Classification and Regression via Integer Optimization

By Dimitris J. Bertsimas, Romy Shioda. 2007

134 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Optimization & Training

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Citations in the corpus

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information (2018, background): “, Curtis and Scheinberg (2017) for a tutorial.”
MurTree: Optimal Decision Trees via Dynamic Programming and Search (2020, methodology): “Bertsimas and Shioda (2007) presented a mixed-integer programming approach for optimal decision tree s that worked well on smaller datasets.”
Learning Optimal Classification Trees Using a Binary Linear Program Formulation (2019, neutral): “The model proposed in (Bertsimas and Shioda 2007) is quadratic in the data set size and therefore requires a lot of preprocessing in order to reduce the number of generated constraints.”
Optimal Generalized Decision Trees via Integer Programming (2016, background): “Another integer model that minimizes misclassification error by choosing general partitions in feature space was proposed in [4], but when solving the model, global optimality certificates were not easily obtained on moderately-sized classification datasets, and the learned partition classifiers rar”
Integer optimization methods for machine learning (2012, methodology): “Still, MIO has already been shown to be effective in feature selection, as well as in classification and regression [Nguyen et al., 2009, Bertsimas and Shioda, 2007, Brooks, 2010].”
IPBoost - Non-Convex Boosting via Integer Programming (2020, methodology): “…and (mixed) integer programming, in particular, has been used successfully to incorporate combinatorial structure in classification, see, e.g., (Bertsimas & Shioda, 2007; Chang et al., 2012; Bertsimas & King, 2015; Bertsimas et al., 2016), as well as, (Günlük et al., 2016; Bertsimas & Dunn,…”
Supervised classification and mathematical optimization (2013, unknown): “However, other areas of Mathematical Optimization play a notable role, among others, Global Optimization [9] [13] [51] [128] [160] [245], Linear Programming [94] [158] [205] Mixed-Integer Programming [25] [39] [50] [77] [220] [228], Nonsmooth Optimization [7] [13] [44] [51] [222] [223], Multicriteri”
Efficient Inference of Optimal Decision Trees (2020, background): “…problem and the efﬁciency of the ﬁrst attempts to infer optimal decision trees, two studies have recently proposed approaches focused on improving the performance of algorithms inferring decision trees with a minimum number of nodes (Bessiere, Hebrard, and O’Sullivan 2009; Narodytska et al. 2018).”
SAT-based Decision Tree Learning for Large Data Sets (2021, methodology): “We can encode weights with DT pb by using different maximum depths for the different classes.”
MurTree: Optimal Classification Trees via Dynamic Programming and Search (2020, methodology): “This objective was used in the original CART paper (Breiman et al. (1984)) and discussed in some of the other optimal decision tree works (Bertsimas and Dunn (2017); Hu et al.”
Optimal trees for prediction and prescription (2018, methodology): “CRIO (Classification and Regression via Integer Optimization), proposed by Bertsimas and Shioda [16], uses MIO to partition and classify the data points.”
Optimization Models for Machine Learning: A Survey (2019, background): “MixedInteger Programming (MIP) models for regression and classification tasks are also investigated in [32].”
Fundamental Diagram of Traffic Flow (2011, methodology): “The FD fitting method is based on a generic formulation proposed by Bertsimas and Shioda (22), which seeks the piecewise linear fit of data with least absolute deviation via a mixed integer program.”
Support Vector Machines with the Ramp Loss and the Hard Margin Loss (2011, background): “Training observations that fall outside the margin that are misclassified have error ∗The author would like to gratefully acknowledge Romy Shioda for ideas arising from numerous discussions.”
Deep learning in business analytics and operations research: Models, applications and managerial implications (2018, background): “…f are common in business analytics: examples from traditional machine learning involve, for instance, linear models (e.g, Bertsimas & King, 2016; Bertsimas & Shioda, 2007 ), decision trees, support vector machines, neural networks (e.g, Delen, Oztekin, & Tomak, 2012; Oztekin, Kizilaslan,…”
Learning fuzzy decision trees using integer programming (2018, background): “Previous work [8], [9], [10] and more recently [11], [12] has already considered such an approach for building crisp decision trees.”
Learning Decision Trees with Flexible Constraints and Objectives Using Integer Optimization (2017, methodology): “A similar approach for more general models is given in [2].”