cost function

Hypothesis:

$$h_{theta}(x) = theta_{0} + theta_{1}(x)$$

Parameters:

$$theta_{0},quad theta_{1}$$

Cost Function:

$$J(theta_{0}, theta_{1}) = frac{1}{2m}sum_{i = 1}^{m}left(h_{theta}(x^{(i)}) - y^{(i)}right)^{2}$$

Simplified:

$$h_{theta}(x) = theta_{1}x \ theta_{1}$$ $$J(theta_{1}) = frac{1}{2m}sum_{i = 1}^{m}left(h_{theta}(x^{(i)}) - y^{(i)}right)^{2} \ \ min_{theta_{0}, theta_{1}}J(theta_{1})$$

在含有两个参数的情况下, 代价函数(cost function)变为更加复杂.

为了更方便的展示上图, 运用轮廓图.

通过将轮廓图展现的代价函数与原始的假设函数对应, 可以直观的了解代价函数.