Gaussian Mixture Model

A probability model that describes data as a weighted combination of several Gaussian distributions, which can have multiple peaks.

A Gaussian mixture model assumes data comes from one of K Gaussian (normal) distributions, each with its own mean, variance (covariance), and weight, with the weights summing to 1. Parameters are usually estimated iteratively with the expectation-maximization (EM) algorithm: first compute each point's probability of belonging to each component, then update the parameters using those probabilities. It's a classic tool for clustering and density estimation. Robot learning has two common uses for it. One is traditional learning from demonstration, which uses a GMM together with Gaussian mixture regression (GMR) to encode trajectories from a handful of demonstrations. The other is as a policy's action head, where the network directly outputs several sets of means, variances, and weights (this is called a mixture density network), representing several valid actions for the same scene. robomimic's BC-RNN-GMM works this way, and it's also one of the main comparison baselines in the Diffusion Policy paper. The number of components has to be fixed in advance, and expressiveness is limited for high-dimensional actions.

ExampleGoing around an obstacle on a table, passing on the left or the right are both fine. A policy with a single Gaussian averages the two into a straight path into the obstacle; a GMM policy can give the left and right options their own components and sample one of them.

Also called

GMM, GMM Policy, GMM Action Head

Related

Mixture Density Network · Action Multimodality · Gaussian Policy · Gaussian Mixture Regression / Task-Parameterized GMM · robomimic · Diffusion Policy

Sources

Mixture model - Wikipedia
robomimic documentation: Algorithms (BC_GMM / BC_RNN_GMM)
Diffusion Policy: Visuomotor Policy Learning via Action Diffusion (arXiv 2303.04137)