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机器学习与优化也有着密切的联系: 许多学习问题被表述为最小化训练样本集上的某些'''损失函数 Loss function'''。损失函数表示正在训练的模型预测结果与实际数据之间的差异（例如，在分类问题中，人们的目标是给一个未知的实例分配其对应标签，而模型经过训练学习到的是如何正确地为一组实例标记事先已知的标签）。这两个领域之间的差异源于泛化的目标: 优化算法可以最小化训练集上的损失，而机器学习关注于最小化未知样本上的损失。

机器学习与优化也有着密切的联系: 许多学习问题被表述为最小化训练样本集上的某些'''损失函数 Loss function'''。损失函数表示正在训练的模型预测结果与实际数据之间的差异（例如，在分类问题中，人们的目标是给一个未知的实例分配其对应标签，而模型经过训练学习到的是如何正确地为一组实例标记事先已知的标签）。这两个领域之间的差异源于泛化的目标: 优化算法可以最小化训练集上的损失，而机器学习关注于最小化未知样本上的损失。

=== Relation to statistics ===

=== 与统计学的关系 Relation to statistics ===

Machine learning and [[statistics]] are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population [[Statistical inference|inferences]] from a [[Sample (statistics)|sample]], while machine learning finds generalizable predictive patterns.<ref>{{cite journal |first=Danilo |last=Bzdok |first2=Naomi |last2=Altman |authorlink2=Naomi Altman |first3=Martin |last3=Krzywinski |title=Statistics versus Machine Learning |journal=[[Nature Methods]] |volume=15 |issue=4 |pages=233–234 |year=2018 |doi=10.1038/nmeth.4642 |pmid=30100822 |pmc=6082636 }}</ref> According to [[Michael I. Jordan]], the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics.<ref name="mi jordan ama">{{cite web|url=https://www.reddit.com/r/MachineLearning/comments/2fxi6v/ama_michael_i_jordan/ckelmtt?context=3 |title=statistics and machine learning|publisher=reddit|date=2014-09-10|accessdate=2014-10-01|language=|author = Michael I. Jordan|author-link=Michael I. Jordan}}</ref> He also suggested the term [[data science]] as a placeholder to call the overall field.<ref name="mi jordan ama" />

Machine learning and [[statistics]] are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population [[Statistical inference|inferences]] from a [[Sample (statistics)|sample]], while machine learning finds generalizable predictive patterns.<ref>{{cite journal |first=Danilo |last=Bzdok |first2=Naomi |last2=Altman |authorlink2=Naomi Altman |first3=Martin |last3=Krzywinski |title=Statistics versus Machine Learning |journal=[[Nature Methods]] |volume=15 |issue=4 |pages=233–234 |year=2018 |doi=10.1038/nmeth.4642 |pmid=30100822 |pmc=6082636 }}</ref> According to [[Michael I. Jordan]], the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics.<ref name="mi jordan ama">{{cite web|url=https://www.reddit.com/r/MachineLearning/comments/2fxi6v/ama_michael_i_jordan/ckelmtt?context=3 |title=statistics and machine learning|publisher=reddit|date=2014-09-10|accessdate=2014-10-01|language=|author = Michael I. Jordan|author-link=Michael I. Jordan}}</ref> He also suggested the term [[data science]] as a placeholder to call the overall field.<ref name="mi jordan ama" />

Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalizable predictive patterns. According to Michael I. Jordan, the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics. He also suggested the term data science as a placeholder to call the overall field.

Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalizable predictive patterns. According to Michael I. Jordan, the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics. He also suggested the term data science as a placeholder to call the overall field.

就方法而言，机器学习和统计学是密切相关的领域，但它们的主要目标是不同的: 统计学从样本中得出总体推论，而机器学习则找到可概括的预测模式。根据迈克尔 · 乔丹的观点，机器学习的思想，从方法论原则到理论工具，在统计学中已经有很长的历史了。他还建议用数据科学这个词作为整个领域的占位符。

就方法而言，机器学习和统计学是密切相关的两个领域，但它们的主要目标是不同的: 统计学侧重从样本中得出总体推论，而机器学习则是找到可概括的预测模式。根据迈克尔 · 乔丹 Michael I. Jordan的观点，机器学习的思想，从方法论原则到理论工具，在统计学中已经有很长的历史了。他还建议用'''数据科学 Data science'''这个词作为整个领域的总称。

Leo Breiman distinguished two statistical modeling paradigms: data model and algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random forest.

Leo Breiman distinguished two statistical modeling paradigms: data model and algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random forest.

Leo Breiman 区分了两种统计建模范式: 数据模型和算法模型，其中“算法模型”或多或少意味着像随机森林这样的机器学习算法。

Leo Breiman 区分了两种统计建模范式: 数据模型和算法模型，其中“算法模型”或多或少意味着像'''随机森林 Random forest，RF'''这样的机器学习算法。

Some statisticians have adopted methods from machine learning, leading to a combined field that they call statistical learning.

Some statisticians have adopted methods from machine learning, leading to a combined field that they call statistical learning.

== {{anchor|Generalization}} Theory ==

== {{anchor|Generalization}} Theory ==