Posts by Collection



Deceptive Credences

R Gong, JB Kadane, MJ Schervish, T Seidenfeld, RB Stern. ERGO (to appear), 2020


Exact Statistical Inference for Differentially Private Data


Differential privacy (DP) is a mathematical framework that protects confidential information in a transparent and quantifiable way. I discuss how two classes of approximate computation techniques can be systematically adapted to produce exact statistical inference using DP data. For likelihood inference, we call for an importance sampling implementation of Monte Carlo expectation-maximization, and for Bayesian inference, an approximate Bayesian computation (ABC) algorithm suitable for possibly complex likelihood. Both approaches deliver exact statistical inference with respect to the joint statistical model inclusive of the differential privacy mechanism, yet do not require analytical access of such joint specification. Highlighted is a transformation of the statistical tradeoff between privacy and efficiency, into the computational tradeoff between approximation and exactness. Open research questions on two fronts are posed: 1) how to afford computationally accessible and (approximately) correct statistical analysis tools to DP data users; 2) how to understand and remedy the effect of any necessary post-processing with statistical analysis.

Resolving Algorithmic Fariness


Algorithms are now widely used to streamline decisions in different contexts: insurance, health care, criminal justice. As some have shown, algorithms can make disproportionately more errors to the detriment of disadvantaged minorities compared to other groups. The literature in computer science has articulated different criteria of algorithmic fairness, each plausible in its own way. Yet, several impossibility theorems show that no algorithm can satisfy more than a few of these fairness criteria at the same time. We set out to investigate why this is so. In this talk, we first show that all criteria of algorithm fairness can be simultaneously satisfied under a peculiar and idealized set of premises. These include assumptions about access to information, representativeness of training data, capacity of the model, and crucially the construct of individual risk as the quantity to be assessed by the algorithm. When these assumptions are relaxed, we invoke a multi-resolution framework to understand the deterioration of the algorithm’s performance in terms of both accuracy and fairness. We illustrate our results using a suite of simulated studies. While our findings do not contradict existing impossibility theorems, they shed light on the reasons behind such failure and offer a path towards a quantitative and principled resolution. Joint work with Marcello Di Bello.

A Gibbs sampler for a class of random convex polytopes


The Dempster-Shafer (DS) theory to statistical inference extends the Bayesian approach by allowing the use of partial and vacuous prior information. It yields three-valued uncertainty assessments representing probabilities for, against, and don’t know about formal assertions of interest. This talk presents a Gibbs algorithm that targets the distribution of a class of random convex polytopes, first described in Dempster (1972) to encapsulate the DS inference for Categorical distributions. Our sampler relies on an equivalence between the iterative constraints of the vertex configuration and the non-negativity of cycles in a fully connected directed graph. Joint work with Pierre E. Jacob, Paul T. Edlefsen and Arthur P. Dempster.