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# First attempt – logistic regression

We start off with probably the most basic classifier, the logistic regression, to be specific multinomial logistic regression as it is a multiclass case. It is a probabilistic linear classifier parameterized by a weight matrix W (also called coefficient matrix) and a bias (also called intercept) vector b. And it maps an input vector x to a set of probabilities P(y=1), P(y=2),. . ., P(y-K) for K possible classes.

A multinomial logistic regression for two possible classes can be represented graphically as follows:

Suppose x is n-dimension, then the weight matrix W is of size n by K with each column Wk representing ...

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