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Garrett Bernstein

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4 papers

2 author rows

NeurIPS Conference 2019 Conference Paper

Differentially Private Bayesian Linear Regression

Garrett Bernstein
Daniel Sheldon

Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regression coefficients. We investigate the problem of Bayesian linear regression, with the goal of computing posterior distributions that correctly quantify uncertainty given privately released statistics. We show that a naive approach that ignores the noise injected by the privacy mechanism does a poor job in realistic data settings. We then develop noise-aware methods that perform inference over the privacy mechanism and produce correct posteriors across a wide range of scenarios.

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NeurIPS Conference 2018 Conference Paper

Differentially Private Bayesian Inference for Exponential Families

Garrett Bernstein
Daniel Sheldon

The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly accounts for noise introduced by the privacy mechanism. It is efficient because it works only with sufficient statistics and not individual data. Unlike other methods, it gives properly calibrated posterior beliefs in the non-asymptotic data regime.

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ICML Conference 2017 Conference Paper

Differentially Private Learning of Undirected Graphical Models Using Collective Graphical Models

Garrett Bernstein
Ryan McKenna
Tao Sun 0008
Daniel Sheldon
Michael Hay
Gerome Miklau

We investigate the problem of learning discrete graphical models in a differentially private way. Approaches to this problem range from privileged algorithms that conduct learning completely behind the privacy barrier to schemes that release private summary statistics paired with algorithms to learn parameters from those statistics. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the noisy sufficient statistics “as is” outperforms general-purpose differentially private learning algorithms. However, it has three limitations: it ignores knowledge about the data generating process, rests on uncertain theoretical foundations, and exhibits certain pathologies. We develop a more principled approach that applies the formalism of collective graphical models to perform inference over the true sufficient statistics within an expectation-maximization framework. We show that this learns better models than competing approaches on both synthetic data and on real human mobility data used as a case study.

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ICML Conference 2015 Conference Paper

Inference in a Partially Observed Queuing Model with Applications in Ecology

Kevin Winner
Garrett Bernstein
Daniel Sheldon

We consider the problem of inference in a probabilistic model for transient populations where we wish to learn about arrivals, departures, and population size over all time, but the only available data are periodic counts of the population size at specific observation times. The underlying model arises in queueing theory (as an M/G/inf queue) and also in ecological models for short-lived animals such as insects. Our work applies to both systems. Previous work in the ecology literature focused on maximum likelihood estimation and made a simplifying independence assumption that prevents inference over unobserved random variables such as arrivals and departures. The contribution of this paper is to formulate a latent variable model and develop a novel Gibbs sampler based on Markov bases to perform inference using the correct, but intractable, likelihood function. We empirically validate the convergence behavior of our sampler and demonstrate the ability of our model to make much finer-grained inferences than the previous approach.

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