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Chapter 3
Logistic regression is used in classification problems. For example, when looking at
medical data, we can use logistic regression to classify whether a person has cancer
or not. In case the output categorical variable has two or more levels, we can use
multinomial logistic regression. Another common technique used for two or more
output variables is one versus all.
For multiclass logistic regression, the cross-entropy loss function is modified as:
pp
llllllll = ∑ ∑ YY iiii log (YY haaaaiiii )
ii=1
Where K is the total number of classes. You can read more about logistic regression
at https://en.wikipedia.org/wiki/Logistic_regression.
Now that you have some idea about logistic regression, let us see how we can apply
it to any dataset.
Logistic regression on the MNIST dataset
Next, we will use the Estimator classifier available in TensorFlow estimator to
classify handwritten digits. We will be using the MNIST (Modified National
Institute of Standards and Technology) dataset. For those working in the field of
deep learning, MNIST is not new, it is like the ABC of machine learning. It contains
images of handwritten digits and a label for each image, indicating which digit it is.
The label contains a value lying between 0-9 depending upon the handwritten digit.
The classifier Estimator takes in the features and the labels. It converts them to onehot
encoded vectors, that is, we have 10 bits representing the output. Each bit can
have a value of either 0 or 1, and being one-hot means that for each image in the
label Y only 1 bit out of the 10 will have a value of 1, and the rest will be 0s. In the
following, you can see the image of a handwritten numeral 5, along with its one-hot
encoded value [0 0 0 0 0 0 0 0 1 0].
kk
jj=1
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