Regression using tree based models

This script evaluates and compares various regression models, including regression trees, random forest, gradient boosting, AdaBoost, XGBoost, and LGBM, using synthetic datasets.

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RandomForestRegressor time with 50 weak learners: 1.5827531859999908
XGBoost time with 50 weak learners: 1.799938091999934
LGBM time with 150 weak learners: 1.8338837840000224

import torch
import matplotlib.pyplot as plt
from sklearn.ensemble import GradientBoostingRegressor as gbr, AdaBoostRegressor as abr
from sklearn.tree import DecisionTreeRegressor
from time import perf_counter

from DLL.MachineLearning.SupervisedLearning.Trees import RegressionTree, RandomForestRegressor, GradientBoostingRegressor, AdaBoostRegressor, XGBoostingRegressor, LGBMRegressor
from DLL.Data.Preprocessing import data_split


n = 100
x = torch.linspace(0, 1, n).unsqueeze(-1)
y = 0.2 * torch.sin(20 * x) + x * x + torch.normal(mean=0, std=0.05, size=(n, 1))
y = y.squeeze()
rand_feats = torch.randint_like(x, 2)
x = torch.cat([x, rand_feats], dim=1)

model = RegressionTree()
model.fit(x, y)
x_test, _ = torch.rand((n, 1)).sort(dim=0)
x_test_rand_feats = torch.randint_like(x_test, 2)
x_test = torch.cat([x_test, x_test_rand_feats], dim=1)
y_pred = model.predict(x_test)

model2 = RandomForestRegressor(n_trees=50, max_depth=10)
start = perf_counter()
model2.fit(x, y)
print(f"RandomForestRegressor time with {model2.n_trees} weak learners: {perf_counter() - start}")
y_pred2 = model2.predict(x_test)

model3 = GradientBoostingRegressor(n_trees=50, learning_rate=0.05, loss="absolute", max_depth=3)
history3 = model3.fit(x, y, metrics=["loss"])
y_pred3 = model3.predict(x_test)

model4 = gbr(n_estimators=10, learning_rate=0.5, loss="absolute_error")
model4.fit(x, y.ravel())
y_pred4 = model4.predict(x_test)

loss_adaboost = "exponential"
model5 = AdaBoostRegressor(n_trees=50, loss=loss_adaboost, max_depth=3)
errors5 = model5.fit(x, y)
y_pred5 = model5.predict(x_test)

model6 = abr(estimator=DecisionTreeRegressor(max_depth=3), n_estimators=50, loss=loss_adaboost)
model6.fit(x, y.ravel())
y_pred6 = model6.predict(x_test)

model7 = XGBoostingRegressor(n_trees=50, learning_rate=0.2, loss="huber", max_depth=3, reg_lambda=0.01, gamma=0, huber_delta=5)
start = perf_counter()
history7 = model7.fit(x, y, metrics=["loss"])
print(f"XGBoost time with {model7.n_trees} weak learners: {perf_counter() - start}")
y_pred7 = model7.predict(x_test)

model8 = LGBMRegressor(n_trees=150, learning_rate=0.2, loss="squared", max_depth=3, reg_lambda=0.01, gamma=0, huber_delta=5, large_error_proportion=0.3, small_error_proportion=0.2)
start = perf_counter()
history8 = model8.fit(x, y, metrics=["loss"])
print(f"LGBM time with {model8.n_trees} weak learners: {perf_counter() - start}")
y_pred8 = model8.predict(x_test)

plt.figure(figsize=(8, 8))
plt.plot(x[:, 0].numpy(), y.numpy(), color="Blue", label="True data")
plt.plot(x_test[:, 0].numpy(), y_pred.numpy(), color="Red", label="Regression tree")
plt.plot(x_test[:, 0].numpy(), y_pred2.numpy(), color="Green", label="Random forest regressor")
plt.plot(x_test[:, 0].numpy(), y_pred3.numpy(), color="Yellow", label="GBR")
plt.plot(x_test[:, 0].numpy(), y_pred4, color="gray", label="SKlearn GBR")
plt.plot(x_test[:, 0].numpy(), y_pred5.numpy(), color="brown", label="AdaBoostRegressor")
plt.plot(x_test[:, 0].numpy(), y_pred6, color="pink", label="SKlearn AdaBoostRegressor")
plt.plot(x_test[:, 0].numpy(), y_pred7.numpy(), color="lightblue", label="XGBoostRegressor")
plt.plot(x_test[:, 0].numpy(), y_pred8.numpy(), color="black", label="LGBMRegressor")
plt.legend(loc="upper left")

fig, ax = plt.subplots(2, 2, figsize=(8, 8))
plt.subplots_adjust(hspace=0.5, wspace=0.5)
ax = ax.ravel()
ax[0].plot(history3["loss"])
ax[0].set_ylabel("Loss")
ax[0].set_xlabel("Tree")
ax[0].set_title("Gradient boosting regressor")
ax[1].plot(errors5, label="errors")
ax[1].plot(model5.confidences, label="confidences")
ax[1].set_ylabel("AdaBoost error")
ax[1].set_xlabel("Tree")
ax[1].set_title("AdaBoost")
ax[1].legend()
ax[2].plot(history7["loss"])
ax[2].set_ylabel("Loss")
ax[2].set_xlabel("Tree")
ax[2].set_title("Extreme gradient boosting regressor")
ax[3].plot(history8["loss"])
ax[3].set_ylabel("Loss")
ax[3].set_xlabel("Tree")
ax[3].set_title("Light gradient boosting machine regressor")

n = 20
X, Y = torch.meshgrid(torch.linspace(-1, 1, n, dtype=torch.float32), torch.linspace(-1, 1, n, dtype=torch.float32), indexing="xy")
x = torch.stack((X.flatten(), Y.flatten()), dim=1)
y = X.flatten() ** 2 + Y.flatten() ** 2 + 0.1 * torch.randn(size=Y.flatten().size()) - 5
x_train, y_train, _, _, x_test, y_test = data_split(x, y, train_split=0.8, validation_split=0.0)

model.fit(x_train, y_train)
z1 = model.predict(x_test)

model2.fit(x_train, y_train)
z2 = model2.predict(x_test)

history3 = model3.fit(x_train, y_train)
z3 = model3.predict(x_test)

model4.fit(x_train, y_train)
z4 = model4.predict(x_test)

errors5 = model5.fit(x_train, y_train)
z5 = model5.predict(x_test)

model6.fit(x_train, y_train)
z6 = model6.predict(x_test)

history7 = model7.fit(x_train, y_train)
z7 = model7.predict(x_test)

history8 = model8.fit(x_train, y_train)
z8 = model8.predict(x_test)

fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x_test[:, 0], x_test[:, 1], y_test, color="Blue", label="True data")
ax.scatter(x_test[:, 0], x_test[:, 1], z1, color="Red", label="Regression tree")
ax.scatter(x_test[:, 0], x_test[:, 1], z2, color="Green", label="Random forest regressor")
ax.scatter(x_test[:, 0], x_test[:, 1], z3, color="Yellow", label="GBR")
ax.scatter(x_test[:, 0], x_test[:, 1], z4, color="gray", label="SKlearn GBR")
ax.scatter(x_test[:, 0], x_test[:, 1], z5, color="brown", label="AdaBoostRegressor")
ax.scatter(x_test[:, 0], x_test[:, 1], z6, color="pink", label="SKlearn AdaBoostRegressor")
ax.scatter(x_test[:, 0], x_test[:, 1], z7, color="lightblue", label="XGBoostRegressor")
ax.scatter(x_test[:, 0], x_test[:, 1], z8, color="black", label="LGBMRegressor")
plt.legend(loc="upper left")

fig, ax = plt.subplots(2, 2, figsize=(8, 8))
plt.subplots_adjust(hspace=0.5, wspace=0.5)
ax = ax.ravel()
ax[0].plot(history3["loss"])
ax[0].set_ylabel("Loss")
ax[0].set_xlabel("Tree")
ax[0].set_title("Gradient boosting regressor")
ax[1].plot(errors5, label="errors")
ax[1].plot(model5.confidences, label="confidences")
ax[1].set_ylabel("AdaBoost error")
ax[1].set_xlabel("Tree")
ax[1].set_title("AdaBoost")
ax[1].legend()
ax[2].plot(history7["loss"])
ax[2].set_ylabel("Loss")
ax[2].set_xlabel("Tree")
ax[2].set_title("Extreme gradient boosting regressor")
ax[3].plot(history8["loss"])
ax[3].set_ylabel("Loss")
ax[3].set_xlabel("Tree")
ax[3].set_title("Light gradient boosting machine regressor")
plt.show()