5 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…
An Empirical Bayes Perspective on Heteroskedastic Mean Estimation
Yanjun Han, Abhishek Shetty, Jacob Shkrob
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observatio…
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…
Prediction from compression for models with infinite memory, with applications to hidden Markov and renewal processes
Yanjun Han, Tianze Jiang, Yihong Wu
Consider the problem of predicting the next symbol given a sample path of length n, whose joint distribution belongs to a distribution class that may have long-term memory. The goa…