1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

Tree-based machine learning models such as random forests, decision trees and gradient boosted trees are popular nonlinear predictive models, yet comparatively little attention has been paid to explaining their predictions. Here we improve the interpretability of tree-based models through three main contributions. (1) A polynomial time algorithm to compute optimal explanations based on game theory. (2) A new type of explanation that directly measures local feature interaction effects. (3) A new set of tools for understanding global model structure based on combining many local explanations of each prediction. We apply these tools to three medical machine learning problems and show how combining many high-quality local explanations allows us to represent global structure while retaining local faithfulness to the original model. These tools enable us to (1) identify high-magnitude but low-frequency nonlinear mortality risk factors in the US population, (2) highlight distinct population subgroups with shared risk characteristics, (3) identify nonlinear interaction effects among risk factors for chronic kidney disease and (4) monitor a machine learning model deployed in a hospital by identifying which features are degrading the model’s performance over time. Given the popularity of tree-based machine learning models, these improvements to their interpretability have implications across a broad set of domains. Tree-based machine learning models are widely used in domains such as healthcare, finance and public services. The authors present an explanation method for trees that enables the computation of optimal local explanations for individual predictions, and demonstrate their method on three medical datasets.

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From Local Explanations to Global Understanding with Explainable AI for Trees.

Reverse search for enumeration

In this chapter we deal with the following nonlinear fractional programming problem: 

$$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$

where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Nonlinear Fractional Programming

Integer programming formulations of discrete hub location problems

It is shown that parametric linear programming algorithms work efficiently for a class of nonconvex quadratic programming problems called generalized linear multiplicative programming problems, whose objective function is the sum of a linear function and a product of two linear functions. Also, it is shown that the global minimum of the sum of the two linear fractional functions over a polytope can be obtained by a similar algorithm. Our numerical experiments reveal that these problems can be solved in much the same computational time as that of solving associated linear programs. Furthermore, we will show that the same approach can be extended to a more general class of nonconvex quadratic programming problems.

Parametric simplex algorithms for solving a special class of nonconvex minimization problems

NP-completeness for calculating power indices of weighted majority games

The linear multiplicative programming problem minimizes a product of two (positive) variables subject to linear inequality constraints. In this paper, we show NP-hardness of linear multiplicative programming problems and related problems.

NP-hardness of linear multiplicative programming and related problems

Finding all the perfect matchings in bipartite graphs

AN INEFFICIENCY MEASUREMENT METHOD FOR MANAGEMENT SYSTEMS Yoshiyasu Yamada Science University 0/ Tokyo Tomomi Mat.sui Manabu Sugiyama University 0/ Tokyo Science University 0/ Tokyo This paper at. first, proposes a new method \"Inverted Data Envelopment Analysis(Inverted DEA)\" for measuring the relative inefficiency of a set of system~ (Decision Making Units). By applying this method, we can identify the relative inefficiency factors of eac h decision making unit (Dl\\fU). The method has, in a sense, an inverse relation with Data Envelopment Analysis (DEA) developed by Charnes, Cooper and Rhodes. More precisely, our proposed measure of t.he inefficiency of any DMU is obt.a.ined as the maximum of a ratio of weighted inputs to weighted outputs subject to the condition that the similar ratios for every DMU be less than or equal to unity. Secondly, we propose a method to classify DMUs by integrat.ing t.he information from DEA and Invert.ed DEA. This met.hod can find the singularity of DMlTs. Finally, we show the practicabilit.y and effect.iveness of the classification method by using real financial and businf'ss activit.y data of the branches of a Japanese department store. © 1994 The Operations Research Society of Japan

https://www.jstage.jst.go.jp/article/jorsj/37/2/37_KJ00001202925/_pdf

Tomomi Matsui

Papers

Parametric simplex algorithms for solving a special class of nonconvex minimization problems

NP-completeness for calculating power indices of weighted majority games

NP-hardness of linear multiplicative programming and related problems

Finding all the perfect matchings in bipartite graphs

An inefficiency measurement method for management systems