Gaussian Product of Experts

A Product of Experts (PoE) contrasts with a mixture of experts by multiplying their individual distributions and normalizing the result, rather than averaging them. A mixture retains multimodal uncertainty where experts disagree; a product enforces a sharp consensus where they overlap.

Experiment

You can interact with different sets of experts in this module: Gaussian Product of Experts.

1. Set Experts to Disagree, Mixture weight A to 0.5, and Probe x to 0.
2. Observe that the Product mean is exactly 0.0 with Product variance 0.5, while the Mixture mean is 0.0 with Mixture variance 2.0. The product is sharper.
3. Set Experts to Agree. Notice that the Mixture variance becomes 1.0 but the Product variance becomes 0.5.
4. Set Experts to Unequal. Notice the product shifts toward the narrower expert.