Question

使用渐变的矢量化版本，如下所述： gradient descent seems to fail

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

theta值未更新，因此无论初始theta值如何这是运行梯度下降后设置的值：

example1：

m = 1
X = [1]
y = [0]
theta = 2
theta = theta - (alpha/m .* (X .* theta-y)' * X)'

theta =

    2.0000

example2：

m = 1
X = [1;1;1]
y = [1;0;1]
theta = [1;2;3]
theta = theta - (alpha/m .* (X .* theta-y)' * X)'

theta =

    1.0000
    2.0000
    3.0000

theta = theta - (alpha/m * (X * theta-y)' * X)';是否是梯度下降的正确矢量化实现？

Answer 1

theta = theta - (alpha/m * (X * theta-y)' * X)';确实是梯度下降的正确矢量化实现。

您完全忘记设置学习率alpha。

设置alpha = 0.01后，您的代码变为：

m = 1                # number of training examples
X = [1;1;1]
y = [1;0;1]
theta = [1;2;3]
alpha = 0.01
theta = theta - (alpha/m .* (X .* theta-y)' * X)'
theta =

   0.96000
   1.96000
   2.96000

梯度下降不更新theta值

1 个答案: