Which kind of “uncertainty” can be quantified?

Random Process

Conformal Prediction

Bootstrap

How to overcome the key limitations of ML?

Anchor 1: Probabilistic Distribution

Distribution is a description of “statistical properties” when the samples go to rational infinity.

In practice, there are two hills on high-dimensional prob distributions:

• The curse of dimensionality (no application can bear with this)
• The unknown relationships between dims
  • If we know sth can help simplify → benefits to reduce the computational costs to an acceptable level

The magic from Bayes

• Bayesian identifies the importance of structure that tames the dimensionality problem, and make the Bayes’ idea self-contained in the freq view, mainly by introducing a conditional formula.

• In the conditional view, people use freq samples reduce the higher-dim to a lower one. Correspondingly, some of the bill / efforts turn to the mapping itself.

• Example: Modern Parameterized ML