• Coursera machine learning 第二周 quiz 答案 Linear Regression with Multiple Variables


    https://www.coursera.org/learn/machine-learning/exam/7pytE/linear-regression-with-multiple-variables

    1。

    Suppose m=4 students have taken some class, and the class had a midterm exam and a final exam. You have collected a dataset of their scores on the two exams, which is as follows:

    midterm exam

    (midterm exam)2

    final exam

    89

    7921

    96

    72

    5184

    74

    94

    8836

    87

    69

    4761

    78

    You'd like to use polynomial regression to predict a student's final exam score from their midterm exam score. Concretely, suppose you want to fit a model of the form hθ(x)=θ0+θ1x1+θ2x2, where x1 is the midterm score and x2 is (midterm score)2. Further, you plan to use both feature scaling (dividing by the "max-min", or range, of a feature) and mean normalization.

    What is the normalized feature x2(2)? (Hint: midterm = 72, final = 74 is training example 2.) Please round off your answer to two decimal places and enter in the text box below.

    答案: -0.37

    平均值 :(7921+5184+8836+4761)/4 = 6675.5

    Max-Min: 8836-4761=4075

    x=(xn-平均值)/(Max-Min

    training example 2   (5184-6675.5)/4075=-0.37

    2。

    You run gradient descent for 15 iterations

    with α=0.3 and compute J(θ) after each

    iteration. You find that the value of J(θ) increases over

    time. Based on this, which of the following conclusions seems

    most plausible?

    α=0.3 is an effective choice of learning rate.

    Rather than use the current value of α, it'd be more promising to try a larger value of α (say α=1.0).

    Rather than use the current value of α, it'd be more promising to try a smaller value of α (say α=0.1).

    答案:B. Rather than use the current value of α, it'd be more promising to try a larger value of α (say α=1.0).

    a越大下降越快,a越小下降越慢。

     

    3。

    Suppose you have m=23 training examples with n=5 features (excluding the additional all-ones feature for the intercept term, which you should add). The normal equation is θ=(XTX)−1XTy. For the given values of m and n, what are the dimensions of θ, X, and y in this equation?

    X is 23×6, y is 23×6, θ is 6×6

    X is 23×5, y is 23×1, θ is 5×5

    X is 23×6, y is 23×1, θ is 6×1

    X is 23×5, y is 23×1, θ is 5×1

    答案:C. X is 23×6, y is 23×1, θ is 6×1

               X n+1 列 ,  y 1 列 , θ  n+1 行 

    4。

    Suppose you have a dataset with m=50 examples and n=15 features for each example. You want to use multivariate linear regression to fit the parameters θ to our data. Should you prefer gradient descent or the normal equation?

    Gradient descent, since it will always converge to the optimal θ.

    The normal equation, since it provides an efficient way to directly find the solution.

    Gradient descent, since (XTX)−1 will be very slow to compute in the normal equation.

    The normal equation, since gradient descent might be unable to find the optimal θ.

    答案: B. The normal equation, since it provides an efficient way to directly find the solution.

    比较梯度下降与normal equation

    梯度下降需要Feature Scaling;normal equation 简单方便不需Feature Scaling。

    normal equation 时间复杂度较大,适用于Feature数量较少的情况。

    当Feature数量<100000时  Normal Equation
    当Feature数量>100000时  Gradient Descent

     

    5。

    Which of the following are reasons for using feature scaling?

    It speeds up solving for θ using the normal equation.

    It prevents the matrix XTX (used in the normal equation) from being non-invertable (singular/degenerate).

    It speeds up gradient descent by making it require fewer iterations to get to a good solution.

    It is necessary to prevent gradient descent from getting stuck in local optima.

    答案 :C. It speeds up gradient descent by making it require fewer iterations to get to a good solution.

    上一题也考到这个点:normal equation 不需要 Feature Scaling,排除AB, 特征缩放减少迭代数量,加快梯度下降,然而不能防止梯度下降陷入局部最优。

  • 相关阅读:
    HDU 4492 Mystery (水题)
    UVA 10480 Sabotage (最大流)
    POJ 2446 Chessboard (二分匹配)
    VS2008下用MFC 的MSComm控件编写串口程序
    退役了~~~
    STL Algorithms 之 unique
    cocos2d中CCCallFuncND传参数的注意事项
    好太太晾衣架市场价格表(仅供参考)
    Linux VNC黑屏(转)
    C++ TinyXml操作(含源码下载)
  • 原文地址:https://www.cnblogs.com/smartweed/p/6783683.html
Copyright © 2020-2023  润新知