Support Vector Regression for Predicting Upper Watershed River Discharge from Rainfall

Project info

• Field of studyForestry and Environment
• LevelMaster's thesis (S2)
• Method typeRegression
• Estimated build time± 5 working days
• Toolsscikit-learn SVR, GridSearchCV, StandardScaler, Pipeline
• PriceUS$22 - US$141

Research goal

Model river discharge from rainfall and forest cover using Support Vector Regression and evaluate the model performance.

Variables

Example result

• 0.77R2 (test)
• 3.23RMSE (test)
• 2.568MAE (test)
• 100Support vectors
• 0.719SV share
• 10C

An RBF-kernel SVR models River discharge with test R2 0.770 and RMSE 3.230; 100 of 139 training points are support vectors.

Computed from illustrative synthetic data, not from a real study.

About Support Vector Regression

Support Vector Regression finds a function that deviates at most epsilon from the data while staying flat, with kernels for nonlinear patterns. It suits small to medium datasets with smooth nonlinear relations.

Steps

1. 1Standardise features (and the target if needed)
2. 2Split into training and test sets
3. 3Choose an RBF kernel and tune C, epsilon, gamma by cross-validation
4. 4Fit SVR with the best hyperparameters
5. 5Evaluate R2 and RMSE on the test set
6. 6Plot the prediction curve against the data

Assumptions to check

• Features must be on comparable scales
• C, epsilon, and gamma strongly affect results and must be tuned
• Training time grows quickly on very large data

Reading and reporting the results

Report the kernel and best hyperparameters, R2, RMSE, and the number of support vectors. Stress that the model is hard to interpret, so the focus is predictive accuracy.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.svm import SVR
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import make_pipeline
from sklearn.model_selection import GridSearchCV, train_test_split
from sklearn.metrics import r2_score, mean_squared_error

rng = np.random.default_rng(5)
n = 250
rainfall = np.sort(rng.uniform(0, 10, n))
river_discharge = np.sin(rainfall) + 0.3 * rainfall + rng.normal(0, 0.2, n)

X = rainfall.reshape(-1, 1)
X_tr, X_te, y_tr, y_te = train_test_split(X, river_discharge, test_size=0.2, random_state=5)
pipe = make_pipeline(StandardScaler(), SVR(kernel="rbf"))
grid = {"svr__C": [1, 10, 100], "svr__epsilon": [0.05, 0.1, 0.2], "svr__gamma": ["scale", 0.1, 1]}
gs = GridSearchCV(pipe, grid, cv=5, scoring="neg_root_mean_squared_error")
gs.fit(X_tr, y_tr)
best = gs.best_estimator_
pred = best.predict(X_te)
print("Best params:", gs.best_params_)
print("Test R2:", round(r2_score(y_te, pred), 3))
print("Test RMSE:", round(mean_squared_error(y_te, pred) ** 0.5, 3))
print("Support vectors:", len(best[-1].support_))

xs = np.linspace(0, 10, 300).reshape(-1, 1)
plt.scatter(X_tr, y_tr, s=10, alpha=0.5, label="Train")
plt.plot(xs, best.predict(xs), "r", label="SVR fit")
plt.legend()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions