Data Augmentation MCMC for Bayesian Inference from Privatized Data
Talk, Workshop on Differential Privacy and Statistical Data Analysis, The Fields Institute, Toronto, Canada
Watch on Fields Institute website or YouTube.
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Imprecise Probabilities in Modern Data Science: Challenges and Opportunities
Talk, SIPTA Seminars, virtual series
Watch on SIPTA website or YouTube.
Measuring Severity in Statistical Inference
Talk, PSA2020/2021, Baltimore, MD
Severity (Mayo, 2018) is a principle of statistical hypothesis testing. It assesses the hypothesis test in relation to the claim it makes, and the data on which the claim is based. Specifically, a claim C passes a severe test with the data at hand, if with high probability the test would have found flaws with C if present, and yet it does not. In this talk, I discuss how the concept of severity can be extended beyond frequentist hypothesis testing to general statistical inference tasks. Reflecting the Popperian notion of falsifiability, severity seeks to establish a stochastic version of modus tollens, as a measure of strength of probabilistic inference. Severity measures the extent to which the inference resulting from an inferential strategy is warranted, in relation to the body of evidence at hand. If the current available evidence leads a method to infer something about the world, then were it not the case, would the method still have inferred it? I discuss the formulation of severity and its properties, and demonstrate its assessment and interpretation in examples that follow either the frequentist or Bayesian traditions as well as beyond. A connection with significance function (Fraser, 1991) and confidence distribution (Xie & Singh, 2013) is drawn. These tools and connections may enable the assessment of severity in a wide range of modern applications that call for evidence-based scientific decision making.
Understanding the Epistemic Utility of Imprecise Probabilities in Statistical Inference
Talk, EPIMP Inaugural Conference, Bristol, UK
Imprecise probabilities have many good uses in statistical inference. The analyst may not know what prior to use for a Bayesian model, what mechanism gave rise to the missing data, or how to make probabilistic statements when non-identifiable parameters are involved. Such kinds of uncertainty are structurally intrinsic to the statistical model, and imprecise probabilities can well articulate them without concocting unwarranted assumptions. On the other hand, imprecise probabilities present unique challenges that call for the judicious judgment on the analyst’s part. The plurality of updating rules leads to seemingly paradoxical phenomena such as dilation and sure loss. In addition, while their results are more robust and informative, IP models are generally difficult to compute. In this talk, I deliberate the benefits and difficulties with imprecise probabilities in statistical inference, using a few examples encountered in practice. I call for a principled method to understand the epistemic utility in the statistical application of imprecise probabilities.
A Gibbs sampler for a class of random convex polytopes
Talk, BFF 6.5 Workshop, virtual
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.
Resolving Algorithmic Fariness
Talk, HMI DAIS Public Seminar, ANU; School of Criminal Justice, University of Lausanne, virtual
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.
Exact Statistical Inference for Differentially Private Data
Talk, U.S. Census Bureau, Washington, DC
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.