Coursera Machine Learning 第三周 quiz Logistic Regression

1.

Suppose that you have trained a logistic regression classifier, and it outputs on a new example  x  a prediction  hθ(x)  = 0.2. This means (check all that apply):

答案AC h(x)=0.2为y=1时的值

Our estimate for  P(y=0|x;θ)  is 0.8.

Our estimate for  P(y=0|x;θ)  is 0.2.

Our estimate for  P(y=1|x;θ)  is 0.2.

Our estimate for  P(y=1|x;θ)  is 0.8.

2.

Suppose you have the following training set, and fit a logistic regression classifier  hθ(x)=g(θ0+θ1x1+θ2x2) .

Which of the following are true? Check all that apply.

答案AB 对于CJ（theta）因为参数的增加将减小，对于D h(x)只能在0到1之间

Adding polynomial features (e.g., instead using  hθ(x)=g(θ0+θ1x1+θ2x2+θ3x21+θ4x1x2+θ5x22)  ) could increase how well we can fit the training data.

At the optimal value of  θ  (e.g., found by fminunc), we will have  J(θ)≥0 .

Adding polynomial features (e.g., instead using  hθ(x)=g(θ0+θ1x1+θ2x2+θ3x21+θ4x1x2+θ5x22)  ) would increase  J(θ)  because we are now summing over more terms.

If we train gradient descent for enough iterations, for some examples  x(i)  in the training set it is possible to obtain  hθ(x(i))>1 .

3.

For logistic regression, the gradient is given by  ∂∂θjJ(θ)=1m∑mi=1(hθ(x(i))−y(i))x(i)j . Which of these is a correct gradient descent update for logistic regression with a learning rate of  α ? Check all that apply.

答案AD 根据公式即可，注意线性回归与逻辑回归的区别

θ:=θ−α1m∑mi=1(hθ(x(i))−y(i))x(i) .

θ:=θ−α1m∑mi=1(θTx−y(i))x(i) .

θj:=θj−α1m∑mi=1(θTx−y(i))x(i)j  (simultaneously update for all  j ).

θ:=θ−α1m∑mi=1(11+e−θTx(i)−y(i))x(i) .

4.

Which of the following statements are true? Check all that apply.

答案BC

D由于使用代价函数为线性回归代价函数，会有很多局部最优值

Linear regression always works well for classification if you classify by using a threshold on the prediction made by linear regression.

The cost function  J(θ)  for logistic regression trained with  m≥1  examples is always greater than or equal to zero.

The sigmoid function  g(z)=11+e−z  is never greater than one ( >1 ).

.For logistic regression, sometimes gradient descent will converge to a local minimum (and fail to find the global minimum). This is the reason we prefer more advanced optimization algorithms such as fminunc (conjugate gradient/BFGS/L-BFGS/etc).

5.Suppose you train a logistic classifier  hθ(x)=g(θ0+θ1x1+θ2x2) . Suppose  θ0=6,θ1=0,θ2=−1 . Which of the following figures represents the decision boundary found by your classifier?

答案C -x2+6>=0 即X2<6时为1 故选C