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Coupling strength

As explained in Machine Learning Algorithms in Depth

A coupling strength is a parameter controlling the influence of one variable's state on a neighboring variable's state in an interaction model.

A coupling strength controls how strongly one node's state influences a neighboring node in an interaction model. In an Ising model, edge weight w_st is constant, w_st = J > 0, and the potential Ψ(x_s, x_t) = exp{x_s J x_t} favors matching states. section 3.3

For image denoising, coupling strength encodes a smoothness preference: neighboring binary pixels are encouraged to share the same color. Neighbor influence enters the mean-field update through m_i = Σ_{j∈N(i)} w_ij μ_j. section 3.3

Mean-field image denoising

Set J in an image-denoising implementation, combine it with noisy Gaussian observations, and use mean-field variational inference to update pixel means. Listing 3.1 initializes J = 1. section 3.3

How Machine Learning Algorithms in Depth covers it

How deep it goes
Defines J through interaction potentials and neighbor means, then applies it in mean-field updates and code.
Examples
Uses a two-dimensional noisy binary-pixel grid and a Python implementation initialized with J = 1.
What it assumes
Assumes binary latent variables, neighboring-node interactions, and the mean-field factorization q(x).
What you can do after
Apply it via mean-field variational inference to encode neighbor agreement in image denoising.
How it connects
Connects Ising models, interaction potentials, image denoising, and mean-field variational inference.
Cover of Machine Learning Algorithms in Depth
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