A-GWR

Implimentation of A-GWR modular framework and S-MGWR spatial model.

Table of Contents

• How to install
  • Libraries
  • MGWR and GWR
• Quick Start
• How does it work
  • What is the Modular framework
    • Pipeline
    • Ensemble
  • What is S-MGWR
• Project Breakdown
  • Modular Framework
    • DataDivider
    • ModularFramework
  • S-MGWR
    • SpaceSearch
    • Cache
• Results

How to Install

Libraries

The libraries used in this project along with the version A-GWR was tested on are as follows

MGWR and GWR

We used a modified version of MGWR and GWR in our code. The modified versions are included here. For more information on GWR code check (link fix)

Quick Start

For more information check the example file in the root directory. Both spatial and ml modules need to have a train and a predict function. A few samples for both spatial and ml modules are listed in the helper/SampleModules directory.

To run the example after navigating to the project location, run:

python -m example

The example code, uses a SMGWR model as spatial module and Random Forest as the general purpose ml module.

How does it work

A-GWR contains two parts, a novel spatial module called S-MGWR, and a framework to combine spatial and general purpose ML models.

What is the Modular framework

We introduce a modular framework to combine spatial models and general purpose models. In traditional methods, such as ordinary least squares, the role of location is often neglected or is not properly captured. Many spatial models such as GWR are introduced to overcome this issue. However, these methods often cannot capture non-linear relations. In A-GWR modular framework, by combining spatial models and general-purpose ml models, we have tried to solve this problem.

We have two methods to combine the modules, the Pipeline (spatial modelfirst) method and the Ensemble (general-purpose model first) method.

Pipeline

The following figure shows how the pipeline method works.

Ensemble

The following figure shows how the Ensemble method works.

What is S-MGWR

S-MGWR is a stateless variation of MGWR spatial model that assigns different localities to different features. S-MGWR extends MGWR by eliminating the need for a history of bandwidth values.

In S-MGWR, the search for bandwidths can be treated like a blackbox optimization and can also be done in parallel.

In our implementation, to speed up the training process, we've also implemented an LRU cache system to keep the recently computed weight values.

Project Breakdown

In this section, we break down the project in more details.

Data

The Data directory, holds the dataset we originally used. In Data/DataHandlers the codes we used to clean or create each dataset is provided.

helpers

In the helpers/SampleModules directory contains a few samples of spatial and ML modules. The Spatial Module contains GWR, MGWR, and S-MGWR. The S-MGWR is configured to perform Successive Halving, SPSA, Bayesian Optimization, and Hill Climbing but can be changed to perform any space search method suitable for the user's application.

Modular Framework

Both pipeline and ensemble methods divide the data into sections. This is done by the data divider code. The modular framework creates an instance of the datadivider and combines it with the target architecture (pipeline or ensemble)

DataDivider

The code for Random, k-means, grid divide is implemented in DataDivider. In addition, for the test data, in order to find the influence of each section on the test data point, the weighted_mean function is implemented.

ModularFramework

This class has the implementation of the modular framework. In the initialization, the spatial model, general purpose model, and the configuration (such as the divide method) is passed to this class.

The train function, based on the method (pipeline, ensemble) creates the threads and runs the appropriate modules.

S-MGWR

This directory contains the implementation codes for the S-MGWR spatial model.

SpaceSearch

To find the best set of bandwidths, some of the most famous hyper parameter optimization algorithms have been implemented. These methods implemented are:

1- Hyperband
2- Successive Halving
3- Simulated Annealing
4- Hill Climbing
5- Golden Section Section
6- Bayesian Optimization
7- Simultaneous perturbation stochastic approximation (SPSA)

Cache

We have also implemented an LRU cache system to store the weights computed for recently used bandwidths

Results

	pGeorgia	pTokyo	pClrwatr	pBerlin	synthData1	synthData2	kingHousePrices	NYCAirBnb
	1-R2	1-R2	1-R2	1-R2	1-R2	1-R2	1-R2	1-R2
A-GWR	0.4161 ± 0.05	0.0164 ± 0.0017	0.9226 ± 0.0645	0.6821 ± 0.0145	0.0137 ± 0.0008	0.061 ± 0.0068	0.1109	0.4181
MGWR	0.4913 ± 0.0689	0.0226 ± 0.0038	0.9622 ± 0.0713	0.6965 ± 0.0039	0.0139 ± 0.0014	0.0999 ± 0.009	0.1341	0.4378
GWR	0.3914 ± 0.0629	0.0215 ± 0.0032	0.9265 ± 0.0577	0.6876 ± 0.0076	0.0805 ± 0.0108	0.1168 ± 0.0068	0.1295	0.4284
Random Forest	0.3878 ± 0.0346	0.0352 ± 0.0024	0.9276 ± 0.0589	0.5825 ± 0.0094	0.1788 ± 0.0041	0.1240 ± 0.0019	0.1216	0.3927
XGBoost	0.6229 ± 0.0832	0.0359 ± 0.0026	1.0304 ± 0.0561	0.6942 ± 0.0182	0.1634 ± 0.0051	0.1042 ± 0.0008	0.1165	0.4092