[HN Gopher] Gaussian Processes from Scratch (2019)
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       Gaussian Processes from Scratch (2019)
        
       Author : softwaredoug
       Score  : 77 points
       Date   : 2021-07-11 18:22 UTC (4 hours ago)
        
 (HTM) web link (peterroelants.github.io)
 (TXT) w3m dump (peterroelants.github.io)
        
       | carbocation wrote:
       | I'm very familiar with regression and really enjoy descriptions
       | that include code. For my personal learning needs, this is
       | probably the best demonstration of GPs that I have seen.
        
       | gentleman11 wrote:
       | I briefly studied stochastic processes as part of querying theory
       | once. What other applications are these concepts used for?
        
         | this-pony wrote:
         | In academia people study stochastic versions of PDEs in order
         | to try to answer regularity and existence questions. Think for
         | example about the famous millennium problem of Navier-Stokes.
         | Sometimes the stochastic viewpoint can even give more results
         | about the non-stochastic setting.
        
       | sillysaurusx wrote:
       | Just want to say, the website itself is totally gorgeous. Love
       | how it looks on mobile, love the math rendering, looks awesome.
       | (And thanks for making the code available too.)
       | 
       | EDIT: Turns out, there's more info here about how to set up a
       | site like this: https://peterroelants.github.io/posts/about-this-
       | blog/
        
       | itissid wrote:
       | A very intuitive entry into gaussian processes comes from Chapter
       | 12 of Statistical Rethinking by Richard McElreath:
       | 
       | He comes at it from the regression side and explains that GP's
       | basically occur when you have continuous variables in your
       | regression problem like ages or income instead of individual
       | units like countries or chimapanzee subjects. Here is a paragraph
       | that sort of explains it
       | 
       | > But what about continuous dimensions of variation like age or
       | income or stature? Indi- viduals of the same age share some of
       | the same exposures. They listened to some of the same music,
       | heard about the same politicians, and experienced the same
       | weather events. And individuals of similar ages also experienced
       | some of these same exposures, but to a lesser extent than
       | individuals of the same age. The covariation falls off as any two
       | individuals be- come increasingly dissimilar in age or income or
       | stature or any other dimension that indexes background
       | similarity. It doesn't make sense to estimate a unique varying
       | intercept for all individuals of the same age, ignoring the fact
       | that individuals of similar ages should have more similar
       | intercepts.
       | 
       | The beauty of the author's explanation is that Mixed slope and
       | Intercept models are very _intuitive_ and so are GP 's which are
       | just their extension to the continuous random variables to model
       | their covariances.
       | 
       | (BTW The author is explains "regression" of the kind used in
       | Controlled Experiments in like social sciences or botanist and
       | not really as an optimization problem in ML to reduce error; The
       | coefficients are interpreted as effect sizes).
        
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       (page generated 2021-07-11 23:00 UTC)