STFeb 25, 2018
New Tests of Uniformity on the Compact Classical Groups as Diagnostics for Weak-star Mixing of Markov ChainsAmir Sepehri
This paper introduces two new families of non-parametric tests of goodness-of-fit on the compact classical groups. One of them is a family of tests for the eigenvalue distribution induced by the uniform distribution, which is consistent against all fixed alternatives. The other is a family of tests for the uniform distribution on the entire group, which is again consistent against all fixed alternatives. We find the asymptotic distribution under the null and general alternatives. The tests are proved to be asymptotically admissible. Local power is derived and the global properties of the power function against local alternatives are explored. The new tests are validated on two random walks for which the mixing-time is studied in the literature. The new tests, and several others, are applied to the Markov chain sampler proposed by \cite{jones2011randomized}, providing strong evidence supporting the claim that the sampler mixes quickly.
LGOct 26, 2020
Interpretable Assessment of Fairness During Model EvaluationAmir Sepehri, Cyrus DiCiccio
For companies developing products or algorithms, it is important to understand the potential effects not only globally, but also on sub-populations of users. In particular, it is important to detect if there are certain groups of users that are impacted differently compared to others with regard to business metrics or for whom a model treats unequally along fairness concerns. In this paper, we introduce a novel hierarchical clustering algorithm to detect heterogeneity among users in given sets of sub-populations with respect to any specified notion of group similarity. We prove statistical guarantees about the output and provide interpretable results. We demonstrate the performance of the algorithm on real data from LinkedIn.
MEAug 31, 2016
The Bayesian SLOPEAmir Sepehri
The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction properties, as well as minimax optimality. This paper introduces the Bayesian SLOPE procedure for linear regression. The classical SLOPE estimate is the posterior mode in the normal regression problem with an appropriate prior on the coefficients. The Bayesian SLOPE considers the full Bayesian model and has the advantage of offering credible sets and standard error estimates for the parameters. Moreover, the hierarchical Bayesian framework allows for full Bayesian and empirical Bayes treatment of the penalty coefficients; whereas it is not clear how to choose these coefficients when using the SLOPE on a general design matrix. A direct characterization of the posterior is provided which suggests a Gibbs sampler that does not involve latent variables. An efficient hybrid Gibbs sampler for the Bayesian SLOPE is introduced. Point estimation using the posterior mean is highlighted, which automatically facilitates the Bayesian prediction of future observations. These are demonstrated on real and synthetic data.