How to Use Maximum a Posteriori Probability (MAP) in Classification Task

1. How do you find the maximum a posteriori probability?
2. Does maximum a posteriori probability use a prior probability distribution?
3. What is the key difference between maximum likelihood approach and maximum a posteriori approach?
4. What's the difference between MLE and MAP inference?

How do you find the maximum a posteriori probability?

To find the MAP estimate, we need to find the value of x that maximizes fX|Y(x|y)=fY|X(y|x)fX(x)fY(y). Note that fY(y) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes fY|X(y|x)fX(x).

Does maximum a posteriori probability use a prior probability distribution?

Maximum a Posteriori estimation is a probabilistic framework for solving the problem of density estimation. MAP involves calculating a conditional probability of observing the data given a model weighted by a prior probability or belief about the model.

What is the key difference between maximum likelihood approach and maximum a posteriori approach?

Maximum A Posteriori

The difference is that the MAP estimate will use more information than MLE does; specifically, the MAP estimate will consider both the likelihood - as described above - and prior knowledge of the system's state, X [6].

What's the difference between MLE and MAP inference?

The difference between MLE/MAP and Bayesian inference

MLE gives you the value which maximises the Likelihood P(D|θ). And MAP gives you the value which maximises the posterior probability P(θ|D). As both methods give you a single fixed value, they're considered as point estimators.