Package 'MRReg'

Title: MDL Multiresolution Linear Regression Framework
Description: We provide the framework to analyze multiresolution partitions (e.g. country, provinces, subdistrict) where each individual data point belongs to only one partition in each layer (e.g. i belongs to subdistrict A, province P, and country Q). We assume that a partition in a higher layer subsumes lower-layer partitions (e.g. a nation is at the 1st layer subsumes all provinces at the 2nd layer). Given N individuals that have a pair of real values (x,y) that generated from independent variable X and dependent variable Y. Each individual i belongs to one partition per layer. Our goal is to find which partitions at which highest level that all individuals in the these partitions share the same linear model Y=f(X) where f is a linear function. The framework deploys the Minimum Description Length principle (MDL) to infer solutions. The publication of this package is at Chainarong Amornbunchornvej, Navaporn Surasvadi, Anon Plangprasopchok, and Suttipong Thajchayapong (2021) <doi:10.1145/3424670>.
Authors: Chainarong Amornbunchornvej [aut, cre]
Maintainer: Chainarong Amornbunchornvej <[email protected]>
License: MIT + file LICENSE
Version: 0.1.5
Built: 2025-02-04 03:09:14 UTC
Source: https://github.com/darkeyes/mrreg

Help Index

FindMaxHomoOptimalPartitions

Description

FindMaxHomoOptimalPartitions is a main function for inferring optimal homogeneous clusters from a multiresolution dataset DataT.

Usage

FindMaxHomoOptimalPartitions(
  DataT,
  gamma = 0.05,
  insigThs = 1e-08,
  alpha = 0.05,
  minInvs = 99,
  polyDegree = 1,
  expFlag = FALSE,
  messageFlag = FALSE
)

Arguments

DataT

contains a multiresolution dataset s.t. DataT$X[i,d] is a value of feature d of individual i, DataT$Y[i] is value of target variable of individual i that we want to fit DataT$Y ~ DataT$X in linear model, and clsLayer[i,j] is a cluster ID of individual i at layer j; clsLayer[i,1] is the first layer that everyone typically belongs to a single cluster.
gamma

is a threshold to ...
insigThs

is a threshold to determine whether a magnitude of a feature coefficient is enough so that the feature is designated as a selected feature.
alpha

is a significance level to determine whether a magnitude of a feature coefficient is enough so that the feature is designated as a selected feature.
minInvs

is a minimum number of individuals for a cluster to be considered for inferring eta(C)cv, otherwise, eta(C)cv=0.
polyDegree

is a degree of polynomial function that is used to fit the data. If it is greater than 1, the polynomial formula is used in lm() instead of "y=.".
expFlag

is an exponential flag to control the formula for data fitting. If it is true, then the exp() formula is used in lm() instead of "y=.".
messageFlag

is a flag. If it is true, the function shows the text regarding the progress of computing.

Value

This function returns Copt, models, nNodes, invOptCls, and minR2cv.

Copt

Copt[p,1] is equal to k implies a cluster that is a pth member of the maximal homogeneous partition is at kth layer and the cluster name in kth layer is Copt[p,2] Copt[p,3] is "Model Information Reduction Ratio" I({C},H0,Hlin) of pth member of the maximal homogeneous partition: positive means the linear model is better than the null model. Lastly,Copt[p,4] is the squared correlation between predicted and real Y in CV step ( eta(C)cv ) of pth member of the maximal homogeneous partition. The greater Copt[p,4], the higher homogeneous degree of this cluster.
clustInfoRecRatio

models[[k]][[j]]$clustInfoRecRatio is the "Cluster Information Reduction Ratio" I(Cj,Cjchildren,H) between the jth cluster in kth layer and its children clusters in (k+1)th layer: positive means current cluster is better than its children clusters. Hence, we should keep this cluster at the member of maximal homogeneous partition instead of its children.
models

models[[j]][[k]] is a linear model of a cluster ID k at the layer j. The models[[j]][[k]]$selFeatureSet represents a set of selected-feature indices of the model where the feature index 1 is the intercept, and the feature index d is the (d-1)th variable DataT$X[,d-1].

invOptCls

invOptCls[i,1] is the layer of optimal cluster of individual i. The optimal cluster of i is invOptCls[i,2].

minR2cv

is the value of eta(C)cv from the cluster that has the lowest eta(C)cv.

DataT

is an updated DataT with the helper variables for plotting and printing results.

Examples

# Running FindMaxHomoOptimalPartitions using simulation data
DataT<-SimpleSimulation(100,type=1)
obj<-FindMaxHomoOptimalPartitions(DataT,gamma=0.05)

linearModelTraining

Description

linearModelTraining is a support function for training linear models for partitions in all layers.

Usage

linearModelTraining(
  DataT,
  insigThs = 1e-08,
  alpha = 0.05,
  messageFlag = FALSE,
  polyDegree = 1,
  expFlag = FALSE
)

Arguments

DataT

contains a multiresolution dataset s.t. DataT$X[i,d] is a value of feature d of individual i, DataT$Y[i] is value of target variable of individual i that we want to fit DataT$Y ~ DataT$X in linear model, and clsLayer[i,j] is a cluster ID of individual i at layer j; clsLayer[i,1] is the first layer that everyone typically belongs to a single cluster.
insigThs

is a threshold to determine whether a magnitude of a feature coefficient is enough so that the feature is designated as a selected feature.
alpha

is a significance level to determine whether a magnitude of a feature coefficient is enough so that the feature is designated as a selected feature.
messageFlag

is a flag. If it is true, the function shows the text regarding the progress of computing.
polyDegree

is a degree of polynomial function that is used to fit the data. If it is greater than 1, the polynomial formula is used in lm() instead of "y=.".
expFlag

is an exponential flag to control the formula for data fitting. If it is true, then the exp() formula is used in lm() instead of "y=.".

Value

This function returns models and DataT.

models

models[[j]][[k]] is a linear model of a cluster ID k at the layer j. The models[[j]][[k]]$selFeatureSet represents a set of selected-feature indices of the model where the feature index 1 is the intercept, and the feature index d is the (d-1)th variable DataT$X[,d-1].

DataT

is a DataT with DataT$nNodes, which is a number of total models from all layers.

Examples

# Running linearModelTraining using simulation data
DataT<-SimpleSimulation(100,type=1)
obj<-linearModelTraining(DataT)

plotOptimalClustersTree

Description

plotOptimalClustersTree is a support function for plotting the hierarchical tree of optimal clusters from FindMaxHomoOptimalPartitions function.

The red node(s) are the optimal homogeneous clusters while the gray nodes are non-optimal clusters.

Usage

plotOptimalClustersTree(resObj)

Arguments

resObj

is an object list, which is the output of FindMaxHomoOptimalPartitions function

Value

No return value, called for plotting the hierarchical tree of optimal clusters.

Examples

# Running FindMaxHomoOptimalPartitions using simulation data
DataT<-SimpleSimulation(100,type=1)
obj<-FindMaxHomoOptimalPartitions(DataT,gamma=0.05)
# Plotting the result
plotOptimalClustersTree(obj)

PrintOptimalClustersResult

Description

PrintOptimalClustersResult is a support function for printing the optimal clusters from FindMaxHomoOptimalPartitions function.

Usage

PrintOptimalClustersResult(resObj, selFeature = FALSE)

Arguments

resObj

is an object list, which is the output of FindMaxHomoOptimalPartitions function
selFeature

is a flag. If it is true, then the function shows the selected feature(s) of each optimal cluster.

Value

No return value, called for printing optimal clusters.

Examples

# Running FindMaxHomoOptimalPartitions using simulation data
DataT<-SimpleSimulation(100,type=1)
obj<-FindMaxHomoOptimalPartitions(DataT,gamma=0.05)
# Printing the result
PrintOptimalClustersResult(obj)

SimpleSimulation

Description

SimpleSimulation is a support function for generating multiresolution datasets.

All simulation types have three layers except the type 6 has four layers.

The type-1 simulation has all individuals belong to the same homogeneous partition in the first layer.

The type-2 simulation has four homogeneous partitions in a second layer. Each partition has its own models.

The type-3 simulation has eight homogeneous partitions in a third layer. Each partition has its own models

The type-4 simulation has one homogeneous partition in a second layer, four homogeneous partitions in a third layer, and eight homogeneous partitions in a fourth layer. Each partition has its own model.

The type-5 simulation is similar to type-4 simulation but Y=h(X) is an exponential function.

The type-6 simulation is similar to type-4 simulation but Y=h(X) is a polynomial function with degree parameter.

Usage

SimpleSimulation(indvN = 10000, type = 1, degree = 2)

Arguments

indvN

is a number of individuals per homogeneous partition.
type

is a type of simulation dataset. There are four types.
degree

is a degree parameter of a polynomial function for type-5 simulation

Value

The function returns a multiresolution dataset.

DataT$X[i, d]

is a value of feature d of individual i

DataT$Y[i]

is value of target variable of individual i that we want to fit DataT$Y ~ DataT$X in linear model
clsLayer[i, j]

is a cluster ID of individual i at layer j; clsLayer[i,1] is the first layer that everyone typically belongs to a single cluster.

DataT$TrueFeature[i]

is equal to d if a true feature is DataT$X[i,d-1] that DataT$Y[i] is dependent with. Note that d = 1 is reserved for the intercept value in a linear model.

Examples

# Running SimpleSimulation to generate a dataset.
DataT<-SimpleSimulation(100,type=1)