4 papers
Elementary Symmetric Polynomial Inequalities for Centered Vectors and Matrices
Yanjun Han, Jonathan Niles-Weed
We prove new inequalities for elementary symmetric polynomials (ESPs) for vectors that sum to zero, and for square matrices with zero row and column sums. We apply these results to…
Besting Good--Turing: Optimality of Non-Parametric Maximum Likelihood for Distribution Estimation
Yanjun Han, Jonathan Niles-Weed, Yandi Shen +1
When faced with a small sample from a large universe of possible outcomes, scientists often turn to the venerable Good--Turing estimator. Despite its pedigree, however, this estima…
Approximate independence of permutation mixtures
Yanjun Han, Jonathan Niles-Weed
We prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call \emph{permutation mixtures}) and their i.i.d. counterparts. Our…
The Discrepancy of Random Rectangular Matrices
Dylan J. Altschuler, Jonathan Niles-Weed
A recent approach to the Beck-Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy. We give a com…