[HN Gopher] Gaussian Processes from Scratch (2019) ___________________________________________________________________ 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). ___________________________________________________________________ (page generated 2021-07-11 23:00 UTC)