Answer:
Answer for the question:
"Show that for a linearly separable dataset, the maximum likelihood solution for the logisitic regression model is obtained by finding a weight vector w whose decision boundary wx. "
is explained in the attachment.
Explanation:
For a linearly separable dataset, the maximum likelihood solution for the logisitic regression model is; increase ||w||2 without bound.
From the math perspective, if we consider the fact that if the data is separable then we can say that;
y*w^T*x ≥0 for every data point (x, y).
The above can be rewritten as; y||w||₂||x||₂cosθ ≥ 0
where;
θ is the angle between the vectors x and w.
In order for us to minimize log(1 + e^(−y(x^T)w)), the exponent will have to be as negative as possible which means that y||w||₂||x||₂cosθ has to be as large and positive as possible.
By separability of the data we know there is some vector w such that the exponent is positive for every data point and so In order to increase y||w||₂||x||₂cosθ, we simply increase ||w||2 without bound.
Read more about regression model at; https://brainly.com/question/17844286
