A Probability distribution, which is used to model some system, often with Uncertainty/Randomness.

These models relate Random variables, using some more or less general assumptions about the nature of the data.

Graphical model

Artificial neural network

See Machine learning

Generative model – Deep generative model

Random-cluster model

Example of probabilistic modeling (particulary in Deep learning paradigm), using the DeepSaber project as example.

_technical outline of ML approach to beat saber problem_

• Supervised learning: song -> level
• But there are many levels that are good for a song
• Learn the probability distribution over beat-saber levels, conditioned on song
• We parametrize the distribution by a neural network with softmax output
• Train by Max Likelihood: find set of parameters that make the training data most likely.
• How do you even express a complicated distribution with a neural network?
  • Insert noise into it: GANs, normalizing flows
  • Divide and conquer (autoregression)!. Decompose distribution into product of conditionals
  • State space
• All of our approaches use autoregression over the sequence
• For each point in the sequence, we tried both GAN, and state space approach to express distribution over block states.