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A naive gradient boosting implementation which I want to share on medium.com
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import numpy as np | |
import pandas as pd | |
from math import e | |
class Node: | |
''' | |
This class defines a node which creates a tree structure by recursively calling itself | |
whilst checking a number of ending parameters such as depth and min_leaf. It uses an exact greedy method | |
to exhaustively scan every possible split point. The gain metric of choice is conservation of varience. | |
This is a Naive solution and does not comapre to Frieman's 2001 Gradient Boosting Machines | |
Input | |
------------------------------------------------------------------------------------------ | |
X: Pandas dataframe | |
y: Pandas Series | |
idxs: indices of values used to keep track of splits points in tree | |
predictions: are the predictions of a gradient boosting algorthim thus far used to calculate the leaf values | |
min_leaf: minimum number of samples needed to be classified as a node | |
depth: sets the maximum depth allowed | |
classification: a flag that indicates if the problem is regression or binary classification | |
Output | |
--------------------------------------------------------------------------------------------- | |
Regression tree that can either be used for classification or regression | |
''' | |
def __init__(self, x, y, idxs, classification, predictions, min_leaf=5, depth = 10): | |
self.x, self.y = x, y | |
self.idxs = idxs | |
self.depth = depth | |
self.min_leaf = min_leaf | |
self.row_count = len(idxs) | |
self.col_count = x.shape[1] | |
self.classification = classification | |
self.predictions = predictions | |
if classification: | |
self.val = self.compute_leaf_value(y[idxs], predictions[idxs]) | |
else: | |
self.val = np.mean(y[idxs]) | |
self.score = float('inf') | |
self.find_varsplit() | |
def find_varsplit(self): | |
''' | |
Scans through every column and calcuates the best split point. | |
The node is then split at this point and two new nodes are created. | |
Depth is only parameter to change as we have added a new layer to tre structure. | |
If no split is better than the score initalised at the begining then no splits further splits are made | |
''' | |
for c in range(self.col_count): self.find_better_split(c) | |
if self.is_leaf: return | |
x = self.split_col | |
lhs = np.nonzero(x <= self.split)[0] | |
rhs = np.nonzero(x > self.split)[0] | |
self.lhs = Node(self.x, self.y, self.idxs[lhs], self.classification, self.predictions, self.min_leaf, depth = self.depth-1) | |
self.rhs = Node(self.x, self.y, self.idxs[rhs], self.classification, self.predictions, self.min_leaf, depth = self.depth-1) | |
def find_better_split(self, var_idx): | |
''' | |
For a given feature calculates the gain at each split. | |
Globally updates the best score if a better split point is found | |
''' | |
x = self.x.values[self.idxs, var_idx] | |
for r in range(self.row_count): | |
lhs = x <= x[r] | |
rhs = x > x[r] | |
if rhs.sum() < self.min_leaf or lhs.sum() < self.min_leaf: continue | |
curr_score = self.find_score(lhs, rhs) | |
if curr_score < self.score: | |
self.var_idx = var_idx | |
self.score = curr_score | |
self.split = x[r] | |
def find_score(self, lhs, rhs): | |
''' | |
Calculates or metric for evaluating split use standard deviation chooses splits where standard | |
deviation is low as it means these points are similar and can be grouped together. | |
''' | |
y = self.y[self.idxs] | |
lhs_std = y[lhs].std() | |
rhs_std = y[rhs].std() | |
return lhs_std * lhs.sum() + rhs_std * rhs.sum() | |
def compute_leaf_value(self, leaf_values, predictions): | |
''' | |
if we are constructing a GBM classifier this is the optimal leaf node | |
value. | |
''' | |
p = self.sigmoid(predictions) | |
denominator = p*(1- p) | |
return(np.sum(leaf_values)/np.sum(denominator)) | |
@staticmethod | |
def sigmoid(x): | |
return 1 / (1 + np.exp(-x)) | |
@property | |
def split_col(self): | |
return self.x.values[self.idxs,self.var_idx] | |
@property | |
def is_leaf(self): | |
return self.score == float('inf') or self.depth <= 0 | |
def predict(self, x): | |
return np.array([self.predict_row(xi) for xi in x]) | |
def predict_row(self, xi): | |
if self.is_leaf: return self.val | |
node = self.lhs if xi[self.var_idx] <= self.split else self.rhs | |
return node.predict_row(xi) | |
class DecisionTreeRegressor: | |
''' | |
Wrapper class that provides a scikit learn interface to the recursive regression tree above | |
Input | |
------------------------------------------------------------------------------------------ | |
X: Pandas dataframe | |
y: Pandas Series | |
idxs: indices of values used to keep track of splits points in tree | |
predictions: are the predictions of a gradient boosting algorthim thus far used to calculate the leaf values | |
min_leaf: minimum number of samples needed to be classified as a node | |
depth: sets the maximum depth allowed | |
classification: a flag that indicates if the problem is regression or binary classification | |
''' | |
def fit(self, X, y, classification ,min_leaf = 5, depth = 5, predictions = []): | |
self.dtree = Node(x = X, y = y, idxs = np.array(np.arange(len(y))), predictions = predictions, min_leaf = min_leaf, depth = depth, classification = classification) | |
return self | |
def predict(self, X): | |
return self.dtree.predict(X.values) | |
class GradientBoostingClassification: | |
''' | |
Applies the methododlgy of gradeint boosting for binary classification only. | |
Uses the Binary logistic loss function to calculate the negative derivate. | |
Input | |
------------------------------------------------------------------------------------------ | |
X: Pandas dataframe | |
y: Pandas Series | |
min_leaf: minimum number of samples needed to be classified as a node | |
depth: sets the maximum depth allowed | |
Boosting_Rounds: number of boosting rounds or iterations | |
Output | |
--------------------------------------------------------------------------------------------- | |
Gradient boosting machine that can be used for binary classification. | |
''' | |
def __init__(self): | |
self.estimators = [] | |
@staticmethod | |
def sigmoid(x): | |
return 1 / (1 + np.exp(-x)) | |
def negativeDerivitiveLogloss(self, y, log_odds): | |
p = self.sigmoid(log_odds) | |
return(y - p) | |
@staticmethod | |
def log_odds(column): | |
''' | |
Calculates the initial log odds prediction of the taget variable | |
''' | |
if isinstance(column, pd.Series): | |
binary_yes = np.count_nonzero(column.values == 1) | |
binary_no = np.count_nonzero(column.values == 0) | |
elif isinstance(column, list): | |
column = np.array(column) | |
binary_yes = np.count_nonzero(column == 1) | |
binary_no = np.count_nonzero(column == 0) | |
else: | |
binary_yes = np.count_nonzero(column == 1) | |
binary_no = np.count_nonzero(column == 0) | |
value = np.log(binary_yes/binary_no) | |
return(np.full((len(column), 1), value).flatten()) | |
def fit(self, X, y, depth = 5, min_leaf = 5, learning_rate = 0.1, boosting_rounds = 5): | |
# use the log odds value of the target variable as our inital prediction | |
self.learning_rate = learning_rate | |
self.base_pred = self.log_odds(y) | |
for booster in range(boosting_rounds): | |
# Calculate the initial Pseudo Residuals using Base Prediction. | |
pseudo_residuals = self.negativeDerivitiveLogloss(y, self.base_pred) | |
# Approximate the residuals | |
boosting_tree = DecisionTreeRegressor().fit(X = X, y = pseudo_residuals, depth = 5, min_leaf = 5, classification = True , predictions = self.base_pred) | |
self.base_pred += self.learning_rate * boosting_tree.predict(X) | |
# store predictors for later | |
self.estimators.append(boosting_tree) | |
def predict(self, X): | |
pred = np.zeros(X.shape[0]) | |
for estimator in self.estimators: | |
pred += self.learning_rate * estimator.predict(X) | |
return self.log_odds(y) + pred | |
class GradientBoostingRegressor: | |
''' | |
Applies the methododlgy of gradeint boosting for regression. | |
Uses the mean squared loss function to calculate the negative derivate. | |
Input | |
------------------------------------------------------------------------------------------ | |
X: Pandas dataframe | |
y: Pandas Series | |
min_leaf: minimum number of samples needed to be classified as a node | |
depth: sets the maximum depth allowed | |
Boosting_Rounds: number of boosting rounds or iterations | |
Output | |
--------------------------------------------------------------------------------------------- | |
Gradient boosting machine that can be used for regression. | |
''' | |
def __init__(self): | |
self.estimators = [] | |
@staticmethod | |
def negativeMeanSquaredErrorDerivitive(y, y_pred): | |
return(2*(y-y_pred)) | |
def fit(self, X, y, depth = 5, min_leaf = 5, learning_rate = 0.1, boosting_rounds = 5): | |
# Start with the mean y value as our initial prediciton | |
self.learning_rate = learning_rate | |
self.base_pred = np.full((X.shape[0], 1), np.mean(y)).flatten() | |
for booster in range(boosting_rounds): | |
# Calculate the initial Pseudo Residuals using Base Prediction. | |
pseudo_residuals = self.negativeMeanSquaredErrorDerivitive(y, self.base_pred) | |
# Approximate the residuals | |
boosting_tree = DecisionTreeRegressor().fit(X = X, y = pseudo_residuals, depth = 5, min_leaf = 5, classification = False , predictions = None) | |
self.base_pred += self.learning_rate * boosting_tree.predict(X) | |
# store predictors for later | |
self.estimators.append(boosting_tree) | |
def predict(self, X): | |
pred = np.zeros(X.shape[0]) | |
for estimator in self.estimators: | |
pred += self.learning_rate * estimator.predict(X) | |
return np.full((X.shape[0], 1), np.mean(y)).flatten() + pred |
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