Publications (48)
Constructive Approximation under Carleman's Condition, with Applications to Smoothed Analysis
Frederic Koehler, Beining Wu
A classical result of Carleman, based on the theory of quasianalytic functions, shows that polynomials are dense in for any such that the moments do n…
Information Theoretic Properties of Markov Random Fields, and their Algorithmic Applications
Linus Hamilton, Frederic Koehler, Ankur Moitra
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been st…
Sampling Approximately Low-Rank Ising Models: MCMC meets Variational Methods
Frederic Koehler, Holden Lee, Andrej Risteski
We consider Ising models on the hypercube with a general interaction matrix , and give a polynomial time sampling algorithm when all but eigenvalues of lie in an inte…
From Boltzmann Machines to Neural Networks and Back Again
Surbhi Goel, Adam Klivans, Frederic Koehler
Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this wor…
Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Distributions and High-Temperature Ising Models
Nima Anari, Vishesh Jain, Frederic Koehler +2
We introduce a notion called entropic independence that is an entropic analog of spectral notions of high-dimensional expansion. Informally, entropic independence of a background d…
A Phase Transition in Arrow's Theorem
Frederic Koehler, Elchanan Mossel
Arrow's Theorem concerns a fundamental problem in social choice theory: given the individual preferences of members of a group, how can they be aggregated to form rational group pr…