A lasso for hierarchical interactions

Bien, Jacob; Taylor, Jonathan; Tibshirani, Robert

doi:10.1214/13-aos1096

Cited by 418 publications

(650 citation statements)

References 41 publications

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“…A comparative analysis is then done with the generalised additive models (GAMs) which are used as benchmark models. In this study, we discuss an application of pairwise hierarchical interactions discussed in Bien et al [24] and Laurinec [25] who showed that the inclusion of interactions improves forecast accuracy.…”

Section: Contextmentioning

confidence: 99%

Probabilistic Hourly Load Forecasting Using Additive Quantile Regression Models

2018

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Short-term hourly load forecasting in South Africa using additive quantile regression (AQR) models is discussed in this study. The modelling approach allows for easy interpretability and accounting for residual autocorrelation in the joint modelling of hourly electricity data. A comparative analysis is done using generalised additive models (GAMs). In both modelling frameworks, variable selection is done using least absolute shrinkage and selection operator (Lasso) via hierarchical interactions. Four models considered are GAMs and AQR models with and without interactions, respectively. The AQR model with pairwise interactions was found to be the best fitting model. The forecasts from the four models were then combined using an algorithm based on the pinball loss (convex combination model) and also using quantile regression averaging (QRA). The AQR model with interactions was then compared with the convex combination and QRA models and the QRA model gave the most accurate forecasts. Except for the AQR model with interactions, the other two models (convex combination model and QRA model) gave prediction interval coverage probabilities that were valid for the 90%, 95% and the 99% prediction intervals. The QRA model had the smallest prediction interval normalised average width and prediction interval normalised average deviation. The modelling framework discussed in this paper has established that going beyond summary performance statistics in forecasting has merit as it gives more insight into the developed forecasting models.

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Section: Contextmentioning

confidence: 99%

Probabilistic Hourly Load Forecasting Using Additive Quantile Regression Models

2018

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“…Moreover, it can be helpful to integrate additional assumptions concerning the model structure to guide the learning process in the spirit of [1,10]. This can be achieved by modifying the Lasso penalization in various ways.…”

Section: Discussionmentioning

confidence: 99%

“…However, they only interactions defined using the and operator. To allow more types of Boolean operations, the works in [1] and [10] incorporate extra information such as the structure of coefficients to guide the learning process. However, these methods need expert knowledge that is not always available.…”

Section: Related Workmentioning

confidence: 99%

Sparse Logistic Regression with Logical Features

Zou

Roos

2016

Advances in Knowledge Discovery and Data Mining

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Abstract. Modeling interactions in regression models poses both computational as well as statistical challenges: the computational resources and the amount of data required to solve them increases sharply with the size of the problem. We focus on logistic regression with categorical variables and propose a method for learning dependencies that are expressed as general Boolean formulas. The computational and statistical challenges are solved by applying a technique called transformed Lasso, which involves a matrix transformation of the original covariates. We compare the method to an earlier related method, LogicReg, and show that our method scales better in terms of the number of covariates as well as the order and complexity of the interactions.

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“…By expressing Equation 10 Electricity, including temperature data used in this study, is discussed in the next sub-sections. The variables used were later selected using the shrinkage method Lasso via hierarchical pairwise interactions discussed in Bien et al (2013), meaning that variables included in the interactions, i.e., cross-effects, will also be included in the main effects.…”

Section: The Generalised Additive-tensor Product Interactions Model Wmentioning

confidence: 99%