 Award ID(s):
 1657471
 NSFPAR ID:
 10101014
 Date Published:
 Journal Name:
 Proceedings of Machine Learning Research
 Volume:
 80
 ISSN:
 26403498
 Page Range / eLocation ID:
 3039
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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We develop differentially private methods for estimating various distributional properties. Given a sample from a discrete distribution p, some functional f, and accuracy and privacy parameters alpha and epsilon, the goal is to estimate f(p) up to accuracy alpha, while maintaining epsilondifferential privacy of the sample. We prove almosttight bounds on the sample size required for this problem for several functionals of interest, including support size, support coverage, and entropy. We show that the cost of privacy is negligible in a variety of settings, both theoretically and experimentally. Our methods are based on a sensitivity analysis of several stateoftheart methods for estimating these properties with sublinear sample complexitiesmore » « less

Weller, Adrian (Ed.)Differential privacy (DP) offers strong theoretical privacy guarantees, though implementations of DP mechanisms may be vulnerable to sidechannel attacks, such as timing attacks. When sampling methods such as MCMC or rejection sampling are used to implement a mechanism, the runtime can leak private information. We characterize the additional privacy cost due to the runtime of a rejection sampler in terms of both (epsilon,delta)DP as well as fDP. We also show that unless the acceptance probability is constant across databases, the runtime of a rejection sampler does not satisfy epsilonDP for any epsilon. We show that there is a similar breakdown in privacy with adaptive rejection samplers. We propose three modifications to the rejection sampling algorithm, with varying assumptions, to protect against timing attacks by making the runtime independent of the data. The modification with the weakest assumptions is an approximate sampler, introducing a small increase in the privacy cost, whereas the other modifications give perfect samplers. We also use our techniques to develop an adaptive rejection sampler for logHolder densities, which also has dataindependent runtime. We give several examples of DP mechanisms that fit the assumptions of our methods and can thus be implemented using our samplers.more » « less

Abstract Background A considerable amount of various types of data have been collected during the COVID19 pandemic, the analysis and understanding of which have been indispensable for curbing the spread of the disease. As the pandemic moves to an endemic state, the data collected during the pandemic will continue to be rich sources for further studying and understanding the impacts of the pandemic on various aspects of our society. On the other hand, naïve release and sharing of the information can be associated with serious privacy concerns.
Methods We use three common but distinct data types collected during the pandemic (case surveillance tabular data, case location data, and contact tracing networks) to illustrate the publication and sharing of granular information and individuallevel pandemic data in a privacypreserving manner. We leverage and build upon the concept of differential privacy to generate and release privacypreserving data for each data type. We investigate the inferential utility of privacypreserving information through simulation studies at different levels of privacy guarantees and demonstrate the approaches in reallife data. All the approaches employed in the study are straightforward to apply.
Results The empirical studies in all three data cases suggest that privacypreserving results based on the differentially privately sanitized data can be similar to the original results at a reasonably small privacy loss (
). Statistical inferences based on sanitized data using the multiple synthesis technique also appear valid, with nominal coverage of 95% confidence intervals when there is no noticeable bias in point estimation. When$$\epsilon \approx 1$$ $\u03f5\approx 1$ and the sample size is not large enough, some privacypreserving results are subject to bias, partially due to the bounding applied to sanitized data as a postprocessing step to satisfy practical data constraints.$$\epsilon <1$$ $\u03f5<1$Conclusions Our study generates statistical evidence on the practical feasibility of sharing pandemic data with privacy guarantees and on how to balance the statistical utility of released information during this process.

Braverman, Mark (Ed.)We present a framework for speeding up the time it takes to sample from discrete distributions $\mu$ defined over subsets of size $k$ of a ground set of $n$ elements, in the regime where $k$ is much smaller than $n$. We show that if one has access to estimates of marginals $\mathbb{P}_{S\sim \mu}[i\in S]$, then the task of sampling from $\mu$ can be reduced to sampling from related distributions $\nu$ supported on size $k$ subsets of a ground set of only $n^{1\alpha}\cdot \operatorname{poly}(k)$ elements. Here, $1/\alpha\in [1, k]$ is the parameter of entropic independence for $\mu$. Further, our algorithm only requires sparsified distributions $\nu$ that are obtained by applying a sparse (mostly $0$) external field to $\mu$, an operation that for many distributions $\mu$ of interest, retains algorithmic tractability of sampling from $\nu$. This phenomenon, which we dub domain sparsification, allows us to pay a onetime cost of estimating the marginals of $\mu$, and in return reduce the amortized cost needed to produce many samples from the distribution $\mu$, as is often needed in upstream tasks such as counting and inference. For a wide range of distributions where $\alpha=\Omega(1)$, our result reduces the domain size, and as a corollary, the costpersample, by a $\operatorname{poly}(n)$ factor. Examples include monomers in a monomerdimer system, nonsymmetric determinantal point processes, and partitionconstrained Strongly Rayleigh measures. Our work significantly extends the reach of prior work of Anari and Derezi\'nski who obtained domain sparsification for distributions with a logconcave generating polynomial (corresponding to $\alpha=1$). As a corollary of our new analysis techniques, we also obtain a less stringent requirement on the accuracy of marginal estimates even for the case of logconcave polynomials; roughly speaking, we show that constantfactor approximation is enough for domain sparsification, improving over $O(1/k)$ relative error established in prior work.more » « less

Abstract We investigate the link between individual differences in science reasoning skills and mock jurors’ deliberation behavior; specifically, how much they talk about the scientific evidence presented in a complicated, ecologically valid case during deliberation. Consistent with our preregistered hypothesis, mock jurors strong in scientific reasoning discussed the scientific evidence more during deliberation than those with weaker science reasoning skills. Summary With increasing frequency, legal disputes involve complex scientific information (Faigman et al., 2014; Federal Judicial Center, 2011; National Research Council, 2009). Yet people often have trouble consuming scientific information effectively (McAuliff et al., 2009; National Science Board, 2014; Resnick et al., 2016). Individual differences in reasoning styles and skills can affect how people comprehend complex evidence (e.g., Hans, Kaye, Dann, Farley, Alberston, 2011; McAuliff & Kovera, 2008). Recently, scholars have highlighted the importance of studying group deliberation contexts as well as individual decision contexts (Salerno & Diamond, 2010; Kovera, 2017). If individual differences influence how jurors understand scientific evidence, it invites questions about how these individual differences may affect the way jurors discuss science during group deliberations. The purpose of the current study was to examine how individual differences in the way people process scientific information affects the extent to which jurors discuss scientific evidence during deliberations. Methods We preregistered the data collection plan, sample size, and hypotheses on the Open Science Framework. Juryeligible community participants (303 jurors across 50 juries) from Phoenix, AZ (Mage=37.4, SD=16.9; 58.8% female; 51.5% White, 23.7% Latinx, 9.9% AfricanAmerican, 4.3% Asian) were paid $55 for a 3hour mock jury study. Participants completed a set of individual questionnaires related to science reasoning skills and attitudes toward science prior to watching a 45minute mock armedrobbery trial. The trial included various pieces of evidence and testimony, including forensic experts testifying about mitochondrial DNA evidence (mtDNA; based on Hans et al. 2011 materials). Participants were then given 45 minutes to deliberate. The deliberations were video recorded and transcribed to text for analysis. We analyzed the deliberation content for discussions related to the scientific evidence presented during trial. We hypothesized that those with stronger scientific and numeric reasoning skills, higher need for cognition, and more positive views towards science would discuss scientific evidence more than their counterparts during deliberation. Measures We measured Attitudes Toward Science (ATS) with indices of scientific promise and scientific reservations (Hans et al., 2011; originally developed by the National Science Board, 2004; 2006). We used Drummond and Fischhoff’s (2015) Scientific Reasoning Scale (SRS) to measure scientific reasoning skills. Weller et al.’s (2012) Numeracy Scale (WNS) measured proficiency in reasoning with quantitative information. The NFCShort Form (Cacioppo et al., 1984) measured need for cognition. Coding We identified verbal utterances related to the scientific evidence presented in court. For instance, references to DNA evidence in general (e.g. nuclear DNA being more conclusive than mtDNA), the database that was used to compare the DNA sample (e.g. the database size, how representative it was), exclusion rates (e.g. how many other people could not be excluded as a possible match), and the forensic DNA experts (e.g. how credible they were perceived). We used word count to operationalize the extent to which each juror discussed scientific information. First we calculated the total word count for each complete jury deliberation transcript. Based on the above coding scheme we determined the number of words each juror spent discussing scientific information. To compare across juries, we wanted to account for the differing length of deliberation; thus, we calculated each juror’s scientific deliberation word count as a proportion of their jury’s total word count. Results On average, jurors discussed the science for about 4% of their total deliberation (SD=4%, range 022%). We regressed proportion of the deliberation jurors spend discussing scientific information on the four individual difference measures (i.e., SRS, NFC, WNS, ATS). Using the adjusted Rsquared, the measures significantly accounted for 5.5% of the variability in scientific information deliberation discussion, SE=0.04, F(4, 199)=3.93, p=0.004. When controlling for all other variables in the model, the Scientific Reasoning Scale was the only measure that remained significant, b=0.003, SE=0.001, t(203)=2.02, p=0.045. To analyze how much variability each measure accounted for, we performed a stepwise regression, with NFC entered at step 1, ATS entered at step 2, WNS entered at step 3, and SRS entered at step 4. At step 1, NFC accounted for 2.4% of the variability, F(1, 202)=5.95, p=0.02. At step 2, ATS did not significantly account for any additional variability. At step 3, WNS accounted for an additional 2.4% of variability, ΔF(1, 200)=5.02, p=0.03. Finally, at step 4, SRS significantly accounted for an additional 1.9% of variability in scientific information discussion, ΔF(1, 199)=4.06, p=0.045, total adjusted Rsquared of 0.055. Discussion This study provides additional support for previous findings that scientific reasoning skills affect the way jurors comprehend and use scientific evidence. It expands on previous findings by suggesting that these individual differences also impact the way scientific evidence is discussed during juror deliberations. In addition, this study advances the literature by identifying Scientific Reasoning Skills as a potentially more robust explanatory individual differences variable than more wellstudied constructs like Need for Cognition in jury research. Our next steps for this research, which we plan to present at APLS as part of this presentation, incudes further analysis of the deliberation content (e.g., not just the mention of, but the accuracy of the references to scientific evidence in discussion). We are currently coding this data with a software program called Noldus Observer XT, which will allow us to present more sophisticated results from this data during the presentation. Learning Objective: Participants will be able to describe how individual differences in scientific reasoning skills affect how much jurors discuss scientific evidence during deliberation.more » « less