Life, the Universe and Machine Learning

point 1: \(x= 1\), \(y=3\) \[ 3 = m + c \]

point 2: \(x= 3\), \(y=1\) \[ 1 = 3m + c \]

point 3: \(x= 2\), \(y=2.5\)

\[2.5 = 2m + c\]

point 1: \(x= 1\), \(y=3\) \[ 3 = m + c + \epsilon_1 \]

point 2: \(x= 3\), \(y=1\) \[ 1 = 3m + c + \epsilon_2 \]

point 3: \(x= 2\), \(y=2.5\) \[ 2.5 = 2m + c + \epsilon_3 \]

Set the mean of Gaussian to be a function. \[ p\left(y_i|x_i\right)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{\left(y_i-f\left(x_i\right)\right)^{2}}{2\sigma^2}\right). \]

This gives us a ‘noisy function’.

This is known as a stochastic process.