Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball

Powers, Scott; Hastie, Trevor; Tibshirani, Robert

doi:10.1177/1471082x18777669

Cited by 13 publications

(10 citation statements)

References 21 publications

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“…The computational cost for fitting a reduced rank multinomial logistic regression can be very high. Powers et al [ 20 ] proposed replacing the rank restriction with a restriction on the nuclear norm which amounts to a convex relaxation of the reduced-rank multinomial regression problem. Our methodology can be adapted to obtain asymptotic inference for the regularized parameter estimates.…”

Section: Discussionmentioning

confidence: 99%

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models

et al. 2018

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Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.

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Section: Discussionmentioning

confidence: 99%

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models

et al. 2018

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“…On the other hand, the penalized CMLR2 and SMLR do not depend on the reference categories. Such kind of MLR-based models offers a symmetric and systematic insight into all categories, and becomes more appealing in the literature; see Friedman et al (2010); Zahid and Tutz (2013a,b); Hastie et al (2015); Powers et al (2018);de Jong et al (2019). Between these two MLRs, the penalized SMLR is preferred in terms of computational convenience and establishment of the statistical properties.…”

Section: Application IImentioning

confidence: 99%

Simplex-based Multinomial Logistic Regression with Diverging Numbers of Categories and Covariates

Fu¹,

Chen²,

Liu³

et al. 2024

STAT SINICA

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Multinomial logistic regression models are popular in multicategory classification analysis, but existing models suffer several intrinsic drawbacks. In particular, the parameters could not be uniquely determined because of the over-specification. Some additional constraints have been imposed to refine the model but such modifications can be inefficient and complicated. In this paper, we propose a novel and efficient simplex-based multinomial logistic regression technique, seamlessly connecting binomial and multinomial cases under a unified framework. Compared with the existing models, our model has less parameters and is free of any constraints, which can be efficiently solved via the Fisher scoring algorithm. In addition, the proposed model enjoys some theoretical advantages including Fisher consistency and sharp comparison inequality. Under mild conditions, we establish the asymptotical normality and convergence for the new model even when the numbers of categories and covariates increase with the sample size. The proposed framework is illustrated by extensive simulations and real applications.

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“…Other recent methods for fitting the multinomial logistic regression model rely on dimension reduction rather than variable selection. Powers et al (2018) proposed a nuclear norm penalized multinomial logistic regression model, which could be characterized as a generalization of the stereotype model of Anderson (1984). Price et al (2019) penalized the euclidean norm of pairwise differences of regression coefficient vectors for each category, which encourages fitted models for which estimated probabilities are identical for some categories.…”

Section: Bivariate Categorical Response Regression Modelmentioning

confidence: 99%

A likelihood-based approach for multivariate categorical response regression in high dimensions

Molstad,

Rothman

2020

Preprint

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We propose a penalized likelihood method to fit the bivariate categorical response regression model. Our method allows practitioners to estimate which predictors are irrelevant, which predictors only affect the marginal distributions of the bivariate response, and which predictors affect both the marginal distributions and log odds ratios. To compute our estimator, we propose an efficient first order algorithm which we extend to settings where some subjects have only one response variable measured, i.e., the semisupervised setting. We derive an asymptotic error bound which illustrates the performance of our estimator in high-dimensional settings. Generalizations to the multivariate categorical response regression model are proposed. Finally, simulation studies and an application in pan-cancer risk prediction demonstrate the usefulness of our method in terms of interpretability and prediction accuracy. An R package implementing the proposed method is available for download at github.com/ajmolstad/BvCategorical.

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Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball

Cited by 13 publications

References 21 publications

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models

Simplex-based Multinomial Logistic Regression with Diverging Numbers of Categories and Covariates

A likelihood-based approach for multivariate categorical response regression in high dimensions

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