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I am a computer science student specialised in machine learning. Recently I fell in love with Probabilistic Graphical Models (and probabilistic programming) because of

  • the flexibility to focus on model engineering rather than choosing amount a handfull of problem specific algorithms.
  • the ability to do quick model prototypes to test what works and what does not work.
  • the ability to infer structures or series of variables that depend on each other.
  • the ability to be able to write a "story" about how the data was generated by stochastic variables, and the reverse the process to infer the variables.

I imagine that Probabilistic Graphical Models would be well suited for data reconstruction in cases where you have multiple inconsistent (missing or conflicting) samples measured from the same real world object. However I cannot seem to find any literature on this. Is there something I am missing? Does it makes sense to use probabilistic graphical models this way?

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An example that crops up in examples from the Figaro manual (Practical Probabilistic Programming by Avi Pfeffer) is the use of an undirected graphical model for defining distributions over pixel RGB values conditioned on neighbouring pixel RGB values.

To clarify, the approach (IIRC) that the author uses is that for a given pixel, the mean of the RGB vector is computed as something like a sample mean of its neighbouring pixels.

The model certainly makes sense, and it's a wonderful book filled with tons of Scala code samples; of course, if you're not using Scala & Figaro, it won't be directly useful, but the ideas are there.

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Yes, it definitely makes sense to do this. I can give two examples in addition to the nice answer by Kevin Li.

There is work on Bayesian record linkage that you might be interested in. In this setting, records emerge from the same real world entity (such as a person's name), but are corrupted by e.g. misspellings or missing middle initials.

Steorts, R., Hall, R., & Fienberg, S. (2014, April). SMERED: A Bayesian approach to graphical record linkage and de-duplication. In Artificial Intelligence and Statistics (pp. 922-930).

https://arxiv.org/abs/1312.4645

There is also work on Bayesian recovery of molecular barcodes after corruption by copying (PCR) errors. In this setting, the real world entity is a short oligonucleotide, and the data-generating process consists of individual substitutions.

Petukhov, V., Guo, J., Baryawno, N., Severe, N., Scadden, D. T., Samsonova, M. G., & Kharchenko, P. V. (2018). dropEst: pipeline for accurate estimation of molecular counts in droplet-based single-cell RNA-seq experiments. Genome Biology, 19(1), 78.

https://link.springer.com/article/10.1186/s13059-018-1449-6

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