Logistic Regression is for classification problem, and the predication value is fixed descrete values, such as 1 for positive or 0 for negative. The essence of logistic regression is:
 hypothesis function is sigmoid function
 cost function: J(theta)
 gradient descent and algorithms
 advantanced optimization with regularization to solve overfitting problem.
Basics about logistic regression
hypothesis function = 1 / (1 + exp(htheta(x))),
where htheta(x) = theta’ x(theta’ is transpose theta)
htheta(x) mean *Probalitiy that y=1, given x parameterized by theta P(y=1  x; theta),12if htheta(x) >= 0.5, then y = 1if htheta(x) < 0.5, then y = 0
Descision Boundary
Our goal is the calculate theta, can classify our traing data with descision boundary.
In the example, the traning data can be classified into 2 categories by a straight line.


Cost function implementation
For the assignment of week3, predicate the adimission by university with 2 exams grade data.
I optimize the implementation with vectoriaztion


Cost function with regularization
Regularzation is for overfitting problem.
 underfit: not fit the training data, with high bias between predications and actual value
 Just Right: great fit
 Overfitting: often with too many features, not so much traning data, fit traing data well, but with hight variance, predict new data not very well


the lambda for regularization can’t be too large:
 large lamba will got very small theta value, and underfit.
 small lambda will got large theta velue, and overfit.
 the lambda for the exerise is 1
Github assignments
Write on the last
After one year, I learn the logistic regression again. Last week, Andrew NG left Baidu. Maybe, these great people thought Baidu is not worth to fight for. Now I still decidated on a Spark project and focus on Spark Streaming. As team leader, I am bearing a great burden and is stressful. It’s a great chance to train my leadership. I am also wondering next opportunity. Learning Machine Learning is right and worth to do. Anyway, even though mist is on the path, just go forward and fight~