Statistical Learning with Sparsity: The Lasso and Generalizations

By Trevor J. Hastie, Robert Tibshirani, Martin J. Wainwright. 2015

2,430 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Nature and Landscape Conservation, Statistical Learning Theory

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Citations in the corpus

Federated learning of predictive models from federated Electronic Health Records (2018, background): “[6] Results in the literature suggest that sparse classifiers (i.e., those that rely on few features), have strong predictive power and generalize well out-of-sample,[7,8] providing at the same time interpretability in both models and results.”
Mathematical optimization in classification and regression trees (2021, methodology): “Alternatively, we can embed the sparsity in the optimization model solved to train the model, as we have seen in the optimal trees reviewed in the previous section, either with LASSO terms (Hastie et al. 2015) or zero-norm terms (Weston et al. 2003).”
From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification (2016, background): “The connection between sparse modeling and interpretability is key in signal processing (Hastie et al., 2015).”
Forecasting Electricity Spot Prices Using Lasso: On Capturing the Autoregressive Intraday Structure (2015, methodology): “For more information on the lasso algorithm from the theoretical and applied point of view we recommend the recently published lasso overview book [26].”
Model Selection Techniques: An Overview (2018, background): “Though originally designed for linear regression, LASSO has been also extended to a wide range of statistical models such as generalized linear models (see [61] and the references therein).”
A Transaction-Cost Perspective on the Multitude of Firm Characteristics (2020, neutral): “See Hastie, Tibshirani, and Wainwright (2015) for an in-depth treatment of the lasso, and for a Bayesian interpretation of the lasso constraint in the context of portfolio choice, see DeMiguel, Garlappi, Nogales, and Uppal (2009a).”
The Optimal Ridge Penalty for Real-world High-dimensional Data Can Be Zero or Negative due to the Implicit Ridge Regularization (2020, methodology): “The standard approach to such problems is “to bet on sparsity” (Hastie et al., 2015) and to use linear models with regularization performing feature selection, such as the lasso (Tibshirani, 1996), the elastic net (Zou and Hastie, 2005), or the Dantzig selector (Candes and Tao, 2007).”
What is an optimal value of k in k-fold cross-validation in discrete Bayesian network analysis? (2020, background): “…a trivial problem, however, as even large empirical data sets (e.g., “big data”) can have small numbers of replications of cases with specific combinations of variables (Hastie et al. 2015) or can be biased by excluding or unnecessarily codi-fying low values of some variables (Stow et al. 2018).”
Causal Interaction in Factorial Experiments: Application to Conjoint Analysis (2018, positive): “In particular, we estimate the selection probability for each AME and AMIE using one minus the proportion of 5000 bootstrap replicates in which all coefficients for the corresponding factor or factor interaction are estimated to be zero (Efron, 2014; Hastie et al., 2015).”
Electricity price forecasting using sale and purchase curves: The X-Model (2015, background): “For more theoretical and applied details on the lasso estimator we suggest Hastie et al. (2015).”
On clustering categories of categorical predictors in generalized linear models (2021, methodology): “Fifth, our approach can also be applied to regularized linear models, i.e., instead of using GLM as the base model we could have used, e.g., a LASSO (Van de Geer, 2008; Hastie et al., 2015) or a Group LASSO (Meier et al., 2008; Detmer et al., 2020).”
Spectral Deconfounding and Perturbed Sparse Linear Models (2018, neutral): “See, for example, the monographs [4, 9, 12].”
Newton Sketch: A Near Linear-Time Optimization Algorithm with Linear-Quadratic Convergence (2015, positive): “, [18, 31]) that the tangent cone of the 1-norm at any s-sparse solution is a subset of the cone {z ∈ R | ‖z‖1 ≤ 2√s‖z‖2}.”