Bayesian Inference

Use case

It is used to calculate the model parameters $\text{w}$ from the data. The a-Posteriori is given as the product of the Likelihood and the Prior.

$$p(\mathbf{w}|\mathbf{x},\mathbf{t},\alpha ,\beta )\propto p(\mathbf{t}|\mathbf{x},\mathbf{w},\beta )p(\mathbf{w}|\alpha )$$

where,

• $\text{w}\to$ Model parameter that has to be learned (for example weights.)
• $\text{x}\to$ Input vector
• $\text{t}\to$ Target
• $\beta \to$ Precision, is the inverse of the variance (${\sigma }^2$). It measures how tightly the data is clustered along the weights.
• $\alpha \to$ Hyper-parameter that is independent of the data Ex: Learning rate, batch size, regularization parameters etc.