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IsotoneOptimization

The goal of IsotoneOptimization is to implement the Sequential Block Merging algorithm for solving isotonic regression with constraints represented by arbitrary directed acyclic graph.

Installation

You can install the development version of IsotoneOptimization from GitHub with:

# install.packages("devtools")
devtools::install_github("Xiwen1997/IsotoneRpkg")

Example

This is a basic example which shows you how to solve a general isotonic regression problem:

library(IsotoneOptimization)
## basic example code

Emat <- t(matrix( c(1,2,  1,3,  1,4,  2,5,  2,6,  3,7,  4,8,  5,8,  6,9,  6,10),2,10))
x_ordered <- solve_isotone_DAG(rnorm(10), rep(1,10), Emat)

Using package igraph, we can better view the ordered vector by regarding isotonic constraints as the edges of a graph. Namely, $x_i\leq x_j$ if there exists an arrow from node $i$ to node $j$

library(igraph)
#> 
#> Attaching package: 'igraph'
#> The following objects are masked from 'package:stats':
#> 
#>     decompose, spectrum
#> The following object is masked from 'package:base':
#> 
#>     union
grid_graph <- graph_from_edgelist(Emat)
V(grid_graph)$name <- as.character(round(x_ordered,2))
plot(grid_graph,  vertex.size = 4,          # Smaller nodes
    vertex.label = V(grid_graph)$name, # Set the labels
    vertex.label.cex = 1,   # Slightly smaller font
    vertex.label.dist = 1.4,  # Offset the labels
    vertex.label.color = "black")

Some typical isotonic constraints, including chain, binary tree, 2d-grid isotonic constraints, can be defined directed. Simply using solve_isotone_chain, solve_isotone_binary_tree, and solve_isotone_2d_grid, you can solve the corresponding isotone optimization problem!