Question

Suppose we have a linearly separable dataset, and we divide the data into training and validation sets. Will a perceptron learned on the training dataset (assuming gradient decent works perfectly well) be guaranteed to have i) 0 error on the training dataset ii) 0 error on the validation dataset. Briefly explain.

Answer 1

i)True

ii)False

Step-by-step explanation:

i. True

The data given is linearly separable. So, the subset of the data will also be linearly separable. And it will pass for all training data as the model is trained using the training set.

The output using a training set guarantees a hyper plane that perfectly fits and the data sets are separated accordingly.

ii. False

Since the data of the validation set is not known, so it may not result in 100 percent accuracy and there will be errors on the data sets.

Even though the perceptron works well with the training set, it may take a bad decision boundary as the samples are unknown.