6 papers
High-Arity Rademacher Complexity and Uniform Laws of Large Numbers
Aaron Anderson, Henry Towsner
We characterize several properties of higher-arity function classes, specifically finite $\VC_k$-dimension, slicewise finite $\VC$-dimension, and finite slicewise Littlestone dimen…
Metric Linear Orders and O-Minimality
Aaron Anderson, Diego Bejarano
In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where…
Examples and Nonexamples of Distal Metric Structures
Aaron Anderson, Itaï Ben Yaacov
This article provides examples of distal metric structures. One source of examples are metric valued fields. By analyzing indiscernible sequences, we show that real closed metric v…
From learnable objects to learnable random objects
Aaron Anderson, Michael Benedikt
We consider the relationship between learnability of a "base class" of functions on a set , and learnability of a class of statistical functions derived from the base class. For…
Generically Stable Measures and Distal Regularity in Continuous Logic
Aaron Anderson
We develop a theory of generically stable and smooth Keisler measures in NIP metric theories, generalizing the case of classical logic. Using smooth extensions, we verify that fund…
NIP and Distal Metric Structures
Aaron Anderson
Model theory, machine learning, and combinatorics each have generalizations of VC-dimension for fuzzy and real-valued versions of set systems. These different dimensions define a u…