Ising model

As explained in Machine Learning Algorithms in Depth

The Ising model is a probabilistic model of binary states on a graph with pairwise interactions favoring aligned neighboring states.

Models binary states on an undirected graph, where neighboring states interact and positive coupling favors alignment. In image denoising, grid nodes represent latent pixels and observations are noisy measurements. section 3.3

Assigns each latent variable xi a state in {−1,+1}; interaction potentials connect neighboring nodes, while Gaussian observations yi link the latent image to measured pixels. Mean-field variational inference approximates the joint posterior with fully factored distributions and updates each node using its neighbors’ means. section 3.3

Image denoising

Recovers a smooth binary image from noisy pixel observations by iteratively updating node means, tracking the ELBO and entropy, and applying coupling strength J with observation noise sigma. section 3.3

Figure 3.5 Mean field VI for Ising model pseudo-code

Use the pseudo-code to follow mean-field variational inference for the Ising model step by step. section 3.3

How Machine Learning Algorithms in Depth covers it

How deep it goes

Derives mean-field coordinate updates and supplies pseudo-code, stopping short of broader inference methods.

Examples

Demonstrates binary image denoising on a two-dimensional grid with noisy pixel observations.

What it assumes

Assumes probability and variational inference concepts while defining graph-based conditional independence and binary states.

What you can do after

Builds mean-field variational inference for an Ising image-denoising model and monitor its ELBO during iteration.

How it connects

Connects Markov random fields, variational inference, mean-field approximation, Gaussian observations, and image denoising.

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Related concepts

• interaction potentialuses · An interaction potential is a positive function assigning a compatibility weight to the joint states of variables connected by an edge.
• Markov random fieldkind of · A Markov random field is a joint distribution over variables represented by an undirected graph whose edges encode conditional independence relationships.

This explainer was generated by Manning's knowledge graph from the text of Machine Learning Algorithms in Depth. The section links point to the parts of the book it draws on.