机器学习笔记(Washington University)- Regression Specialization-week four

Posted

tags:

篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了机器学习笔记(Washington University)- Regression Specialization-week four相关的知识,希望对你有一定的参考价值。

1. Ridge regression

A way to automatically balance between bias and varaince situations and regulate

overfitting when using many features. because the model has a lot of flexibility to explain

the data.

 

2. Overfitting

Formally, when we can find a model with higher traning error but lower true error compared

with the trained model, then the trained model is overfiting the dataset.

Overfitting is associated with very large magnitude estimated coefficients.

And Not like enough data,if we have few observations, the model will overfit rapidly as the

model complexity increases.

 

3. Desired total cost

want to balance:

1. How well function fits data.

2. Magnitude of coefficientrs.

Total cost = measure of fit + measure of magnitude of coefficients

measure of magnitude of coefficients = sum of squares  of regression coefficients (L2 Norm)

技术分享

so the regression is selected to minimize:

 

技术分享(lambda is the tuning parameter)

when lambda is small, just as before,  W = W(least square solution)

when lambda is large, W = 0

when lambda is in between, then  0<= |W|<=W(least square solution)

so the lambda is controlling the model complexity.

 

4. The formula for the new gradient

技术分享

 

5. solution

Close-form :

we can set the gradient to zero, and we can get the solution like shown below

技术分享

 

 

 

when lambda is zero, it is the old solution,

when lambda is infinity, we are like to divide by infinity, so the solution to W is zero

the first item is invertible, even if the observations (N) is smaller than D(faetures)

when the intercept is kept out from shrinking, we just set the (1,1)  element of I to be zero

 

Gradient descent:

技术分享

The interpretation of this formula is:

No matter what, we firstly shrink the W vector, then we modify it to fit our data.

when the intercept is kept out from shrinking, we just add a if-statement to set 

the w0 to update just like the old solution. no lambda involved.

 

6. K-fold cross validataion

The data set is divided into K blocks

For a certain lambda

For K=1...K

1. Estimate w on the training blocks

2.compute error on validation blocks: error_K(labda)

then we compute the average error of all the error_K, we will choose the best lamda to minimize this error.

leave-one-out cross validation just means that K=N(data size)

Typically, K=5 or 10

 

以上是关于机器学习笔记(Washington University)- Regression Specialization-week four的主要内容,如果未能解决你的问题,请参考以下文章

机器学习笔记(Washington University)- Regression Specialization-week four

机器学习笔记(Washington University)- Classification Specialization-week 3

机器学习笔记(Washington University)- Regression Specialization-week five

机器学习笔记(Washington University)- Regression Specialization-week six

机器学习笔记(Washington University)- Regression Specialization-week one

机器学习笔记(Washington University)- Clustering Specialization-week four