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UID:pretalx-juliacon-2026-C8UGPM@pretalx.com
DTSTART;TZID=CET:20260814T154500
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DESCRIPTION:Automatic differentiation (AD) is deeply embedded in the Julia 
 ecosystem. Thanks to dual numbers and generic programming\, derivatives of
 ten “just work” across packages. However\, this is not always the case
 . In certain situations (e.g.\, when transcendental functions are evaluate
 d via partial fraction expansions) propagating dual numbers through the im
 plementation may fail\, and for good numerical reasons.\n\nIn this talk\, 
 we present the case of `beta_inc` and `beta_inc_inv` from `SpecialFunction
 s.jl`. Their original implementations relied on partial fraction expansion
 s carefully designed for `Float64` evaluation. While this approach yields 
 numerically stable function values\, it does not automatically provide cor
 rect derivatives under AD. Crucially\, differentiating the partial fractio
 n expansion is not equivalent to computing the partial fraction expansion 
 of the derivative — the latter being significantly more involved.\n\nDra
 wing from the numerical analysis literature (this challenge is not Julia-s
 pecific)\, we implemented exact derivatives for these functions\, as propo
 sed in pull request #506. This work enables the standard automatic differe
 ntiation tools to handle these functions seemlessly. \n\nThese derivatives
  are central to e.g. statistical computing: they are used in the Beta cumu
 lative distribution and quantile functions\, the Student’s t cumulative 
 distribution and quantile functions\, and most importantly for us the mult
 ivariate Student’s t distribution\, which has been asked about several t
 ime on discourse. Prior to this work\, fully differentiable implementation
 s of these models were not available in Distributions.jl.\n\nThis talk goe
 s through the story of `SpecialFunctions.jl`'s pull request #506 titled 
 “Exact chainrules derivatives for beta_inc and beta_inc_inv”\, which s
 olves all these issues and will hopefully be merged by Juliacon.
DTSTAMP:20260502T104025Z
LOCATION:Room 4
SUMMARY:Missing derivative: the example of `beta_inc` and `beta_inc_inv` - 
 Oskar Laverny
URL:https://pretalx.com/juliacon-2026/talk/C8UGPM/
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