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https://orcid.org/0000-0002-6453-9545 + + + Fengyu + Xie + https://orcid.org/0000-0002-1169-1690 + + + + 12 + 21 + 2023 + + + 5867 + + + 10.21105/joss.05867 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.10246640 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/5867 + + + + 10.21105/joss.05867 + https://joss.theoj.org/papers/10.21105/joss.05867 + + + https://joss.theoj.org/papers/10.21105/joss.05867.pdf + + + + + + Statistical learning with sparsity: The lasso +and generalizations + Hastie + 1498712169 + 2015 + Hastie, T., Tibshirani, R., & +Wainwright, M. 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Cluster +expansions of multicomponent ionic materials: Formalism and methodology. +Physical Review B, 106(14), 144202. +https://doi.org/10.1103/PhysRevB.106.144202 + + + + + + From 0b331ca2434c3d7c1512cd5590026d79e1a40117 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Thu, 21 Dec 2023 11:33:04 +0000 Subject: [PATCH 3/4] Creating 10.21105.joss.05867.jats --- joss.05867/10.21105.joss.05867.jats | 1127 +++++++++++++++++++++++++++ 1 file changed, 1127 insertions(+) create mode 100644 joss.05867/10.21105.joss.05867.jats diff --git a/joss.05867/10.21105.joss.05867.jats b/joss.05867/10.21105.joss.05867.jats new file mode 100644 index 0000000000..d58c386c78 --- /dev/null +++ b/joss.05867/10.21105.joss.05867.jats @@ -0,0 +1,1127 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +5867 +10.21105/joss.05867 + +sparse-lm: Sparse linear regression models in +Python + + + +https://orcid.org/0000-0002-6453-9545 + +Barroso-Luque +Luis + + + +* + + +https://orcid.org/0000-0002-1169-1690 + +Xie +Fengyu + + + + + + +Materials Sciences Division, Lawrence Berkeley National +Laboratory, Berkeley CA, 94720, USA + + + + +Department of Materials Science and Engineering, University +of California Berkeley, Berkeley CA, 94720, USA + + + + +* E-mail: + + +10 +7 +2023 + +8 +92 +5867 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +scikit-learn +cvxpy +linear regression +regularization +structured sparsity + + + + + + Summary +

Sparse linear regression models are a powerful tool for capturing + linear relationships in high dimensional spaces. Sparse models have + only a small number of nonzero parameters —even if the number of + covariates used in estimation is large—as a result they can be easier + to fit and interpret compared to dense models + (Hastie + et al., 2015). Regression objectives resulting in sparse linear + models such as the Lasso + (Tibshirani, + 2018; + Zou, + 2006) and Best Subset Selection + (Hocking + & Leslie, 1967) have been widely used in a variety of + fields. However, many regression problems involve covariates that have + a natural underlying structure, such as group or hierarchical + relationships, that can be further leveraged to obtain improved model + performance and interpretability. Such structured regression problems + occur in a wide range of fields including genomics + (Chen + & Wang, 2021), bioinformatics + (Ma + et al., 2007), medicine + (Kim + et al., 2012), econometrics + (Athey + & Imbens, 2017), chemistry + (Gu + et al., 2018), and materials science + (Leong + & Tan, 2019). Several generalizations of the Lasso + (Friedman + et al., 2010; + Simon + et al., 2013; + Wang + & Tian, 2019; + Yuan + & Lin, 2006) and Best Subset Selection + (Bertsimas + et al., 2016; + Bertsimas + & King, 2016) have been developed to effectively exploit + additional structure in linear regression. The + sparse-lm Python package provides a flexible, + comprehensive, and user-friendly implementation of (structured) sparse + linear regression models, which allows researchers to easily + experiment and choose the best regression model for their specific + problem.

+
+ + Statement of need +

The sparse-lm Python package implements a + variety of sparse linear regression models based on convex objectives + (generalizations of the Lasso) and mixed integer quadratic programming + objectives (generalizations of Best Subset Selection) that support a + flexible range of ways to introduce structured sparsity. The linear + models in sparse-lm are implemented to be + compatible with scikit-learn + (Buitinck + et al., 2013; + Pedregosa + et al., 2011), in order to enable interoperability with the + wide range of tools and workflows available. The regression + optimization problems in sparse-lm are + implemented and solved using cvxpy + (Diamond + & Boyd, 2016), which allows users to choose from a variety + of well-established open-source and proprietary solvers. In + particular, for regression problems with mixed integer programming + objectives, access to state-of-the-art proprietary solvers enables + solving larger problems that would otherwise be unsolvable within + reasonable time limits.

+

A handful of pre-existing Python libraries implement a subset of + sparse linear regression models that are also + scikit-learn compatible. + celer + (Massias + et al., 2018) and groupyr + (Richie-Halford + et al., 2021) include efficient implementations of the Lasso + and Group Lasso. group-lasso + (Moe, + 2020) is another scikit-learn compatible + implementation of the Group Lasso. skglm + (Bertrand + et al., 2022) includes several implementations of sparse linear + models based on regularization using combinations of + + + p + ( + + p{1/2,2/3,1,2}) + norms and pseudo-norms. And abess + (Zhu + et al., 2022) includes an implementation of Best Subset + Selection and + + 0 + pseudo-norm regularization.

+

The aforementioned packages include highly performant versions of + the specific models they implement. However, none of these packages + implement the full range of sparse linear models available in + sparse-lm, nor do they support the flexibility + to modify the optimization objective and choose among many open-source + and commercially available solvers. sparse-lm + satisfies the need for a flexible and comprehensive library that + enables easy experimentation and comparisons of different sparse + linear regression algorithms within a single package.

+
+ + Background + +

Schematic of a linear model with grouped covariates with + hierarchical relations. Groups of covariates are represented with + different colors and hierarchical relationships are represented with + arrows (i.e. group 3 depends on group 1). The figure was inspired by + Ref. + (Richie-Halford + et al., 2021).

+ +
+

Structured sparsity can be introduced into regression problems in + one of two ways: convex group regularization or mixed integer + quadratic programming with linear constraints. The first way to obtain + structured sparsity is by using regularization based on + generalizations of the Lasso, such as the Group Lasso and the Sparse + Group Lasso + (Friedman + et al., 2010; + Simon + et al., 2013; + Wang + & Tian, 2019; + Yuan + & Lin, 2006). The Sparse Group Lasso regression problem can + be expressed as follows,

+

+ + β*=argminβ||𝐗β𝐲||22+(1α)λ𝐠G|𝐠|||β𝐠||2+αλ||β||1

+

where + + 𝐗 + is the design matrix, + + 𝐲 + is the response vector, and + + β + are the regression coefficients. + + 𝐠 + are groups of covariate indices, + + G + is the set of all such groups being considered, and + + + β𝐠|𝐠| + are the covariate coefficients in group + + 𝐠. + + + λ+ + and + + α[0,1] + are regularization hyperparameters. The parameter + + + α[0,1] + controls the relative weight between the single covariate + + + 1 + regularization and the group regularization term. When + + + α=0, + the regression problem reduces to the Group Lasso objective, and when + + + α=1, + the problem reduces to the Lasso objective.

+

The (Sparse) Group Lasso can be directly used to obtain a grouped + sparsity pattern. Hierarchical sparsity patterns can be obtained by + extending the Group Lasso to allow overlapping groups, which is + referred to as the Overlap Group Lasso + (Hastie + et al., 2015).

+

The second method to obtain structured sparsity is by introducing + linear constraints into the regression objective. Introducing linear + constraints is straight-forward in mixed integer quadratic programming + (MIQP) formulations of the Best Subset Selection + (Bertsimas + et al., 2016; + Bertsimas + & King, 2016). The general MIQP formulation of Best Subset + Selection with grouped covariates and hierarchical constraints can be + expressed as follows,

+

+

where + + z𝐠 + are binary slack variables that indicate whether the covariates in + each group + + 𝐠 + are included in the model. The first set of inequality constraints + ensure that coefficients + + β𝐠 + are nonzero if and only if their corresponding slack variable + + + z𝐠=1. + + + M + is a fixed parameter that can be estimated from the data + (Bertsimas + et al., 2016). The second inequality constraint introduces + general sparsity by ensuring that at most + + + k + coefficients are nonzero. If + + G + includes only singleton groups of covariates then the MIQP formulation + is equivalent to the Best Subset Selection problem, otherwise it is a + generalization that enables group-level sparsity structure. The last + inequality constraint can be used to introduce hierarchical structure + into the model. Finally, we have also included an + + + 2 + regularization term controlled by the hyperparameter + + + λ, + which is useful when dealing with poorly conditioned design + matrices.

+

The user-friendly implementation of statistical regression models + with structured sparsity parametrized via Group Lasso or Best Subset + Selection based objectives in sparse-lm, along + with the flexibility to choose from a variety of established solvers, + enables researchers to quickly iterate, experiment and benchmark + performance when choosing the best regression model for their specific + problem. sparse-lm has already been used to + build linear models with structured sparsity in a handful of material + science studies + (Barroso-Luque + et al., 2022; + Xie + et al., 2023; + Zhong + et al., 2022, + 2023).

+
+ + Usage +

Since the linear regression models in + sparse-lm are implemented to be compatible with + scikit-learn + (Buitinck + et al., 2013; + Pedregosa + et al., 2011), they can be used independently or as part of a + workflow—such as in a hyperparameter selection class or a pipeline— in + similar fashion to any of the available models in the + sklearn.linear_model module.

+ + Implemented regression models +

The table below shows the regression models that are implemented + in sparse-lm as well as available + implementations in other Python packages. A checkmark + ( + + ) + indicates that the model selected is implemented in the package + located in the corresponding column.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Modelsparse-lmcelergroupyrgroup-lassoskglmabess
(Adaptive) Lasso + + + + + +
(Adaptive) Group Lasso + + + + + + + + + +
(Adaptive) Sparse Group Lasso + + + + + + + +
(Adaptive) Ridged Group Lasso + + + +
Best Subset Selection + + + +
Ridged Best Subset Selection + +
+ + 0 + pseudo-norm + +
+ + 02 + mixed-norm + +
+ + 1/2 + psuedo-norm + +
+ + 2/3 + psuedo-norm + +
+
+

Note that only sparse-lm includes adaptive + versions of Lasso based estimators. However, some of the third party + packages, notably skglm and + abess, include additional penalties and + regression objectives that are not implemented in + sparse-lm.

+
+ + Implemented model selection and composition tools +

In addition to the regression models in the table above, a few + model selection and composition models are also implemented. These + models are listed below:

+ + +

One standard deviation rule grid search cross-validation

+
+ +

Line search cross-validation

+
+ +

Stepwise composite estimator

+
+
+

The package can be downloaded through the + Python + Package Index. Documentation, including an API reference + and examples, can be found in the + online + documentation.

+
+
+ + Acknowledgements +

The first author (L.B.L.) is the lead developer of + sparse-lm, and the lead and corresponding + author. The second author (F.X.) is a main contributor to the package. + Both authors drafted, reviewed and edited the manuscript.

+

L.B.L. and F.X. would like acknowledge the contributions from + Peichen Zhong, Ronald L. Kam, and Tina Chen to the development of + sparse-lm. L.B.L gratefully acknowledges + support from the National Science Foundation Graduate Research + Fellowship under Grant No. DGE 1752814.

+
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