PRML 1.3〜1.4

I returned to my family home the day before yesterday. In the Shinkansen which went to Gifu from Tokyo, I read 1.3〜1.4 (and the beginning part of 1.5) of PRML.

• 1.3 Model Selection

It is possible to optimize parameters of by machine learning technique using training data set. But it is another problem to determine the number of parameters of . There is an optimal number of parameters (or complexity parameters) that give the best generalization.

If data is plentiful, then "trying" is good approach. For this "trying" approach, we need training data set for optimization of model parameters and validation data set for comparing the model with a range of values for its complexity parameters.

In many applications, however, the supply of data will be limited, and in order to build good models, we wish to use as much of the available data as possible for training. However, small validation set will give a relatively noisy esimate of predictive performance. One solution to this dilemma is to use cross-validation.

• 1.4 The Curse of Dimensionality