scholarly journals Plurisubharmonic approximation and boundary values of plurisubharmonic functions

2014 ◽  
Vol 413 (2) ◽  
pp. 700-714 ◽  
Author(s):  
Lisa Hed ◽  
Håkan Persson
Keyword(s):  
Boundary Values ◽  
Plurisubharmonic Functions

APPROXIMATION OF NEGATIVE PLURISUBHARMONIC FUNCTIONS WITH GIVEN BOUNDARY VALUES

2010 ◽  
Vol 21 (09) ◽  
pp. 1135-1145 ◽  
Author(s):  
LISA HED
Keyword(s):  
Plurisubharmonic Function ◽  
Boundary Values ◽  
Plurisubharmonic Functions

In this paper, we study the approximation of negative plurisubharmonic functions with given boundary values. We want to approximate a plurisubharmonic function by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

THE DIRICHLET PROBLEM FOR MAXIMAL PLURISUBHARMONIC FUNCTIONS ON ANALYTIC VARIETIES IN ℂn

2009 ◽  
Vol 20 (04) ◽  
pp. 521-528 ◽  
Author(s):  
FRANK WIKSTRÖM
Keyword(s):  
Dirichlet Problem ◽  
Continuous Function ◽  
Plurisubharmonic Function ◽  
Boundary Values ◽  
Regular Domain ◽  
Analytic Variety ◽  
Plurisubharmonic Functions ◽  
Analytic Varieties

Let Ω be a B-regular domain in ℂn and let V be a locally irreducible analytic variety in Ω. Given a continuous function [Formula: see text], we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by ϕ and furthermore that u is continuous on [Formula: see text].

Convergence in capacity of plurisubharmonic functions with given boundary values

2017 ◽  
Vol 28 (03) ◽  
pp. 1750018 ◽  
Author(s):  
Nguyen Xuan Hong ◽  
Nguyen Van Trao ◽  
Tran Van Thuy
Keyword(s):  
Boundary Values ◽  
Plurisubharmonic Functions ◽  
Monge Ampere ◽  
Stability Results ◽  
Convergence In Capacity

In this paper, we study the convergence in the capacity of sequence of plurisubharmonic functions. As an application, we prove stability results for solutions of the complex Monge–Ampère equations.

scholarly journals gbt-HIPS: Explaining the Classifications of Gradient Boosted Tree Ensembles

2021 ◽  
Vol 11 (6) ◽  
pp. 2511
Author(s):  
Julian Hatwell ◽  
Mohamed Medhat Gaber ◽  
R. Muhammad Atif Azad
Keyword(s):  
State Of The Art ◽  
Heuristic Method ◽  
Good Explanation ◽  
Classification Rule ◽  
Data Sets ◽  
Classification Models ◽  
Boundary Values ◽  
Class Label ◽  
Input Space ◽  
Boosted Tree

This research presents Gradient Boosted Tree High Importance Path Snippets (gbt-HIPS), a novel, heuristic method for explaining gradient boosted tree (GBT) classification models by extracting a single classification rule (CR) from the ensemble of decision trees that make up the GBT model. This CR contains the most statistically important boundary values of the input space as antecedent terms. The CR represents a hyper-rectangle of the input space inside which the GBT model is, very reliably, classifying all instances with the same class label as the explanandum instance. In a benchmark test using nine data sets and five competing state-of-the-art methods, gbt-HIPS offered the best trade-off between coverage (0.16–0.75) and precision (0.85–0.98). Unlike competing methods, gbt-HIPS is also demonstrably guarded against under- and over-fitting. A further distinguishing feature of our method is that, unlike much prior work, our explanations also provide counterfactual detail in accordance with widely accepted recommendations for what makes a good explanation.

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