Geographical-Gaussian-Process-Regression

KO | EN

gitlite — search

#javascript #ai #golang #machine-learning #rust #deep-learning #docker #nodejs #awesome-list #vue #security #ios #openai #open-source

Geographical-Gaussian-Process-Regression

(★ 117)

Geographical Gaussian Process Regression (GGPR) model for spatial prediction and exploratory spatial data analysis

파일 탐색기

최종 버전 다운로드 (.zip)

- example.txt
chicago.geojson
geoshapley.py
GGPR_ESDA_Chicago.ipynb
GGPR_ESDA_UK.ipynb
GGPR_Prediction.ipynb
leave_data.geojson
README.md
Simulated_data.ipynb

// repository documentation

Was this content helpful?

★ 0 (0 ratings)

### Geographical Gaussian Process Regression
Geographical Gaussian Process Regression (GGPR): A Spatial Machine Learning Model Based on **Spatial Similarity**:

defined as [A-Xing Zhu et al. (2018)](https://doi.org/10.1080/19475683.2018.1534890): *"The more similar geographic configurations of two points (areas), the more similar the values (processes) of the target variable at these two points (areas)".*

GGPR has two functions: **spatial prediction** and **exploratory spatial data analysis (ESDA)**. For spatial prediction, GGPR uses spatial similarity as a kernel function to calibrate the GPR model and then predicts the values of unknown observations. To perform ESDA, we build on the spatial prediction function by adding a Matern kernel with spatial coordinates, as it effectively captures spatial dependence in spatial data. This approach offers two benefits. First, it allows GGPR to achieve explainability through GeoShapley (We strongly recommend using the uploaded version in our code). Second, GGPR can capture global geographic trends while effectively depicting local details and irregularities, thereby considering spatial dependence and spatial similarity to enhance GGPR’s capability in ESDA.

### Problem Statement
1.Most existing ML in spatial data can lead to overly optimistic performance and biased errors due to the conflict between spatial autocorrelation and the independent and identically distributed (i.i.d.) assumption.

2.Spatial ML models based on spatial dependence and spatial heterogeneity often require dense samples to satisfy the spatial stationarity assumption, making them inappropriate for small-sample prediction.

3.Few studies offered explainable tools to interpret black-box ML models and capture spatial effects for assisting the spatially decision-making research.

### Abstract
This study proposes a new spatial machine learning model called Geographical Gaussian Process Regression (GGPR). GGPR is extended from Gaussian Process Regression (GPR) by using the principle of spatial (geographic) similarity for calibration, and it is designed to conduct spatial prediction and exploratory spatial data analysis (ESDA). GGPR addresses several key challenges in spatial machine learning. First, as a probabilistic model, GGPR avoids the conflict between spatial autocorrelation and the assumption of independent and identically distributed (i.i.d.), thus enhancing the model’s objectivity and reliability in spatial prediction. Second, GGPR is suitable for small-sample prediction that most existing models can hardly handle. Finally, integrated with GeoShapley, GGPR is an explainable model can measure spatial effects and explain the outcomes. Evaluated on two distinct datasets, GGPR demonstrates superior predictive performance compared to other popular machine learning models across various sampling ratios, with its advantage becoming particularly pronounced at smaller sampling ratios. As an ESDA model, GGPR demonstrates enhanced accuracy, better computational efficiency, and a comparable ability to measure spatial effects against both Multiscale Geographically Weighted Regression (MGWR) and Geographical Random Forests (GRF). In short, GGPR offers spatial data scientists a new method for predicting and exploring complex geographical processes.

### Spatial Prediction
For spatial prediction, GGPR outperformed traditional GPR family models, Random Forests (RF), and eXtreme Gradient Boosting (XGBoost) across both datasets, with its advantages being particularly evident in small-sample predictions.

The following figure illustrates the impact of noise on the performance of GGPR across two datasets. To ensure model robustness, we recommend setting the noise level for GGPR at or around 10<sup>-1</sup> (0.1).
<img src="https://github.com/user-attachments/assets/f0074911-0317-444c-a001-dcf1c55e6e4e" width="1000">

### Exploratory Spatial Data Analysis 
It is important to note that when used as an ESDA model, the GGPR model is employed to predict its own data (in-sample prediction) to maximally learn spatial patterns and capture geographic phenomena, a practice similar to that of MGWR and GRF. To avoid the over-fitting, we employed five-fold cross validation to train GGPR to get the best parameters. Then, we reintroduced the entire dataset into the model for in-sample prediction to fit the model, and subsequently used GeoShapley Python package to explain the results, obtaining the distribution of GeoShapley values.

As shown in following figure, by comparing the true spatially varying coefficients, we can observe that both MGWR and GGPR are capable of capturing spatial effects, and their coefficient estimation results are very similar. Although our simulated dataset includes more noise than [Ziqi Li (2024)](https://github.com/Ziqi-Li/geoshapley), they are essentially similar in nature. By comparing the ability of traditional machine learning models (GPR, XGBoost, RF, SVM) presented in [Ziqi Li (2024)](https://github.com/Ziqi-Li/geoshapley) to capture spatial effects, we observe that GGPR demonstrates significant advantages. This effectively highlights GGPR’s strength as a spatial machine learning model in understanding geographic processes.
<img src="https://github.com/user-attachments/assets/a2b88e33-97f6-40f1-9c3f-7d9f91ecb62d" width="1000">

We presented the explainable results for the referendum dataset.
<img src="https://github.com/user-attachments/assets/32926b16-89ec-4d44-b763-5dc7b82c19d7" width="1000">
<img src="https://github.com/user-attachments/assets/3a66e4b5-3d37-4762-8d23-a9041c3b9d99" width="1000">
<img src="https://github.com/user-attachments/assets/bd258063-d4ca-4499-be9c-7f95ee3a0ea0" width="1000">

### Dataset
Two datasets were used to evaluate the performance of GGPR: ride-hailing service demand in Chicago [(Ziqi Li, 2022)](https://github.com/Ziqi-Li/SHAP_spatial_data_paper) and the referendum on EU membership in the UK [(Evan Odell, 2020)](https://cran.r-project.org/src/contrib/Archive/parlitools/).

### Reference:
To cite this paper: Zhenzhi Jiao & Ran Tao (2025). Geographical Gaussian Process Regression (GGPR): A Spatial Machine Learning Model Based on Spatial Similarity. Geographical Analysis.  https://doi.org/10.1111/gean.12423

Zhu, A. X., Lu, G., Liu, J., Qin, C. Z., & Zhou, C. (2018). Spatial prediction based on Third Law of Geography. Annals of GIS, 24(4), 225-240.

Li, Z. (2024). GeoShapley: A Game Theory Approach to Measuring Spatial Effects in Machine Learning Models. Annals of the American Association of Geographers, 1-21.

Li, Z. (2022). Extracting spatial effects from machine learning model using local interpretation method: An example of SHAP and XGBoost. Computers, Environment and Urban Systems, 96, 101845.

Geographical-Gaussian-Process-Regression

파일 탐색기

오늘의 추천 프로젝트

Was this content helpful?

Recent Feedback

Geographical-Gaussian-Process-Regression

파일 탐색기

오늘의 추천 프로젝트

Was this content helpful?

Recent Feedback

Download README