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nLab > Latest Changes: Bayesian reasoning

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 19th 2019

    I added a couple more references to Bayesian reasoning used in physics.

    diff, v15, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 7th 2021

    Added reference to

    diff, v16, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 12th 2021

    Added the reference

    • Kotaro Kamiya, John Welliaveetil, A category theory framework for Bayesian learning (arXiv:2111.14293)

    diff, v17, current

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 31st 2022

    Added a reference

    diff, v18, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 31st 2022

    Scanning through the article, I didn’t see an explation of its title: What does “the Bayesian brain” refer to?

    Googling for the term yields this page by a “Wellcome Centre” (I gather this is a branch of the Wellcome Trust? brr).

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 2nd 2023

    Seriously, if anyone knows let’s add a comment: What does the Bayesian brain refer to? At face value it sounds odd, in any case it should be briefly explained.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 3rd 2023

    Let’s see

    The “free energy” framework not only underpins a modern understanding of predictive coding, but has more broadly been proposed as a unified theory of brain function [45], and latterly of all adaptive or living systems [53–56]. In the neuroscientic context, it constitutes a theory of the Bayesian brain, by which most or all brain function can be understood as implementing approximate Bayesian inference [57]; in the more broadly biological (or even metaphysical) contexts, this claim is generalized to state that all life can be understood in this way.

    [57] is

    • David C Knill and Alexandre Pouget. “The Bayesian Brain: The Role of Uncertainty in Neural Coding and Computation”. In: TRENDS in Neurosciences 27.12 (2004), pp. 712–719. doi: 10.1016/j.tins.2004.10.007. http://www.sciencedirect. com/science/article/pii/S0166223604003352.

    I’ll take a look.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2023

    Thanks! That looks useful.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 3rd 2023

    I’ve added in that paper to a new section in the references on bayesian reasoning and neuroscience.

    diff, v20, current

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 3rd 2023

    I don’t know how important these developments are. The free energy approach of Karl Friston is certainly receiving plenty of attention.

    Over the years I’ve been interested in attempts to find something more universal in Bayesian inference, not just a subjective logic, but something objective. Way back, there was Jorg Lemm’s ’Bayesian field theory’ drawing parallels between QFT and Bayesian inference. I see here you remark in response

    I think everybody will agree that the general pattern of statistical mechanics is indeed about more about inference than about nature per se. But at some point you want to apply all this to a particular case. Usually this amounts to specifying a Hamiltonian function.

    And the precise details of that function is what encodes information about nature.

    So there is a bit of information about nature - encoded in a Hamiltonian - and then there are means to extract certain parts of that information (entropy maximization, etc.).

    Interestingly, while quantum mechanics is in a way nothing but statistical mechanics analytically continued to the complex plane, we usually tend to regard not just the Hamiltonian in quantum mechanics as encoding information about nature, but also the rest of the formalism.

    Whether that “rest of the formalism” is really just a manifestation of our thinking or a genuine aspect of nature is hotly debated in all those discussions concerning the “interpretation of quantum mechanics”.

    Then there were discussions on the emergence of subjective logic in the mind that emerged from matter, as here. The program to discover these structures at the level of neuroscience is ambitious, but then maybe there can’t be too many ways for the universe to evolve structures within it that can (partially) understand it.

    • CommentRowNumber11.
    • CommentAuthortsmithe
    • CommentTimeJan 5th 2023
    Hello Urs, David,

    someone pointed out to me this discussion, so I thought I would respond briefly. The "Bayesian brain" is a term of art in computational neuroscience which means different things to different people (as is often the way in computational neuroscience..), but roughly means what I wrote in the text that David has quoted: that the dynamics of many/most neural circuits can be understood as implementing approximate Bayesian inference.

    Unfortunately, the way this idea is treated in computational neuroscience leaves a lot to be desired, both mathematically and philosophically, and I'm slowly trying to help make sense of things. To do this job properly means taking into account some of the lines of thought that David has linked to, and indeed the idea (that David's quotation of mine hints at) that all life can be similarly understood should end up as the expression of a certain universal property (satisfied perhaps by a descendant of the "free energy" framework) -- though I'm not sure that this is the "something objective" that David seeks.

    Anyway, I hope to have more to say about all this soon. Meanwhile, I'm always interested in new perspectives.
    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2023

    Thanks.

    I haven’t yet managed to look inside

    • David C. Knill, Alexandre Pouget: The Bayesian Brain: The Role of Uncertainty in Neural Coding and Computation, in Trends in Neurosciences 27 12 (2004) 712–719 [doi:10.1016/j.tins.2004.10.007]

    but from the abstract it seems like the corresponding technical term they proposed is “Bayesian coding hypothesis”.

    Would it be correct to say that your article is concerned with “mathematical foundations for a compositional account of the Bayesian coding hypothesis”?

    • CommentRowNumber13.
    • CommentAuthortsmithe
    • CommentTimeJan 5th 2023
    I think that may be correct to say, but "Bayesian coding hypothesis" is not a term that is in common use, as far as I am aware. Another related term is "predictive coding", and indeed my thesis work was in large part related to formalizing Bayesian "free energy" accounts of predictive coding such as sketched by [0] or described by [1] or [2] -- but the term "predictive coding" has an even longer history and is equally ill specified. Moreover, the "Bayesian brain" idea ultimately wants to be more general than that specific "coding hypothesis": in some sense, it shouldn't matter which particular "coding" or circuitry or algorithm an adaptive system instantiates; what is supposed to be important is rather that it implements approximate inference, and this can be described abstractly.

    [0] https://doi.org/10.1016/j.jmp.2015.11.003
    [1] https://doi.org/10.1016/j.neuron.2012.10.038
    [2] https://doi.org/10.1098/rstb.2008.0300
    • CommentRowNumber14.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 5th 2023

    Thanks, Toby. I’ve just today enjoyed reading through the ’Future directions’ chapter of your thesis. Quite a vision!

    • CommentRowNumber15.
    • CommentAuthortsmithe
    • CommentTimeJan 6th 2023
    Thanks, David! Lots of work to do now :)
    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023

    added pointer to:

    diff, v22, current

1 to 16 of 16

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