1,286 research outputs found
A Kernel Test for Three-Variable Interactions
We introduce kernel nonparametric tests for Lancaster three-variable
interaction and for total independence, using embeddings of signed measures
into a reproducing kernel Hilbert space. The resulting test statistics are
straightforward to compute, and are used in powerful interaction tests, which
are consistent against all alternatives for a large family of reproducing
kernels. We show the Lancaster test to be sensitive to cases where two
independent causes individually have weak influence on a third dependent
variable, but their combined effect has a strong influence. This makes the
Lancaster test especially suited to finding structure in directed graphical
models, where it outperforms competing nonparametric tests in detecting such
V-structures
Geometry-Aware Adaptation for Pretrained Models
Machine learning models -- including prominent zero-shot models -- are often
trained on datasets whose labels are only a small proportion of a larger label
space. Such spaces are commonly equipped with a metric that relates the labels
via distances between them. We propose a simple approach to exploit this
information to adapt the trained model to reliably predict new classes -- or,
in the case of zero-shot prediction, to improve its performance -- without any
additional training. Our technique is a drop-in replacement of the standard
prediction rule, swapping argmax with the Fr\'echet mean. We provide a
comprehensive theoretical analysis for this approach, studying (i)
learning-theoretic results trading off label space diameter, sample complexity,
and model dimension, (ii) characterizations of the full range of scenarios in
which it is possible to predict any unobserved class, and (iii) an optimal
active learning-like next class selection procedure to obtain optimal training
classes for when it is not possible to predict the entire range of unobserved
classes. Empirically, using easily-available external metrics, our proposed
approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet
and scales to hundreds of thousands of classes. When no such metric is
available, Loki can use self-derived metrics from class embeddings and obtains
a 10.5% improvement on pretrained zero-shot models such as CLIP
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