# 【机器学习技术】高斯过程初探

## 高斯过程回归

<a href="http://www.codecogs.com/eqnedit.php?latex=t=y(x)+N(0,{\beta}^{-1})" target="_blank">

$t=y(x)+N(0,{\beta}^{-1})$
t=y(x)+N(0,{\beta}^{-1})
</a>

<a href="http://www.codecogs.com/eqnedit.php?latex=p(\mathbf{t}|\mathbf{y})=N(\mathbf{t}|\mathbf{y},\beta^{-1}\mathbf{I}_N)" target="_blank">
$p(\mathbf{t}|\mathbf{y})=N(\mathbf{t}|\mathbf{y},\beta^{-1}\mathbf{I}_N)$
p(\mathbf{t}|\mathbf{y})=N(\mathbf{t}|\mathbf{y},\beta^{-1}\mathbf{I}_N)
</a>

<a href="http://www.codecogs.com/eqnedit.php?latex=p(\mathbf{y})=N(\mathbf{y}|\mathbf{0},\mathbf{K})" target="_blank">
$p(\mathbf{y})=N(\mathbf{y}|\mathbf{0},\mathbf{K})$
p(\mathbf{y})=N(\mathbf{y}|\mathbf{0},\mathbf{K})
</a>

<a href="http://www.codecogs.com/eqnedit.php?latex=p(\mathbf{t})=\int&space;p(\mathbf{t}|\mathbf{y})p(\mathbf{y})d\mathbf{y}=N(\mathbf{t}|\mathbf{0},\mathbf{C})" target="blank">
$p(\mathbf{t})=\int&space;p(\mathbf{t}|\mathbf{y})p(\mathbf{y})d\mathbf{y}=N(\mathbf{t}|\mathbf{0},\mathbf{C})$
p(\mathbf{t})=\int p(\mathbf{t}|\mathbf{y})p(\mathbf{y})d\mathbf{y}=N(\mathbf{t}|\mathbf{0},\mathbf{C})
</a>

<a href="http://www.codecogs.com/eqnedit.php?latex=C(x_n,x_m)=k(x_n,x_m)+\beta^{-1}\delta
{nm}" target="_blank">
$C(x_n,x_m)=k(x_n,x_m)+\beta^{-1}\delta_{nm}$
C(x_n,x_m)=k(x_n,x_m)+\beta^{-1}\delta_{nm}
</a>

<a href="http://www.codecogs.com/eqnedit.php?latex=p(\mathbf{t}{N+1})=N(\mathbf{t}{N+1}|\mathbf{0},\mathbf{C}_{N+1})" target="blank">

$p(\mathbf{t}_{N+1})=N(\mathbf{t}_{N+1}|\mathbf{0},\mathbf{C}_{N+1})$
p(\mathbf{t}_{N+1})=N(\mathbf{t}_{N+1}|\mathbf{0},\mathbf{C}_{N+1})
</a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\mathbf{C}
{N+1}=\begin{pmatrix}&space;\mathbf{C}_N&space;&&space;\mathbf{k}\&space;\mathbf{k}^T&space;&&space;c&space;\end{pmatrix}" target="_blank">
$\mathbf{C}_{N+1}=\begin{pmatrix}&space;\mathbf{C}_N&space;&&space;\mathbf{k}\\&space;\mathbf{k}^T&space;&&space;c&space;\end{pmatrix}$
\mathbf{C}_{N+1}=\begin{pmatrix} \mathbf{C}_N & \mathbf{k}\ \mathbf{k}^T & c \end{pmatrix}
</a>

<a href="http://www.codecogs.com/eqnedit.php?latex=p(t*|\mathbf{t})=N(\mathbf{kTC_N{-1}t},c-\mathbf{kTC_N^{-1}k})" target="_blank">
$p(t^*|\mathbf{t})=N(\mathbf{k^TC_N^{-1}t},c-\mathbf{k^TC_N^{-1}k})$
p(t^*|\mathbf{t})=N(\mathbf{k^TC_N^{-1}t},c-\mathbf{k^TC_N^{-1}k})
</a>

## 参考资料

Github博客主页(http://jasonding1354.github.io/)
GitCafe博客主页(http://jasonding1354.gitcafe.io/)
CSDN博客(http://blog.csdn.net/jasonding1354)