For a given number of training samples, when we increase the predictor's capacity, the difference between the empirical risk and the expected risk should :

True or False ?

The empirical risk computed on the test set (aka test risk, test error) is an unbiased estimated of the expected risk.

If the difference between the performance of your classifier on train and test sets is small, and both performances are high (good),  what may be happening?

Suppose we have an array of sample brain scans X of shape (256 × 240 × 240 × 4), and an array Y of target segmentation for tumors, of shape (256 × 240 × 240 × 1), just like in practice session 6.

Scans are in 2D, and we do not care about masks here.

The first dimension corresponds to a patient, the second and third to image rows and columns, and the last dimension to modalities for X or class for Y.

Segmentation is performed by training a pixel classifier.

Among the following approaches to create train and validation sets from an original train set, what is the appropriate one?

For a given predictor capacity, when we increase the number of training samples, the difference between the empirical risk and the expected risk should :

True or False ?

The empirical risk computed on the train set (aka train risk, train error) is an unbiased estimated of the expected risk.

If the difference between the performance of your classifier on train and test sets is small, and both performances are low (not good),  what may be happening?

If the difference between the performance of your classifier on train and test sets is important, what may be happening?

What is the capacity of the family of affine functions (lines) in bounded (i.e. any compact subset of) ?

Remind that, for classification, the capacity of F is defined by Vapnik & Chervonenkis as the largest n such that there exist a set of examples Dn such that one can always find an f ∈ F which gives the correct answer for all examples in Dn, for any possible labeling.

The error of some classifier can be decomposed into several terms.

Select these terms among the following ones.