Exploring LightGBM: Leaf-Sensible Progress with GBDT and GOSS

LightGBM is a extremely environment friendly gradient boosting framework. It has gained traction for its velocity and efficiency, significantly with massive and sophisticated datasets. Developed by Microsoft, this highly effective algorithm is thought for its distinctive means to deal with massive volumes of information with vital ease in comparison with conventional strategies.

On this submit, we’ll experiment with LightGBM framework on the Ames Housing dataset. Specifically, we’ll shed some gentle on its versatile boosting methods—Gradient Boosting Determination Tree (GBDT) and Gradient-based One-Aspect Sampling (GOSS). These methods supply distinct benefits. By way of this submit, we’ll evaluate their efficiency and traits.

We start by organising LightGBM and proceed to look at its utility in each theoretical and sensible contexts.

Let’s get began.

LightGBM
Photograph by Marcus Dall Col. Some rights reserved.

Overview

This submit is split into 4 elements; they’re:

Introduction to LightGBM and Preliminary Setup
Testing LightGBM’s GBDT and GOSS on the Ames Dataset
Tremendous-Tuning LightGBM’s Tree Progress: A Concentrate on Leaf-wise Technique
Evaluating Characteristic Significance in LightGBM’s GBDT and GOSS Fashions

Introduction to LightGBM and Preliminary Setup

LightGBM (Gentle Gradient Boosting Machine) was developed by Microsoft. It’s a machine studying framework that gives the required parts and utilities to construct, prepare, and deploy machine studying fashions. The fashions are based mostly on resolution tree algorithms and use gradient boosting at its core. The framework is open supply and may be put in in your system utilizing the next command:

This command will obtain and set up the LightGBM bundle together with its needed dependencies.

Whereas LightGBM, XGBoost, and Gradient Boosting Regressor (GBR) are all based mostly on the precept of gradient boosting, a number of key distinctions set LightGBM aside on account of each its default behaviors and a spread of optionally available parameters that improve its performance:

Unique Characteristic Bundling (EFB): As a default function, LightGBM employs EFB to scale back the variety of options, which is especially helpful for high-dimensional sparse knowledge. This course of is automated, serving to to handle knowledge dimensionality effectively with out in depth handbook intervention.
Gradient-Based mostly One-Aspect Sampling (GOSS): As an optionally available parameter that may be enabled, GOSS retains cases with massive gradients. The gradient represents how a lot the loss perform would change if the mannequin’s prediction for that occasion modified barely. A big gradient implies that the present mannequin’s prediction for that knowledge level is way from the precise goal worth. Cases with massive gradients are thought-about extra vital for coaching as a result of they signify areas the place the mannequin wants vital enchancment. Within the GOSS algorithm, cases with massive gradients are also known as “under-trained” as a result of they point out areas the place the mannequin’s efficiency is poor and wishes extra focus throughout coaching. The GOSS algorithm particularly retains all cases with massive gradients in its sampling course of, making certain that these important knowledge factors are at all times included within the coaching subset. Then again, cases with small gradients are thought-about “well-trained” as a result of the mannequin’s predictions for these factors are nearer to the precise values, leading to smaller errors.
Leaf-wise Tree Progress: Whereas each GBR and XGBoost usually develop bushes level-wise, LightGBM default tree development technique is leaf-wise. Not like level-wise development, the place all nodes at a given depth are break up earlier than shifting to the following degree, LightGBM grows bushes by selecting to separate the leaf that leads to the biggest lower within the loss perform. This method can result in uneven, irregular bushes of bigger depth, which may be extra expressive and environment friendly than balanced bushes grown level-wise.

These are a number of traits of LightGBM that differentiate it from the standard GBR and XGBoost. With these distinctive benefits in thoughts, we’re ready to delve into the empirical aspect of our exploration.

Testing LightGBM’s GBDT and GOSS on the Ames Dataset

Constructing on our understanding of LightGBM’s distinct options, this phase shifts from concept to apply. We are going to make the most of the Ames Housing dataset to carefully check two particular boosting methods inside the LightGBM framework: the usual Gradient Boosting Determination Tree (GBDT) and the revolutionary Gradient-based One-Aspect Sampling (GOSS). We intention to discover these methods and supply a comparative evaluation of their effectiveness.

Earlier than we dive into the mannequin constructing, it’s essential to organize the dataset correctly. This entails loading the info and making certain all categorical options are appropriately processed, taking full benefit of LightGBM’s dealing with of categorical variables. Like XGBoost, LightGBM can natively deal with lacking values and categorical knowledge, simplifying the preprocessing steps and resulting in extra strong fashions. This functionality is essential because it immediately influences the accuracy and effectivity of the mannequin coaching course of.

# Import libraries to run LightGBM import pandas as pd import lightgbm as lgb from sklearn.model_selection import cross_val_score # Load the Ames Housing Dataset knowledge = pd.read_csv(‘Ames.csv’) X = knowledge.drop(‘SalePrice’, axis=1) y = knowledge[‘SalePrice’] # Convert categorical columns to ‘class’ dtype categorical_cols = X.select_dtypes(embrace=[‘object’]).columns X[categorical_cols] = X[categorical_cols].apply(lambda x: x.astype(‘class’)) # Outline the default GBDT mannequin gbdt_model = lgb.LGBMRegressor() gbdt_scores = cross_val_score(gbdt_model, X, y, cv=5) print(f”Common R² rating for default Gentle GBM (with GBDT): {gbdt_scores.imply():.4f}”) # Outline the GOSS mannequin goss_model = lgb.LGBMRegressor(boosting_type=”goss”) goss_scores = cross_val_score(goss_model, X, y, cv=5) print(f”Common R² rating for Gentle GBM with GOSS: {goss_scores.imply():.4f}”)

# Import libraries to run LightGBM

import pandas as pd

import lightgbm as lgb

from sklearn.model_selection import cross_val_rating

# Load the Ames Housing Dataset

knowledge = pd.read_csv(‘Ames.csv’)

X = knowledge.drop(‘SalePrice’, axis=1)

y = knowledge[‘SalePrice’]

# Convert categorical columns to ‘class’ dtype

categorical_cols = X.select_dtypes(embrace=[‘object’]).columns

X[categorical_cols] = X[categorical_cols].apply(lambda x: x.astype(‘class’))

# Outline the default GBDT mannequin

gbdt_model = lgb.LGBMRegressor()

gbdt_scores = cross_val_score(gbdt_model, X, y, cv=5)

print(f“Common R² rating for default Gentle GBM (with GBDT): {gbdt_scores.imply():.4f}”)

# Outline the GOSS mannequin

goss_model = lgb.LGBMRegressor(boosting_type=‘goss’)

goss_scores = cross_val_score(goss_model, X, y, cv=5)

print(f“Common R² rating for Gentle GBM with GOSS: {goss_scores.imply():.4f}”)

Outcomes:

Common R² rating for default Gentle GBM (with GBDT): 0.9145 Common R² rating for Gentle GBM with GOSS: 0.9109

Common R² rating for default Gentle GBM (with GBDT): 0.9145

Common R² rating for Gentle GBM with GOSS: 0.9109

The preliminary outcomes from our 5-fold cross-validation experiments present intriguing insights into the efficiency of the 2 fashions. The default GBDT mannequin achieved a median R² rating of 0.9145, demonstrating strong predictive accuracy. Then again, the GOSS mannequin, which particularly targets cases with massive gradients, recorded a barely decrease common R² rating of 0.9109.

The slight distinction in efficiency is perhaps attributed to the best way GOSS prioritizes sure knowledge factors over others, which may be significantly useful in datasets the place mispredictions are extra concentrated. Nevertheless, in a comparatively homogeneous dataset like Ames, the benefits of GOSS might not be totally realized.

Tremendous-Tuning LightGBM’s Tree Progress: A Concentrate on Leaf-wise Technique

One of many distinguishing options of LightGBM is its means to assemble resolution bushes leaf-wise somewhat than level-wise. This leaf-wise method permits bushes to develop by optimizing loss reductions, probably main to higher mannequin efficiency however posing a danger of overfitting if not correctly tuned. On this part, we discover the affect of various the variety of leaves in a tree.

We begin by defining a sequence of experiments to systematically check how completely different settings for num_leaves have an effect on the efficiency of two LightGBM variants: the standard Gradient Boosting Determination Tree (GBDT) and the Gradient-based One-Aspect Sampling (GOSS). These experiments are essential for figuring out the optimum complexity degree of the fashions for our particular dataset—the Ames Housing Dataset.

# Experiment with Leaf-wise Tree Progress import pandas as pd import lightgbm as lgb from sklearn.model_selection import cross_val_score # Load the Ames Housing Dataset knowledge = pd.read_csv(‘Ames.csv’) X = knowledge.drop(‘SalePrice’, axis=1) y = knowledge[‘SalePrice’] # Convert categorical columns to ‘class’ dtype categorical_cols = X.select_dtypes(embrace=[‘object’]).columns X[categorical_cols] = X[categorical_cols].apply(lambda x: x.astype(‘class’)) # Outline a spread of leaf sizes to check leaf_sizes = [5, 10, 15, 31, 50, 100] # Outcomes storage outcomes = {} # Experiment with completely different leaf sizes for GBDT outcomes[‘GBDT’] = {} print(“Testing completely different ‘num_leaves’ for GBDT:”) for leaf_size in leaf_sizes: mannequin = lgb.LGBMRegressor(boosting_type=”gbdt”, num_leaves=leaf_size) scores = cross_val_score(mannequin, X, y, cv=5, scoring=’r2′) outcomes[‘GBDT’][leaf_size] = scores.imply() print(f”num_leaves = {leaf_size}: Common R² rating = {scores.imply():.4f}”) # Experiment with completely different leaf sizes for GOSS outcomes[‘GOSS’] = {} print(“nTesting completely different ‘num_leaves’ for GOSS:”) for leaf_size in leaf_sizes: mannequin = lgb.LGBMRegressor(boosting_type=”goss”, num_leaves=leaf_size) scores = cross_val_score(mannequin, X, y, cv=5, scoring=’r2′) outcomes[‘GOSS’][leaf_size] = scores.imply() print(f”num_leaves = {leaf_size}: Common R² rating = {scores.imply():.4f}”)

# Experiment with Leaf-wise Tree Progress

import pandas as pd

import lightgbm as lgb

from sklearn.model_selection import cross_val_rating

# Load the Ames Housing Dataset

knowledge = pd.read_csv(‘Ames.csv’)

X = knowledge.drop(‘SalePrice’, axis=1)

y = knowledge[‘SalePrice’]

# Convert categorical columns to ‘class’ dtype

categorical_cols = X.select_dtypes(embrace=[‘object’]).columns

X[categorical_cols] = X[categorical_cols].apply(lambda x: x.astype(‘class’))

# Outline a spread of leaf sizes to check

leaf_sizes = [5, 10, 15, 31, 50, 100]

# Outcomes storage

outcomes = {}

# Experiment with completely different leaf sizes for GBDT

outcomes[‘GBDT’] = {}

print(“Testing completely different ‘num_leaves’ for GBDT:”)

for leaf_size in leaf_sizes:

mannequin = lgb.LGBMRegressor(boosting_type=‘gbdt’, num_leaves=leaf_size)

scores = cross_val_score(mannequin, X, y, cv=5, scoring=‘r2’)

outcomes[‘GBDT’][leaf_size] = scores.imply()

print(f“num_leaves = {leaf_size}: Common R² rating = {scores.imply():.4f}”)

# Experiment with completely different leaf sizes for GOSS

outcomes[‘GOSS’] = {}

print(“nTesting completely different ‘num_leaves’ for GOSS:”)

for leaf_size in leaf_sizes:

mannequin = lgb.LGBMRegressor(boosting_type=‘goss’, num_leaves=leaf_size)

scores = cross_val_score(mannequin, X, y, cv=5, scoring=‘r2’)

outcomes[‘GOSS’][leaf_size] = scores.imply()

print(f“num_leaves = {leaf_size}: Common R² rating = {scores.imply():.4f}”)

Outcomes:

Testing completely different ‘num_leaves’ for GBDT: num_leaves = 5: Common R² rating = 0.9150 num_leaves = 10: Common R² rating = 0.9193 num_leaves = 15: Common R² rating = 0.9158 num_leaves = 31: Common R² rating = 0.9145 num_leaves = 50: Common R² rating = 0.9111 num_leaves = 100: Common R² rating = 0.9101 Testing completely different ‘num_leaves’ for GOSS: num_leaves = 5: Common R² rating = 0.9151 num_leaves = 10: Common R² rating = 0.9168 num_leaves = 15: Common R² rating = 0.9130 num_leaves = 31: Common R² rating = 0.9109 num_leaves = 50: Common R² rating = 0.9117 num_leaves = 100: Common R² rating = 0.9124

Testing completely different ‘num_leaves’ for GBDT:

num_leaves = 5: Common R² rating = 0.9150

num_leaves = 10: Common R² rating = 0.9193

num_leaves = 15: Common R² rating = 0.9158

num_leaves = 31: Common R² rating = 0.9145

num_leaves = 50: Common R² rating = 0.9111

num_leaves = 100: Common R² rating = 0.9101

Testing completely different ‘num_leaves’ for GOSS:

num_leaves = 5: Common R² rating = 0.9151

num_leaves = 10: Common R² rating = 0.9168

num_leaves = 15: Common R² rating = 0.9130

num_leaves = 31: Common R² rating = 0.9109

num_leaves = 50: Common R² rating = 0.9117

num_leaves = 100: Common R² rating = 0.9124

The outcomes from our cross-validation experiments present insightful knowledge on how the num_leaves parameter influences the efficiency of GBDT and GOSS fashions. Each fashions carry out optimally at a num_leaves setting of 10, reaching the very best R² scores. This means {that a} reasonable degree of complexity suffices to seize the underlying patterns within the Ames Housing dataset with out overfitting. This discovering is especially attention-grabbing, provided that the default setting for num_leaves in LightGBM is 31.

For GBDT, rising the variety of leaves past 10 results in a lower in efficiency, suggesting that an excessive amount of complexity can detract from the mannequin’s generalization capabilities. In distinction, GOSS reveals a barely extra tolerant habits in the direction of increased leaf counts, though the enhancements plateau, indicating no additional positive factors from elevated complexity.

This experiment underscores the significance of tuning num_leaves in LightGBM. By rigorously choosing this parameter, we are able to successfully stability mannequin accuracy and complexity, making certain strong efficiency throughout completely different knowledge eventualities. Additional experimentation with different parameters at the side of num_leaves might probably unlock even higher efficiency and stability.

Evaluating Characteristic Significance in LightGBM’s GBDT and GOSS Fashions

After fine-tuning the num_leaves parameter and assessing the essential efficiency of the GBDT and GOSS fashions, we now shift our focus to understanding the affect of particular person options inside these fashions. On this part, we discover a very powerful options by every boosting technique by means of visualization.

Right here is the code that achieves this:

# Importing libraries to check function significance between GBDT and GOSS: import pandas as pd import numpy as np import lightgbm as lgb from sklearn.model_selection import KFold import matplotlib.pyplot as plt import seaborn as sns # Put together knowledge knowledge = pd.read_csv(‘Ames.csv’) X = knowledge.drop(‘SalePrice’, axis=1) y = knowledge[‘SalePrice’] categorical_cols = X.select_dtypes(embrace=[‘object’]).columns X[categorical_cols] = X[categorical_cols].apply(lambda x: x.astype(‘class’)) # Arrange Ok-fold cross-validation kf = KFold(n_splits=5) gbdt_feature_importances = [] goss_feature_importances = [] # Iterate over every break up for train_index, test_index in kf.break up(X): X_train, X_test = X.iloc[train_index], X.iloc[test_index] y_train, y_test = y.iloc[train_index], y.iloc[test_index] # Practice GBDT mannequin with optimum num_leaves gbdt_model = lgb.LGBMRegressor(boosting_type=”gbdt”, num_leaves=10) gbdt_model.match(X_train, y_train) gbdt_feature_importances.append(gbdt_model.feature_importances_) # Practice GOSS mannequin with optimum num_leaves goss_model = lgb.LGBMRegressor(boosting_type=”goss”, num_leaves=10) goss_model.match(X_train, y_train) goss_feature_importances.append(goss_model.feature_importances_) # Common function significance throughout all folds for every mannequin avg_gbdt_feature_importance = np.imply(gbdt_feature_importances, axis=0) avg_goss_feature_importance = np.imply(goss_feature_importances, axis=0) # Convert to DataFrame feat_importances_gbdt = pd.DataFrame({‘Characteristic’: X.columns, ‘Significance’: avg_gbdt_feature_importance}) feat_importances_goss = pd.DataFrame({‘Characteristic’: X.columns, ‘Significance’: avg_goss_feature_importance}) # Type and take the highest 10 options top_gbdt_features = feat_importances_gbdt.sort_values(by=’Significance’, ascending=False).head(10) top_goss_features = feat_importances_goss.sort_values(by=’Significance’, ascending=False).head(10) # Plotting plt.determine(figsize=(16, 12)) plt.subplot(1, 2, 1) sns.barplot(knowledge=top_gbdt_features, y=’Characteristic’, x=’Significance’, orient=”h”, palette=”viridis”) plt.title(‘Prime 10 LightGBM GBDT Options’, fontsize=18) plt.xlabel(‘Significance’, fontsize=16) plt.ylabel(‘Characteristic’, fontsize=16) plt.xticks(fontsize=13) plt.yticks(fontsize=14) plt.subplot(1, 2, 2) sns.barplot(knowledge=top_goss_features, y=’Characteristic’, x=’Significance’, orient=”h”, palette=”viridis”) plt.title(‘Prime 10 LightGBM GOSS Options’, fontsize=18) plt.xlabel(‘Significance’, fontsize=16) plt.ylabel(‘Characteristic’, fontsize=16) plt.xticks(fontsize=13) plt.yticks(fontsize=14) plt.tight_layout() plt.present()

# Importing libraries to check function significance between GBDT and GOSS:

import pandas as pd

import numpy as np

import lightgbm as lgb

from sklearn.model_selection import KFold

import matplotlib.pyplot as plt

import seaborn as sns

# Put together knowledge

knowledge = pd.read_csv(‘Ames.csv’)

X = knowledge.drop(‘SalePrice’, axis=1)

y = knowledge[‘SalePrice’]

categorical_cols = X.select_dtypes(embrace=[‘object’]).columns

X[categorical_cols] = X[categorical_cols].apply(lambda x: x.astype(‘class’))

# Arrange Ok-fold cross-validation

kf = KFold(n_splits=5)

gbdt_feature_importances = []

goss_feature_importances = []

# Iterate over every break up

for train_index, test_index in kf.break up(X):

X_train, X_test = X.iloc[train_index], X.iloc[test_index]

y_train, y_test = y.iloc[train_index], y.iloc[test_index]

# Practice GBDT mannequin with optimum num_leaves

gbdt_model = lgb.LGBMRegressor(boosting_type=‘gbdt’, num_leaves=10)

gbdt_model.match(X_train, y_train)

gbdt_feature_importances.append(gbdt_model.feature_importances_)

# Practice GOSS mannequin with optimum num_leaves

goss_model = lgb.LGBMRegressor(boosting_type=‘goss’, num_leaves=10)

goss_model.match(X_train, y_train)

goss_feature_importances.append(goss_model.feature_importances_)

# Common function significance throughout all folds for every mannequin

avg_gbdt_feature_importance = np.imply(gbdt_feature_importances, axis=0)

avg_goss_feature_importance = np.imply(goss_feature_importances, axis=0)

# Convert to DataFrame

feat_importances_gbdt = pd.DataFrame({‘Characteristic’: X.columns, ‘Significance’: avg_gbdt_feature_importance})

feat_importances_goss = pd.DataFrame({‘Characteristic’: X.columns, ‘Significance’: avg_goss_feature_importance})

# Type and take the highest 10 options

top_gbdt_features = feat_importances_gbdt.sort_values(by=‘Significance’, ascending=False).head(10)

top_goss_features = feat_importances_goss.sort_values(by=‘Significance’, ascending=False).head(10)

# Plotting

plt.determine(figsize=(16, 12))

plt.subplot(1, 2, 1)

sns.barplot(knowledge=top_gbdt_features, y=‘Characteristic’, x=‘Significance’, orient=‘h’, palette=‘viridis’)

plt.title(‘Prime 10 LightGBM GBDT Options’, fontsize=18)

plt.xlabel(‘Significance’, fontsize=16)

plt.ylabel(‘Characteristic’, fontsize=16)

plt.xticks(fontsize=13)

plt.yticks(fontsize=14)

plt.subplot(1, 2, 2)

sns.barplot(knowledge=top_goss_features, y=‘Characteristic’, x=‘Significance’, orient=‘h’, palette=‘viridis’)

plt.title(‘Prime 10 LightGBM GOSS Options’, fontsize=18)

plt.xlabel(‘Significance’, fontsize=16)

plt.ylabel(‘Characteristic’, fontsize=16)

plt.xticks(fontsize=13)

plt.yticks(fontsize=14)

plt.tight_layout()

plt.present()

Utilizing the identical Ames Housing dataset, we utilized a ok-fold cross-validation methodology to keep up consistency with our earlier experiments. Nevertheless, this time, we focused on extracting and analyzing the function significance from the fashions. Characteristic significance, which signifies how helpful every function is in developing the boosted resolution bushes, is essential for deciphering the habits of machine studying fashions. It helps in understanding which options contribute most to the predictive energy of the mannequin, offering insights into the underlying knowledge and the mannequin’s decision-making course of.

Right here’s how we carried out the function significance extraction:

Mannequin Coaching: Every mannequin (GBDT and GOSS) was skilled throughout completely different folds of the info with the optimum num_leaves parameter set to 10.
Significance Extraction: After coaching, every mannequin’s function significance was extracted. This significance displays the variety of instances a function is used to make key choices with splits within the bushes.
Averaging Throughout Folds: The significance was averaged over all folds to make sure that our outcomes have been secure and consultant of the mannequin’s efficiency throughout completely different subsets of the info.

The next visualizations succinctly current these variations in function significance between the GBDT and GOSS fashions:

The evaluation revealed attention-grabbing patterns in function prioritization by every mannequin. Each the GBDT and GOSS fashions exhibited a powerful desire for “GrLivArea” and “LotArea,” highlighting the elemental position of property dimension in figuring out home costs. Moreover, each fashions ranked ‘Neighborhood’ extremely, underscoring the significance of location within the housing market.

Nevertheless, the fashions started to diverge of their prioritization from the fourth function onwards. The GBDT mannequin confirmed a desire for “BsmtFinSF1,” indicating the worth of completed basements. Then again, the GOSS mannequin, which prioritizes cases with bigger gradients to appropriate mispredictions, emphasised “OverallQual” extra strongly.

As we conclude this evaluation, it’s evident that the variations in function significance between the GBDT and GOSS fashions present invaluable insights into how every mannequin perceives the relevance of varied options in predicting housing costs.

Additional Studying

Tutorials

Ames Housing Dataset & Knowledge Dictionary

Abstract

This weblog submit launched you to LightGBM’s capabilities, highlighting its distinctive options and sensible utility on the Ames Housing dataset. From the preliminary setup and comparability of GBDT and GOSS boosting methods to an in-depth evaluation of function significance, we’ve uncovered invaluable insights that not solely exhibit LightGBM’s effectivity but in addition its adaptability to advanced datasets.

Particularly, you discovered:

Exploration of mannequin variants: Evaluating the default GBDT with the GOSS mannequin supplied insights into how completely different boosting methods may be leveraged relying on the info traits.
The best way to experiment with leaf-wise technique: Adjusting the num_leaves parameter influences mannequin efficiency, with an optimum setting offering a stability between complexity and accuracy.
The best way to visualize function significance: Understanding and visualizing which options are most influential in your fashions can considerably affect the way you interpret the outcomes and make choices. This course of not solely clarifies the mannequin’s inner workings but in addition aids in enhancing mannequin transparency and trustworthiness by figuring out which variables most strongly affect the result.

Do you have got any questions? Please ask your questions within the feedback beneath, and I’ll do my greatest to reply.

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Exploring LightGBM: Leaf-Sensible Progress with GBDT and GOSS

Overview

Introduction to LightGBM and Preliminary Setup

Testing LightGBM’s GBDT and GOSS on the Ames Dataset

Tremendous-Tuning LightGBM’s Tree Progress: A Concentrate on Leaf-wise Technique

Evaluating Characteristic Significance in LightGBM’s GBDT and GOSS Fashions

Additional Studying

Tutorials

Ames Housing Dataset & Knowledge Dictionary

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Overview

Introduction to LightGBM and Preliminary Setup

Testing LightGBM’s GBDT and GOSS on the Ames Dataset

Tremendous-Tuning LightGBM’s Tree Progress: A Concentrate on Leaf-wise Technique

Evaluating Characteristic Significance in LightGBM’s GBDT and GOSS Fashions

Additional Studying

Tutorials

Ames Housing Dataset & Knowledge Dictionary

Abstract

Get Began on The Newbie’s Information to Knowledge Science!

Study the mindset to develop into profitable in knowledge science tasks

Kick-start your knowledge science journey with hands-on workouts

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