Жасалған алгоритмнің дәлдігін өлшеу шаралары

Measure of algorithm accuracy
For supervised learning applications in machine learning and statistical learning theory, generalization error (also known as the out of sample error or the risk) is a measure of how accurately an algorithm is able to predict outcome values for previously unseen data. Because learning algorithms are evaluated on finite samples, the evaluation of a learning algorithm may be sensitive to sampling error. As a result, measurements of prediction error on the current data may not provide much information about predictive ability on new data. Generalization error can be minimized by avoiding overfitting in the learning algorithm. The performance of a machine learning algorithm is visualized by plots that show values of estimates of the generalization error through the learning process, which are called learning curves.

A number of algorithms have been proven to be stable and as a result have bounds on their generalization error. A list of these algorithms and the papers that proved stability is available here.

The concepts of generalization error and overfitting are closely related. Overfitting occurs when the learned function becomes sensitive to the noise in the sample. As a result, the function will perform well on the training set but not perform well on other data from the joint probability distribution of and Thus, the more overfitting occurs, the larger the generalization error. The amount of overfitting can be tested using cross validation methods, that split the sample into simulated training samples and testing samples. The model is then trained on a training sample and evaluated on the testing sample. The testing sample is previously unseen by the algorithm and so represents a random sample from the joint probability distribution of and This test sample allows us to approximate the expected error and as a result approximate a particular form of the generalization error. Many algorithms exist to prevent overfitting. The minimization algorithm can penalize more complex functions (known as Tikhonov regularization), or the hypothesis space can be constrained, either explicitly in the form of the functions or by adding constraints to the minimization function (Ivanov regularization). The approach to finding a function that does not overfit is at odds with the goal of finding a function that is sufficiently complex to capture the particular characteristics of the data. This is known as the bias–variance tradeoff. Keeping a function simple to avoid overfitting may introduce a bias in the resulting predictions, while allowing it to be more complex leads to overfitting and a higher variance in the predictions. It is impossible to minimize both simultaneously.