Coursera, Machine Learning, notes

 

Basic theory

(i) Supervised learning (parametric/non-parametric algorithms, support vector machines, kernels, neural networks, )  regression, classification.

(ii) Unsupervised learning (clustering, dimensionality reduction, recommender systems, deep learning)

 

Others:

Reinforcement learning, recommender systems

 

SSE(和方差、误差平方和)：The sum of squares due to error

 

MSE(均方差、方差)：Mean squared error

 

RMSE(均方根、标准差)：Root mean squared error

 

 

Linear regression

• Gradient Descent algorithm:

 

     cost function:

  

  % correspoding code to compute gradient decent 

    h = X * theta;

    theta = theta - alpha/m * (X' * (h - y));

    

• Normal Equation 标准方程/正规方程

 

Gradient Descent vs Normal Equation

time complexity for Gradient Decent is O(kn2) 

Locally weighted regression: 只考虑待预测点附件的training data

 

 

 

Logistic regression

 

    a classfication algorithm

 

 

Cost function:

 

 

 

 

 

• Gradient Descent algorithm

          其中偏导数的推导如下：

       

 

Newton's method: much faster than Gradient Decent.

 

上图是求f(θ)=0时候的θ, 如果对f(θ)积分的最大值或者最小值

Newton’s method gives a way of getting to f(θ) = 0. What if we want to use it to maximize some function ℓ? The maxima of ℓ correspond to points where its first derivative ℓ ′ (θ) is zero. So, by letting f(θ) = ℓ ′ (θ), we can use the same algorithm to maximize ℓ, and we obtain update rule: 

θ := θ − ℓ ′(θ) / ℓ ′′(θ)

在python里，

 

 

Logistic Regression (Classification) decision boundary:

 

 

 

 

        

      

Neural Network

cost function:

 

           

          

back propagation algorithm:

 

https://www.coursera.org/learn/machine-learning/supplement/pjdBA/backpropagation-algorithm

 

1. we can use Gradient checking to check if the backpropagation algorithm is working correctly.
2. need randomly initialize theta

 

 

Diagnostic

Diagnostic 用来分析学习算法是不是正常工作，如果不正常工作，进一步找出原因

                       

怎么来评估learning algorithm 是否工作呢？ 

 

可以评估hypothesis 函数， 具体可以把所以input数据分成一部分training set, 另一部分作为test set 来验证，Andrew 建议 70%/30% 这个比例来划分，然后看用training set 得到的hypothesis 在 test set 上是否工作

 

 

• 一旦发现hypothesis 不工作，可以用model selection 来重新找hypothesis

 

• 怎么确定 degree of polynomial （hypothesis方程的次数）, 

1.  把input data 按照60/20/20% 分成3组 training set/ cross validation set/ test set
2.  基于traing按照1-10 degree 先给出不同次数的hypothesis 函数，然后用cross validation set 实验不同次数的hypothesis方程, 得到最好结果的hypothesis
3. 基于test set 可以给出 test report

 

• 怎么确定 lamda (0, 0,01, 0,02, 0.04, 0.08, ..., 10)

 

 

 

• Learning curves:

 

high bias:

 

high variance: (high gap)

 

If a learning algorithm is suffering from high bias, getting more training data will not (by itself) help much.

If a learning algorithm is suffering from high variance, getting more training data is likely to help.

 

• How to upgrade your model?

 

1. Getting more training examples: Fixes high variance
2. Trying smaller sets of features: Fixes high variance
3. Adding features: Fixes high bias
4. Adding polynomial features: Fixes high bias
5. Decreasing λ: Fixes high bias
6. Increasing λ: Fixes high variance.

 

 

• Support Vector Machine

 

 

Unsupervised Learning 　　

• K-means
• Dimentionality Reduction

 

Generative learning algo

 

 

 

Q&A

What is overfitting problem?

        

1. How to reduce overfitting problem?

• reduce the number of features
• regularization. Keep all the features, but reduce the magnitude of parameters θ j 

 

2. besises Gradient Decent, what other algorithms we can use ?

• besides Gradient Decent,  there are some optimization algorithms like Conjugate gradient, BFGS, L-BFGS. 
• These 3 optimization algorithms don't need maually pick ， and they are often faster than Gradient Decent, but more 

 

Reference:

http://blog.csdn.net/ligang_csdn/article/details/53838743

 

 

Terms:

'parametric' learning algo

• which has fixed set of parameters Theta, like linear regression

'non-parameter' learning algo

• in which no. of parameters grow with m.
• one specific algo is Locally weighted regression (Loess， or LWR), 这个算法不需要我们自己选feature，原理是只拟合待预测点附近的点的曲线

 

Discriminative algo: 对y建模 p(y|x)

Generative algo: 对x建模p(x|y)

 

GDA - Gaussian Discriminant Analysis，x 连续，y 不连续 

Naive Bayes - 比如垃圾邮件分类器，x 是不连续的，y 也是不连续的