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)**,1

2

3if htheta(x) >= 0.5, then y = 1

if 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.1

2if (theta'x) >= 0, then htheta(x) >= 0.5, then y = 1

if (theta'x) < 0, then htheta(x) < 0.5, then y = 0## Cost function implementation

For the assignment of week3, predicate the adimission by university with 2 exams grade data.

I optimize the implementation with vectoriaztion

1 | function [J, grad] = costFunction(theta, X, y) |

## 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

1 | function [J, grad] = costFunctionReg(theta, X, y, lambda) |

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~