Characterizing the optimal solutions to the isotonic regression problem for identifiable functionals

2021 ◽  
Author(s):  
Alexander I. Jordan ◽  
Anja Mühlemann ◽  
Johanna F. Ziegel
Keyword(s):  
Isotonic Regression ◽  
Optimal Solutions ◽  
Regression Problem

An Isotonic Regression Problem for Infinite-Dimensional Parameters

1999 ◽  
Vol 103 (2) ◽  
pp. 359-384
Author(s):  
R. Khattree ◽  
D. P. Schmidt ◽  
I. E. Schochetman
Keyword(s):  
Isotonic Regression ◽  
Regression Problem ◽  
Infinite Dimensional ◽  
Dimensional Parameters

Analyzing an extension of the isotonic regression problem

Metrika ◽  
2006 ◽  
Vol 66 (1) ◽  
pp. 19-30 ◽  
Author(s):  
J. Santos Domínguez-Menchero ◽  
Gil González-Rodríguez
Keyword(s):  
Isotonic Regression ◽  
Regression Problem

A test for a multiple isotonic regression problem

Biometrika ◽  
1988 ◽  
Vol 75 (1) ◽  
pp. 181-184 ◽  
Author(s):  
KENTARO NOMAKUCHI ◽  
NING-ZHONG SHI
Keyword(s):  
Isotonic Regression ◽  
Regression Problem

The Isotonic Regression Problem and its Dual

1972 ◽  
Vol 67 (337) ◽  
pp. 140-147 ◽  
Author(s):  
R. E. Barlow ◽  
H. D. Brunk
Keyword(s):  
Isotonic Regression ◽  
Regression Problem

Combinatorial Optimization of Clustering Decisions: An Application to Refine Psychiatric Diagnoses

2018 ◽  
Author(s):  
Jordan Stevens ◽  
Douglas Steinley ◽  
Cassandra L. Boness ◽  
Timothy J Trull ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
Alcohol Use Disorder ◽  
Point Of View ◽  
Psychiatric Diagnoses ◽  
Optimal Solutions ◽  
Specific Function ◽  
Significant Information ◽  
Diagnosis Group ◽  
Clustering Problems ◽  
Unique Application

Using complete enumeration (e.g., generating all possible subsets of item combinations) to evaluate clustering problems has the benefit of locating globally optimal solutions automatically without the concern of sampling variability. The proposed method is meant to combine clustering variables in such a way as to create groups that are maximally different on a theoretically sound derivation variable(s). After the population of all unique sets is permuted, optimization on some predefined, user-specific function can occur. We apply this technique to optimizing the diagnosis of Alcohol Use Disorder. This is a unique application, from a clustering point of view, in that the decision rule for clustering observations into the diagnosis group relies on both the set of items being considered and a predefined threshold on the number of items required to be endorsed for the diagnosis to occur. In optimizing diagnostic rules, criteria set sizes can be reduced without a loss of significant information when compared to current and proposed, alternative, diagnostic schemes.

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