Lecture 13 & Workshop 3: Logistic Regression with Regularisation

Question 1

The model is built based on the notion underlying y=1..
e.g. y=1 means tumor is malignant
y = 0 means tumor is benign.
=> model is trying to predict if tumor is ?.

Answer 1

The model is built based on the notion underlying y=1..
e.g. y=1 means tumor is malignant
y = 0 means tumor is benign.
=> model is trying to predict if tumor is malignant.

Question 2

Logistic regression is a special case of linear regression where y = {??}

Answer 2

Logistic regression is a special case of linear regression where y = {0, 1}

Question 3

Model for logistic regression:
h(x) = g(??) using logit function g

h(x) can be interpreted as the estimated ? that ?? on input x.

Answer 3

Model for logistic regression:
h(x) = g(theta^T * x) using logit function g

h(x) can be interpreted as the estimated probability that y=1 on input x.

Question 4

Logit/ sigmoid function :

g (theta^T * x ) = 1 / [1 + ??]

Answer 4

Logit/ sigmoid function :

g (theta^T * x = 1 / [1 + e^(-theta^T *x)]

Question 5

to have a ? cost / best fitted line of h(x):
if y=1 => we want h(x) is close to ?
if y=0 => we want h(x) is close to ?.

Answer 5

to have a low cost / best fitted line of h(x):
if y=1 => we want h(x) is close to 1
if y=0 => we want h(x) is close to 0.

Question 6

Logistic Cost function:
when y=1:
J(theta) = (-1/?) * Sum [??? ]

Answer 6

Logistic Cost function:
when y=1:
J(theta) = (-1/m) * Sum [y * log ( h(x) ) ]
m: number of observations

Question 7

Logistic Cost function when y = 0:

J (theta) = (-1/m) * Sum [???]

Answer 7

Logistic Cost function when y = 0:
J (theta) = (-1/m) * Sum [log ( 1 - h(x) )]
m: number of observations