Partition Function
Chapter 17: Score Function and Energy-Based Models — Partition Function Z
From the book
Chapter 17: Score Function and Energy-Based Models. In the chapter mind map this icon labels Partition Function Z. The discussion below is excerpted and lightly edited from § Partition Function Z in Mathematics for AI and Machine Learning.
Let $\mathbf{x} \in \mathbb{R}^d$ be a continuous random variable with density $p(\mathbf{x})$. The score function is defined as
What this drawing shows
What you see. Integration domain $\int e^{-E}\,dx$ fills in while $Z$ stays intractable, highlighting normalization of energy-based models.
In the mind map. Chapter 17 — Partition Function Z. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 17: Score Function and Energy-Based Models — see the mind-map node Partition Function Z.
