Machine Learning week 3

J(θ) will be a convex function, so gradient descent should converge to the global minimum.

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.

The positive and negative examples cannot be separated using a straight line. So, gradient descent will fail to converge.

Because the positive and negative examples cannot be separated using a straight line, linear regression will perform as well as logistic regression on this data.

答案选AB。可以由H函数看出来应该是个convex function

θ:=θ−α1m∑mi=1(θTx−y(i))x(i).

θ:=θ−α1m∑mi=1(hθ(x(i))−y(i))x(i).

θ:=θ−α1m∑mi=1(11+e−θTx(i)−y(i))x(i).

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

答案选BC 在logistic regression中h(x)应注意

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

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).

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

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

答案选CD  不是因为存在局部最小值而选择的更加优化的算法。