How to model data with a probability distribution? For example, if data looks like a circle or symmetric, we may model it with a Gaussian distribution:
Bayesian Inference what can we do with posterior distribution $p(\theta|x)$ that we can not do with point estimate: For example we can estimate by $\theta_{\text{MAP}} = \arg \max_{\theta} p(\theta|x)$
Maximum Likelihood Estimation: Suppose that we have a probabilistic model of generating random data $x \in \mathcal{X}$ derived from function $P_{\theta}(x)$ that is parametrized by $\theta$.
Searching for optimal transport encourages a mapping that minimizes the total cost of transporting mass from $\alpha$ to $\beta$, as initially formulated by Monge (1781).