线性回归梯度

Question

我有非常基本的线性回归样本。下面的实现（没有正则化）

class Learning:

    def assume(self, weights, x):

        return np.dot(x, np.transpose(weights))

    def cost(self, weights, x, y, lam):

        predict = self.assume(weights, x) \

            .reshape(len(x), 1)

        val = np.sum(np.square(predict - y), axis=0)

        assert val is not None

        assert val.shape == (1,)

        return val[0] / 2 * len(x)

    def grad(self, weights, x, y, lam):

        predict = self.assume(weights, x)\

            .reshape(len(x), 1)

        val = np.sum(np.multiply(

            x, (predict - y)), axis=0)

        assert val is not None

        assert val.shape == weights.shape

        return val / len(x)

我想检查渐变，它是否有效，与scipy.optimize.

learn = Learning()

INPUTS = np.array([[1, 2],

          [1, 3],

          [1, 6]])

OUTPUTS = np.array([[3], [5], [11]])

WEIGHTS = np.array([1, 1])

t_check_grad = scipy.optimize.check_grad(

    learn.cost, learn.grad, WEIGHTS,INPUTS, OUTPUTS, 0)

print(t_check_grad)

# Output will be 73.2241602235811!!!

我从头到尾手动检查了所有计算。它实际上是正确的实现。但是在输出中我看到了非常大的差异！是什么原因？

Answer 1

在您的成本函数中，您应该返回val[0] / (2 * len(x))而不是val[0] / 2 * len(x). 然后你会有print(t_check_grad) # 1.20853633278e-07