Homework Assignment 3 Cross-validation

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1. Cross-validation is a useful strategy for model selection, especially when the training data is small. However, it cannot be used for early-stopping (in other words, you
cannot pick the best fold). Why is this the case?
2. In multiclass classification, given the definitions in the lecture notes, derive the
following distance function. defined as
D(y

,M,x) = −log pM∗(x)
= −ay
∗ +log
K

k=1
exp(ak),
3. Given the definition of the distance function above, derive a learning rule step-bystep for each column vector wc of the weight matrix W (Equation 1.28 in the lecture
notes).
4. Multiclass Classification on MNIST Please download https://github.
com/nyu-dl/Intro_to_ML_Lecture_Note/blob/master/homeworks/
hw3.ipynb and follow its instructions.
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