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→{{anchor|Generalization}} Theory
一些统计学家采用了机器学习的方法，形成了一个他们称之为'''“统计学习 Statistical learning”'''的综合领域。
一些统计学家采用了机器学习的方法，形成了一个他们称之为'''“统计学习 Statistical learning”'''的综合领域。
== {{anchor|Generalization}} Theory ==
== {{anchor|Generalization}} 理论 Theory ==
{{Main|Computational learning theory|Statistical learning theory}}
{{Main|Computational learning theory|Statistical learning theory}}
A core objective of a learner is to generalize from its experience. Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.
A core objective of a learner is to generalize from its experience. Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.
学习者的一个核心目标是从经验中进行总结。在这种情况下，'''泛化 Generalization'''指的是学习机器在经历了一个学习数据集之后，能够准确地执行新的、未知的例子 / 任务的能力。这些训练的例子来自于一些通常不为人知的概率分布（被认为是事件空间的代表），学习者必须建立一个关于这个空间的通用模型，才能保证其能够在新案例中产生足够准确的预测。
The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory. Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The bias–variance decomposition is one way to quantify generalization error.
The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory. Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The bias–variance decomposition is one way to quantify generalization error.
机器学习算法及其性能的计算分析是'''理论计算机科学 Theoretical computer science'''的一个分支，也被称为'''机器学习理论 Computational learning theory'''。由于训练集是有限的，未来是不确定的，学习理论通常不能保证算法的性能。相反，性能的概率界限是相当常见的。'''偏差-方差分解 Bias–variance decomposition'''就是量化泛化'''误差 Errors and residuals'''的一种方法。
For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has under fitted the data. If the complexity of the model is increased in response, then the training error decreases. But if the hypothesis is too complex, then the model is subject to overfitting and generalization will be poorer.
For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has under fitted the data. If the complexity of the model is increased in response, then the training error decreases. But if the hypothesis is too complex, then the model is subject to overfitting and generalization will be poorer.
为了在泛化情景下获得最佳性能，假设的复杂性应该与数据所依赖的功能的复杂性相匹配。如果假设（模型结构）没有问题本身那么复杂，那么模型就不能很好地拟合数据。如果在响应时增加模型的复杂度，训练误差就会减小。但如果假设过于复杂，则模型容易过拟合，导致模型泛化能力较差。
In addition to performance bounds, learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results. Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.
In addition to performance bounds, learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results. Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.
除了性能界限，学习理论家们还研究学习的时间复杂性和可行性。在机器学习理论中，若一个计算被认为是可行的，当且仅当它可以在复杂度为多项式的时间范围内完成。关于时间复杂度的结果有两种。正样结果表明，有些模式的函数可以在多项式时间复杂度内学习到。但同时负样结果表明，某些模式并不能在多项式时间内学习到。
== Approaches ==
== Approaches ==