Outline

1.算法思想

2.概念解釋

3.Sklearn Code

Part 1.算法思想：

• 目的：計(jì)算logistic Function，根據(jù)概率閾值設(shè)定進(jìn)行二元分類

• 核心步驟：算出概率（P） & 提升精度（log-loss）

• 具體實(shí)施：

step1. f = m1x1+m2x2+……+b -->

step2. log-odds = log(f) -->

step3. P = sigmoid(log-odds) -->

step4. according to threshold紫岩，give the classification -->

step5. minimize log-loss(gradient descent)

Part 2.概念解釋

• sigmoid function：

image

• log-loss Function：

image

如何理解log-loss Fuction：針對(duì)某一個(gè)sample泉蝌，當(dāng)y=1時(shí)揩晴，loss function對(duì)應(yīng)以下左圖；當(dāng)y=0時(shí)诅愚，loss function對(duì)應(yīng)以下右圖。

image

y=1/0的概率越高刹前，loss越小雌桑。這是符合算法邏輯要求的。所有樣本相加拣技，再利用梯度下降的算法耍目，獲得對(duì)于整體而言的最低的loss。

• Threshold：

1.閾值通常設(shè)為0.5

2.如下第一幅圖所示莫辨。下圖可以想象為根據(jù)大量實(shí)際數(shù)據(jù)和logistic regression算出來的概率與實(shí)際預(yù)測有無癌癥的hist-gram分布毅访。

image

3.當(dāng)我們調(diào)整閾值0.5-->0.4,無癌癥但被預(yù)測為有癌癥的數(shù)量增加（誤判增加俺抽，精度減少），有癌癥確診增加（被預(yù)測為無癌癥的數(shù)量減少磷斧，漏判減少，召回率增加）冕末。這個(gè)案例說明閾值的設(shè)定侣颂，往往是依據(jù)需求選擇的，重大疾病檢出更多的是需要召回率藻肄，而非精度拒担。

image

Part 3.Sklearn Code:

import numpy as np
from sklearn.linear_model import LogisticRegression
from exam import hours_studied_scaled, passed_exam, exam_features_scaled_train, exam_features_scaled_test, passed_exam_2_train, passed_exam_2_test, guessed_hours_scaled

# Create and fit logistic regression model here
model = LogisticRegression()
model.fit(hours_studied_scaled,passed_exam)

# Save the model coefficients and intercept here
calculated_coefficients = model.coef_
intercept = model.intercept_

print(calculated_coefficients)
print(intercept)

# Predict the probabilities of passing for next semester's students here
passed_predictions = model.predict_proba(guessed_hours_scaled)

# Create a new model on the training data with two features here
model_2 = LogisticRegression()
model_2.fit(exam_features_scaled_train,passed_exam_2_train)

# Predict whether the students will pass here
passed_predictions_2 = model_2.predict(exam_features_scaled_test)
print(passed_predictions_2)
print(passed_exam_2_test)