Rule Induction Partitioning Estimator

Margot, Vincent; Baudry, Jean-Patrick; Guilloux, Frédéric; Wintenberger, Olivier

doi:10.1007/978-3-319-96133-0_22

Cited by 5 publications

(8 citation statements)

References 8 publications

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“…The discretization of features is a common solution to control the complexity of a rule generator. In [37], for example, the authors use entropy minimization heuristics to discretize features and, for the algorithms Bayesian rule lists (BRL) [36], SIRUS [21,22] and Rule Induction Partioning Estimator (RIPE) [38], the authors have discretized the features by using their empirical quantiles. We refer to [39] for an overview of the common discretization methods.…”

Section: Q-stability Scorementioning

confidence: 99%

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A New Method to Compare the Interpretability of Rule-Based Algorithms

Margot¹,

Luta

2021

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Interpretability is becoming increasingly important for predictive model analysis. Unfortunately, as remarked by many authors, there is still no consensus regarding this notion. The goal of this paper is to propose the definition of a score that allows for quickly comparing interpretable algorithms. This definition consists of three terms, each one being quantitatively measured with a simple formula: predictivity, stability and simplicity. While predictivity has been extensively studied to measure the accuracy of predictive algorithms, stability is based on the Dice-Sorensen index for comparing two rule sets generated by an algorithm using two independent samples. The simplicity is based on the sum of the lengths of the rules derived from the predictive model. The proposed score is a weighted sum of the three terms mentioned above. We use this score to compare the interpretability of a set of rule-based algorithms and tree-based algorithms for the regression case and for the classification case.

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Section: Q-stability Scorementioning

confidence: 99%

“…Rules are selected according to their statistical properties to form a "quasi-covering". The covering is then turned into a partition using the so-called partitioning trick [38] to form a consistent estimator of the regression function.…”

Section: Brief Overview Of the Selected Algorithmsmentioning

confidence: 99%

A New Method to Compare the Interpretability of Rule-Based Algorithms

Margot¹,

Luta

2021

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“…By creating binary vectors of size #C, whose value is 1 if x fulfills the rule's condition and 0 otherwise, this cell identification is a simple sequence of vectorial operations. Figure 3 is an illustration of this process (we refer to Margot et al (2018) for more details).…”

Section: Rule-based Algorithms Using Partitions and Quasi-coveringsmentioning

confidence: 99%

“…Under some conditions, the approximation error of the prediction is low thanks to the ERM principle. The variance will be controlled through the significance condition (see Definition 2.1 below) as in the RIPE algorithm of Margot et al (2018).…”

Section: Rule-based Algorithms Using Partitions and Quasi-coveringsmentioning

confidence: 99%

Consistent regression using data-dependent coverings

Margot¹,

Baudry²,

Guilloux³

et al. 2021

Electron. J. Statist.

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We introduce a procedure to generate an estimator of the regression function based on a data-dependent quasi-covering of the feature space. A quasi-partition is generated from the quasi-covering and the estimator predicts the conditional empirical expectation over the cells of the quasi-partition. We provide sufficient conditions to ensure the consistency of the estimator. Each element of the quasi-covering is labeled as significant or insignificant. We avoid the condition of cell shrinkage commonly found in the literature for data-dependent partitioning estimators. This reduces the number of elements in the quasi-covering. An important feature of our estimator is that it is interpretable.The proof of the consistency is based on a control of the convergence rate of the empirical estimation of conditional expectations, which is interesting in itself.

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“…By creating binary vectors of size #C n , whose value is 1 if x fulfilled the rule's condition and 0 otherwise, this cell identification becomes a simple sequence of vectorial operations. Figure 3 is an illustration of this process (cf Margot et al [2018] for more details).…”

Section: Rule-based Algorithms Using Partitions and Coveringsmentioning

confidence: 99%

Consistent Regression using Data-Dependent Coverings

Margot,

Baudry,

Guilloux

et al. 2019

Preprint

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We introduce a novel method to generate interpretable regression function estimators. The idea is based on data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a partition. The estimator predicts the empirical conditional expectation over the cells of the partitions generated from the coverings. Thus, such estimator has the same form as those issued from data-dependent partitioning algorithms. We give sufficient conditions to ensure the consistency, avoiding the sufficient condition of shrinkage of the cells that appears in the former literature. Doing so, we reduce the number of covering elements. We show that such coverings are interpretable and each element of the covering is tagged as significant or insignificant.The proof of the consistency is based on a control of the error of the empirical estimation of conditional expectations which is interesting on its own.

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Rule Induction Partitioning Estimator

Cited by 5 publications

References 8 publications

A New Method to Compare the Interpretability of Rule-Based Algorithms

A New Method to Compare the Interpretability of Rule-Based Algorithms

Consistent regression using data-dependent coverings

Consistent Regression using Data-Dependent Coverings

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