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機器學習基石 (When ((Types of Learning (Learning with Different Output Space Y…

- - - - definition
        
        improve performance measure
        
        acquire skill from data
      - components
        
        target function
        
        data
        
        output
        
        hypothesis
        
        input
    - - Perceptron Hypothesis Set
        
        由許多區分平面的直線構成，+1 or -1
        
        直線稱為 linear classifiers
      - Perceptron Learning Algorithm(PLA)
        
        選擇最好直線的演算法
        
        procedure
        
        Wt+1<-Wt+YnXn
        
        如果Yn=1 ，把法向量轉向該點，欲使該點在新的法向量同側，反之亦然
        
        find a mistake Wt (Xn,Yn)
        
        which means sign(WtXn) !=Yn
        
        until a full cycle of not encountering mistakes
        
        線性可分，linear separable
        
        parameters
        
        Y:labels +1 or -1
        
        H: hypothesis lines
        
        start from W0 (線的法向量)
        
        X: a vector of customer features
        
        Correctness
        
        linear seperable
        
        perfect line Wf
        
        YnWfXn > min(YnWfXn )>0 for every Xn
        
        Yn=sign(WfXn) for perfect line Wf
        
        current line Wt
        
        updating with XnYn
        
        WfWt+1=Wf(Wt+min(YnWfXn )) > WfWt+0
        
        兩線內積變大
        
        1 more item...
        
        changed only when mistake
        
        YnWtXn<=0
        
        長度成長受限
        
        1 more item...
        
        Non-Separable Data
        
        Learning with noise
        
        Packet Algorithm
        
        using separable algo.
        
        iterate K times
        
        choose less mistakes line
    - - Data label Yn
        
        Unsupervised learning
        
        clustering
        
        Reinforcement Learning
        
        Supervised Learning
        
        知道Yn
      - protocol f (Xn,Yn)
        
        Batch Learning
        
        一批數據
        
        填鴨式
        
        Online
        
        數據實時更新
        
        老師教學
        
        Active Learning
        
        機器主動問問題
      - Learning with Different Output Space Y
        
        Binary Classify
        
        Multiclass Classify
        
        Regression
        
        structural learning
      - input space X
        
        concrete features
        
        硬幣分類
        
        raw features
        
        手寫數字辨識
        
        abstract features
        
        購買行為預測
    - - No Free Lunch
        
        算法只在input distribution 有效
      - Probability to the Rescue
        
        統計學上樣本推估母體
        
        彈珠/彈珠罐
        
        known Ein/ Unknown Eout
      - Bad Data
        
        Datasets:N
        
        Hypothesis:M
        
        M有限N足夠大
        
        union upper bound: 2M*exp(-2cN)
- - - - Two core problems
        
        Ein=Eout
        
        Need small M
        
        Conflict
        
        Ein small enough
        
        Need big M
      - Effective Number of Line
        
        union bound is overestimated
        
        from infinite M to limited categories M
      - dichotomy
        
        所有點可以有多少種 +1 or -1 的可能
        
        upper bound : 2**N
        
        growth function:mH
        
        remove dependence by taking max of all possibles
      - break point
        
        from K, growth function starts to shatter
        
        no shattered means less than 2**N
        
        no
        
        2**N
        
        K
        
        N**K-1
    - - bounding function
        
        B(N,k)
        
        B(N,1)=1
        
        B(N,k)=2**N, N<k
        
        B(N,k)=2**n-1,N=k
        
        B(N,k)=B(N-1,k)+B(N-1,k-1)
        
        B(N,k)<=sigma(C(N,i))
      - A Pictorial Proof
    - - 4/26