Machine Learning 简明教程

Machine Learning - Statistics

统计学是机器学习中至关重要的工具，因为它有助于我们理解数据中的底层模式。它为我们提供了描述、总结和分析数据的方法。让我们来看看机器学习的一些统计基础知识。

Statistics is a crucial tool in machine learning because it helps us understand the underlying patterns in the data. It provides us with methods to describe, summarize, and analyze data. Let’s see some of the basics of statistics for machine learning.

Descriptive Statistics

描述性统计是统计学的一个分支，用于对数据进行汇总和分析。它包括平均值、中值、众数、方差和标准差等指标。这些指标有助于我们了解数据的集中趋势、可变性和分布。

Descriptive statistics is a branch of statistics that deals with the summary and analysis of data. It includes measures such as mean, median, mode, variance, and standard deviation. These measures help us understand the central tendency, variability, and distribution of the data.

在机器学习中，描述性统计可用于汇总数据、识别异常值和检测模式。例如，我们可以使用平均值和标准差来描述数据集的分布。

In machine learning, descriptive statistics can be used to summarize the data, identify outliers, and detect patterns. For example, we can use the mean and standard deviation to describe the distribution of a dataset.

在 Python 中，我们可以使用 NumPy 和 Pandas 等库计算描述性统计。以下是一个示例 −

In Python, we can calculate descriptive statistics using libraries such as NumPy and Pandas. Below is an example −

Example

import numpy as np
import pandas as pd

data = np.array([1, 2, 3, 4, 5])
df = pd.DataFrame(data, columns=["Values"])
print(df.describe())

这将输出数据集的摘要，包括数量、平均值、标准差、最小值和最大值，如下所示 −

This will output a summary of the dataset, including the count, mean, standard deviation, minimum, and maximum values as follows −

         Values
count    5.000000
mean     3.000000
std      1.581139
min      1.000000
25%      2.000000
50%      3.000000
75%      4.000000
max      5.000000

Inferential Statistics

推断统计是统计学的一个分支，用于基于数据样本对总体进行预测和推断。它涉及使用假设检验、置信区间和回归分析对数据进行推断。

Inferential statistics is a branch of statistics that deals with making predictions and inferences about a population based on a sample of data. It involves using hypothesis testing, confidence intervals, and regression analysis to draw conclusions about the data.

在机器学习中，可以利用推断统计根据现有数据对新数据进行预测。例如，我们可以使用回归分析根据房屋的特征（例如卧室和浴室的数量）预测房屋的价格。

In machine learning, inferential statistics can be used to make predictions about new data based on existing data. For example, we can use regression analysis to predict the price of a house based on its features, such as the number of bedrooms and bathrooms.

在 Python 中，我们可以使用 Scikit-Learn 和 StatsModels 等库执行推断统计。以下是一个示例 −

In Python, we can perform inferential statistics using libraries such as Scikit-Learn and StatsModels. Below is an example −

Example

import statsmodels.api as sm
import numpy as np

X = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 6, 8, 10])

X = sm.add_constant(X)
model = sm.OLS(y, X).fit()

print(model.summary())

这将输出回归模型的摘要，包括系数、标准误差、t 统计量和 p 值，如下所示 −

This will output a summary of the regression model, including the coefficients, standard errors, t-statistics, and p-values as follows −

在下一章中，我们将详细讨论机器学习中常用的各种描述性和推论性统计度量，以及 Python 实现示例。

In the next chapter, we will discuss various descriptive and inferential statistics measures, which are commonly used in machine learning, in detail along with Python implementation example.