统计在机器学习、人工智能、神经网络中的应用

Question

我希望这是正确的论坛，因为我找不到一个似乎完全相关的论坛。问题是，从适用于机器学习、人工智能和神经网络的角度来看，统计中的任何一个主题真的有用吗？

(A)描述性统计

Analysis of Quantitative Data:
- Measures of central tendancy
- Measures of dispersion
- Moments
- Skewness and Kurtosis
Correlation of bivariate data:
- Fitting of curves
- Correlation coefficient
- Rank Correlation
- Intra-class Corelation
Regression and Multiple Correlations
- Linear Regression
- Plane of Regression
- Multiple Correlation
- Partial Correlation
Theory of Attributes
- Classification of Attributes
- Independence of Attributes
- Association of Attributes

(B)概率论

Basic Concepts in Probability
- Introduction to Probability
- Different Approaches to Probability Theory
- Laws of Probability
- Bayes' Theorem
Random Variables and Expectation
- Random Variables
- Bivariate Discrete Random Variables
- Bivariate Continuous Random Variables
- Mathematical Expectation
Discrete Probability Distributions
- Binomial Distributions
- Poisson Distributions
- Discrete Uniform and Hypergeometric Distributions
- Geometric and Negative Binomial Distributions
Continuous Probability Distributions
- Normal Distributions
- Area Property of Normal Distributions
- Continuous Uniform and Exponential Distributions
- Gamma and Beta Distributions

C)统计推断

 Sampling Distributions
 - Introduction to Sampling Distributions
 - Sampling Distributions of Statistics
 - Standard Sampling Distributions
 Estimation
 - Introduction to Estimation
 - Point Estimation
 - Interval Estimation for One Population
 - Interval Estimation for Two Populations
 Testing of Hypothesis
 - Concepts of Testing of Hypothesis
 - Large Sample Tests
 - Small Sample Tests
 - Chi-Square and F-Tests
 Non-Parametric Tests
 - One-Sample Tests
 - Two-Sample Tests
 - k-Sample Tests
 - Analysis of Frequencies

D)统计技术

Sampling Designs
- Introduction to Sample Surveys
- Simple Random Sampling
- Stratified Random Sampling
- Other Sampling Schemes
Analysis of Variance
- Introduction
- One-way Analysis of Variance
- Two-way Analysis of Variance
- Two-way Analysis of Variance with m Observations per call
Design of Experiments
- Completely Randomized Design
- Randomized block Design
- Latin Square Design
- Factorial Experiments
Random Numbers Generation and Simulation Techniques
- Random Numbers Generation for Discrete Variables
- Random Numbers Generation for Continuous Variables
- Simulation Techniques
- Applications of Simulation

(E)工业统计-一

Process Control
- Introduction to Statistical Quality Control
- Control Charts for Variables
- Control Charts for Attributes
- Control Charts for Defects
Product Control
- Acceptance Sampling Plans
- Rectifying Sampling Plans
- Single Sampling Plans
- Double Sampling Plans
Decision and Game Theory
- Introduction to Decision Theory
- Decision making Process
- Two-Person Zero-Sum Games with Saddle Point
- Two-Person Zero-Sum Games without Saddle Point
Reliability Theory
- Introduction to Reliability
- Reliability Evaluation of Simple System
- Reliability Evaluation of k-out-of-n and StandBy System
- Reliability Evaluation of Complex System

F)工业统计-二

Optimisation Techniques I 
- Introduction to Operations Research
- Linear Programming Problems
- Simplex Method
- Transportation Problems
Optimisation Techniques II
- Assignment Problems
- Queueing Theory
- Sequencing Problems
- Inventory Models
Regression Modelling
- Simple Linear Regression
- Statistical Inference in Simple Linear Regression
- Multiple Linear Regression
- Selection of Variables and Testing Model Assumptions
Time Series Modelling
- Trend Component Analysis
- Seasonal Component Analysis
- Stationary Processes
- Time Series Models

编辑:回复@SmallChess；老实说，这两个领域对我来说都是新的，但我觉得它们真的很有趣。最终，我希望在物理领域工作，并能够在那里应用它。例如，以下链接：

link1 link2 link3

也许这还是相当广泛的。但到目前为止我还没有发现任何具体的东西。我可以缩小范围的最好方法可能是通过上面的链接和下面的摘录：

机器学习在物理学中的应用，就像它在其他科学或工业领域中的应用一样，即在处理复杂问题和/或大量数据时，让计算机共享艰苦思考的部分。

“几乎所有我们称之为物理的东西都由相当简单的模型组成，建立和理解简单模型的冲动推动了我们所做的许多事情。这方面的主要例外是:观测天文学和高能实验，如CERN的大型强子对撞机，可以有效地应用机器学习。另一个有希望的应用是湍流建模。”

我希望这有助于缩小范围。谢谢。

Answer 1

我同意@Emre。对我来说，它们对机器学习都很重要。当然，这取决于你在机器学习中到底想做什么。例如，如果你只是在做图像识别，你不需要理解时间序列。

另一个例子，“决策和博弈论”对于棋类游戏中的机器学习是绝对重要的(例如强化自我学习)。

这里列出的一切都适用于机器学习--机器学习实际上只是学习未知函数的统计算法。

你为什么不告诉我们你想做什么，我们告诉你该学什么？

在你的名单中，我认为最重要的五个是(主观的)：

• 正态分布
• 线性回归
• 随机变量
• 数学期望
• 二项分布

Answer 2

我同意@SmallChess，但我有一些补充。(因为我还不能发表评论)

有两个概念可以帮助您理解大多数学习算法：

1. 梯度下降
2. 蒙特卡罗树搜索

这两个概念帮助我理解了大多数其他概念。希望我帮了你。