Algebraic structure in models and data

Data contains algebraic structure, which can be leveraged to
understand the systems it describes. I will discuss my work to extend
linear algebra to the multilinear setting of tensors. We will see how
multilinear algebra gives interpretable insights from multimodal data
and how it enables the solving of an inverse problem from analysis of
time series data.

Algebraic structure can be used to interrogate models. I will describe
my work to establish a correspondence between notions from invariant
theory and properties of statistical models with a group structure on
their parameter space. This correspondence enables understanding the
parameters in existing models that explain observed data, as well as
construction of new models that capture otherwise inaccessible
characteristics of, for example, biological systems.