  Currently, it is hard to reap the benefits of deep learning for Bayesian
methods, which allow the explicit specification of prior knowledge and
accurately capture model uncertainty. We present Prior-Data Fitted Networks
(PFNs). PFNs leverage large-scale machine learning techniques to approximate a
large set of posteriors. The only requirement for PFNs to work is the ability
to sample from a prior distribution over supervised learning tasks (or
functions). Our method restates the objective of posterior approximation as a
supervised classification problem with a set-valued input: it repeatedly draws
a task (or function) from the prior, draws a set of data points and their
labels from it, masks one of the labels and learns to make probabilistic
predictions for it based on the set-valued input of the rest of the data
points. Presented with a set of samples from a new supervised learning task as
input, PFNs make probabilistic predictions for arbitrary other data points in a
single forward propagation, having learned to approximate Bayesian inference.
We demonstrate that PFNs can near-perfectly mimic Gaussian processes and also
enable efficient Bayesian inference for intractable problems, with over
200-fold speedups in multiple setups compared to current methods. We obtain
strong results in very diverse areas such as Gaussian process regression,
Bayesian neural networks, classification for small tabular data sets, and
few-shot image classification, demonstrating the generality of PFNs. Code and
trained PFNs are released at
https://github.com/automl/TransformersCanDoBayesianInference.
