IPC Lab Seminar

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Abstract

A fundamental obstacle in learning information from data is the presence of nonlinear redundancies and dependencies in the statistics of the data. Information-theoretic metrics are powerful in quantifying the dependencies among the random variables. Discrete Fourier analysis on the other hand provides an essential tool to characterize the nonlinearities of functions. In this talk, I will show how the two approaches are related and can be used to remove nonlinear redundancies.
In the first part of the talk, I will present a novel Fourier expansion for functions of correlated binary random variables. Starting from unsupervised learning, I will use entropy to quantify feature-redundancies and define the notion of information sufficiency. Then, based on the Fourier framework, I will present a new measure for removing redundant features. Next, in the supervised settings, I will present new theoretical results bridging the Bayesian error rate with the Fourier coefficients. Based on that, I will present a supervised algorithm for feature subset selection.

In the second part of the talk, I will take a step further and discuss learning classical patterns from quantum data. In this problem, the samples are quantum states with classical labels and the predictors are quantum measurements. I will introduce a quantum counterpart of PAC as a new theoretical foundation for learning from quantum data.  I will point out major difficulties arising from the quantum nature of the problem, including the no-cloning principle and measurement compatibility. Then, I will present new bounds on the quantum sample complexity of several measurement classes. I will make use of a Fourier expansion for quantum operators on qubits and present the quantum low-degree algorithm.

About the speaker

Mohsen Heidari is currently a postdoctoral research associate at the Center for Science of Information, NSF Science & Technology Center at Purdue University. He obtained a Ph.D. degree in Electrical Engineering in 2019 and an M.Sc. degree in Applied Mathematics in 2017, both from the University of Michigan. Before that, he obtained his B.Sc. and M.Sc. degree in Electrical Engineering from the Sharif University of Technology in 2011 and 2013, respectively. Mohsen’s research interests lie in machine learning, information theory, and quantum information theory.

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