Data Is as Data Does: The Influence of Computation on Inference - 2024

Title : Data Is as Data Does: The Influence of Computation on Inference Author(s): Simons Institute Link(s) : https://www.youtube.com/watch?v=ZVec7pw0bgw

Main message: The 'crystal ball' of (approximate) inference that takes in the model and data and gives an updated model given the data, itself makes assumptions and its own choices which we often do not account for.

He shows an example of GP regression using CGGP, Nystrom approximations, and SVGP where the posteriors are different even though the model and data is the same.

This relates to AI4Science, since the whole notion of data and model letting us infer scientific problems also relies on these AI methods, involving similar approximations, and this leads to weak science in general (we would have things we are not controlling for).

So how to solve this - is the 'computational machine' changing the likelihood? the prior? They end up thinking of this issue as the introduction of an effective dataset induced by the computation. Now, we can view the 'crystal ball' as something that takes in a model and data and gives an updated belief given effective data.

For GP regression, these ideas can lead to a clean decomposition for the combined uncertainty (from finite data and limited computations), see (, ). Can be viewed as a Probabilistic Numerics treatment for representer weights (i.e. the linear algebra solves) in GP regression.