Thank you for the nice library and some questions about pgmax HOT 4 CLOSED

Hi Lukas,
Thank you for using PGMax and for your positive feedback. Please find an answer to your questions below:

• The log potentials are initialized when the factors / factor groups are added to the factor graph. For instance in the ising model notebook https://github.com/deepmind/PGMax/blob/main/examples/ising_model.ipynb the log_potential_matrix argument specifies the log potentials of the PairwiseFactorGroup (which, in this case, are shared across all the pairwise factors)

factor_group = fgroup.PairwiseFactorGroup(
    variables_for_factors=variables_for_factors,
    log_potential_matrix=0.8 * np.array([[1.0, -1.0], [-1.0, 1.0]]),
)
fg.add_factors(factor_group)

The log potentials are only set to 0 if no initialization is given: see https://github.com/deepmind/PGMax/blob/54baa4a2c550e396fc1ff946cb09976f078ea6ff/pgmax/fgroup/enum.py#L65 for EnumFactorGroup and https://github.com/deepmind/PGMax/blob/54baa4a2c550e396fc1ff946cb09976f078ea6ff/pgmax/fgroup/enum.py#L240 for PairwiseFactorGroup

• The evidence has to be given in log-space. If you want to run inference by conditioning on some variable assignment, you can set the evidence similarly to the one for the variables X in https://github.com/deepmind/PGMax/blob/main/examples/pmp_binary_deconvolution.ipynb:

uX = np.zeros((X_gt.shape) + (2,))
uX[..., 0] = (2 * X_gt - 1) * logit(pX)

Let us know if this helps,
Best,
Antoine

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1. Mmmmh why do you want to run inference if you already know all your variables assignments? Or do you want to fix some variables and infer the remaining ones?
   If the latter, you can set the evidence of the variables that you want to condition on similarly to theuX I shared.

   Also, when you say that you were manually specifying solution with lower energy than PGMax, were you computing the energy with compute_energy? If so, could you please rebase and try again, the sign of the energy returned by this function was flipped, we have fixed this.

   Regarding the initialization, you can try playing with the messages initialization here and see if it improves inference -- for the analogy, you can think of it as changing the starting point x_0 when you run gradient descent

   Finally, the inference speed is determined by the num_iters parameters in run_bp
   Also note that loopy BP is not guaranteed to converge in undirected model.

2. Sure, you can set the evidence to NEG_INF.
   To go into the details, using logit(1e-100) here is equivalent to having a noisy channel between the variables X and the pixels, which we found to be useful as it leaves more flexibility during inference (ie a very small subset of the X variables may be decoded differently than the pixels which may lead to a better solution).

3. You can certainly define factors for as many variables as you want!
   See for instance the ORFactorGroup defined in https://github.com/deepmind/PGMax/blob/main/examples/pmp_binary_deconvolution.ipynb. You can do the same for EnumFactorGroup -- note that factor_configs would need to be of the corresponding size

Hope it helps,
Antoine

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Hi @antoine-dedieu,

thank you for the quick answer, but two questions would still be open:

1. Is there any way to initialize pgmax so that it converges to a better energy and/or faster? We have seen cases where we can manually provide map_states with lower energy than the inference result and would like to use this.

2. Are there known issues with very small log potentials? I see in your notebook that you use logit(pX) = logit(1e-100) = -230, is this the smallest recommended unary?

3. Are factors between 3 variables possible?

Thank you :)

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Thank you Antoine for your answers, I'll close the issue.

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