzi

Artificial intelligence and operations research: challenges and opportunities in planning and scheduling

CARLA P. GOMES
2000 Knowledge engineering review (Print)  
Randomization of Branch-and-Bound The standard approach used by the OR community to solve mixed integer programming problems (MIP) is branch-and-bound search.  ...  We considered examples based on logistics planning problems, formulated as mixed integer programming problems.  ... 
doi:10.1017/s0269888900001090 fatcat:ujl5jthik5akxaanwvh2jemldy

Modelling hidden structure of signals in group data analysis with modified (Lr, 1) and block-term decompositions [article]

Pavel Kharyuk, Ivan Oseledets
2018 arXiv   pre-print
A new generalization of block tensor decomposition was considered in application to group data analysis. Suggested approach was evaluated on multilabel classification task for a set of images.  ...  Acknowledgements The work was supported by Russian Foundation for Basic Research (RFBR), research project No. 16-31-00494-mol_a.  ...  It should be noted that if each T i is a CP block, they are additionally constrained to have rank-1 factor-matrices for a subset of modes in each term.  ... 
arXiv:1808.02316v1 fatcat:wxuz66szavacdabojtbvzozkbe

BayesMallows: An R Package for the Bayesian Mallows Model [article]

Øystein Sørensen, Marta Crispino, Qinghua Liu, Valeria Vitelli
2019 arXiv   pre-print
BayesMallows is an R package for analyzing data in the form of rankings or preferences with the Mallows rank model, and its finite mixture extension, in a Bayesian probabilistic framework.  ...  The Mallows model is a well-known model, grounded on the idea that the probability density of an observed ranking decreases exponentially fast as its distance to the location parameter increases.  ...  The IS estimateẐ n (α) is computed on a grid of α values provided by the user, and then a smooth estimate obtained via a polynomial fit is returned to the user, who can also select the degree of the polynomial  ... 
arXiv:1902.08432v1 fatcat:avhy556yufgb7djhwp6mqan5iy

Preference-based Online Learning with Dueling Bandits: A Survey [article]

Viktor Bengs, Robert Busa-Fekete, Adil El Mesaoudi-Paul, Eyke Hüllermeier
2021 arXiv   pre-print
in the course of a sequential decision process.  ...  Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.  ...  Acknowledgments Eyke Hüllermeier, Adil El Mesaoudi-Paul and Viktor Bengs gratefully acknowledge financial support by the German Research Foundation (DFG).  ... 
arXiv:1807.11398v2 fatcat:jsu6gap5pbgbtm735fgf4aqwmu

Comparing and selecting spatial predictors using local criteria

Jonathan R. Bradley, Noel Cressie, Tao Shi
2014 Test (Madrid)  
“Model selection in linear mixed models.”  ...  We call this approach local predictor selection, which was introduced by Bradley et al. (2012).  ... 
doi:10.1007/s11749-014-0415-1 fatcat:554lpagg4ffybkqyy2qgmc6cnq

Structured Prediction Cascades [article]

David Weiss, Benjamin Sapp, Ben Taskar
2012 arXiv   pre-print
We learn cascades by optimizing a novel convex loss function that controls the trade-off between the filtering efficiency and the accuracy of the cascade, and provide generalization bounds for both accuracy  ...  We also extend our approach to intractable models using tree-decomposition ensembles, and provide algorithms and theory for this setting.  ...  Standard statistical model selection techniques (Mallows, 1973; Vapnik and Chervonenkis, 1974; Akaike, 1974; Devroye et al., 1996; Barron et al., 1999; explore a hierarchy of models of increasing complexity  ... 
arXiv:1208.3279v1 fatcat:ru4l45dvinh3lptf7mvymyxzee

Scalable bundling via dense product embeddings [article]

Madhav Kumar, Dean Eckles, Sinan Aral
2020 arXiv   pre-print
We combine the results from the experiment with product embeddings using a hierarchical model that maps bundle features to their purchase likelihood, as measured by the add-to-cart rate.  ...  Bundling, the practice of jointly selling two or more products at a discount, is a widely used strategy in industry and a well examined concept in academia.  ...  Jiang et al. (2011) also study bundling in the context of an online retailer selling books and use non-linear mixed integer programming to recommend the next best product given what it is currently in  ... 
arXiv:2002.00100v1 fatcat:lqms7l4irjht5mclmuvl6ttzzq
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