Tight Lower Bounds for Differentially Private Selection

A pervasive task in the differential privacy literature is to select the $k$ items of "highest quality" out of a set of $d$ items, where the quality of each item depends on a sensitive dataset that must be protected. Variants of this task arise naturally in fundamental problems like feature selection and hypothesis testing, and also as subroutines for many sophisticated differentially private algorithms. The standard approaches to these tasks---repeated use of the exponential mechanism or the sparse vector technique---approximately solve this problem given a dataset of $n = O(\sqrt{k}\log d)$ samples. We provide a tight lower bound for some very simple variants of the private selection problem. Our lower bound shows that a sample of size $n = \Omega(\sqrt{k} \log d)$ is required even to achieve a very minimal accuracy guarantee. Our results are based on an extension of the fingerprinting method to sparse selection problems. Previously, the fingerprinting method has been used to provide tight lower bounds for answering an entire set of $d$ queries, but often only some much smaller set of $k$ queries are relevant. Our extension allows us to prove lower bounds that depend on both the number of relevant queries and the total number of queries

The Limits of Post-Selection Generalization

While statistics and machine learning offers numerous methods for ensuring generalization, these methods often fail in the presence of adaptivity---the common practice in which the choice of analysis depends on previous interactions with the same dataset. A recent line of work has introduced powerful, general purpose algorithms that ensure post hoc generalization (also called robust or post-selection generalization), which says that, given the output of the algorithm, it is hard to find any statistic for which the data differs significantly from the population it came from. In this work we show several limitations on the power of algorithms satisfying post hoc generalization. First, we show a tight lower bound on the error of any algorithm that satisfies post hoc generalization and answers adaptively chosen statistical queries, showing a strong barrier to progress in post selection data analysis. Second, we show that post hoc generalization is not closed under composition, despite many examples of such algorithms exhibiting strong composition properties

Gastrointestinal symptoms of infantile colic and their change after light needling of acupuncture: a case series study of 913 infants

<p>Abstract</p> <p>Background</p> <p>Infantile colic is a common painful clinical condition associated with signs of distended intestines and an increase in colon peristalsis. However, clinical documentation of observed gastrointestinal functions in the condition is still lacking. Even though the ailment is common, no clear treatment guidelines exist. While acupuncture with minimal stimulation has been shown to be effective in reducing crying behaviour of infants suffering from colic, the documented effect of acupuncture on gastrointestinal function in children with infantile colic is scarce. This case series study aims to document the symptoms of routinely rated gastrointestinal function and the changes in these symptoms after minimal acupuncture in a larger group of children with infantile colic.</p> <p>Methods</p> <p>This study included 913 infants with normal weights, and lengths at birth. The infants' mean age was 5.4 weeks when the observations started, and had colic symptoms since two weeks after birth. Light needling stimulation of the acupuncture point LI4 was performed for 10-20 seconds bilaterally on a daily basis for a mean of 6.2 consecutive days. A questionnaire with verbal rating scales for the parents' evaluation was used before and after the treatment period.</p> <p>Results</p> <p>Before treatment the infants were assessed by the parents in terms of 'often have inflated stomachs' (99%) and 'seldom drool' (76%), 'regurgitate' (53%) and 'belch' (62%). Moreover, the reported frequency of defecation was 5-8 times per day (64%), with a yellowish-green colour (61%) and with a water-thin consistency (74%). After treatment, the variables of inflated stomachs, drooling and regurgitating were systematically changed, and rated by the parents as occurring 'sometimes' while belching was rated as occurring 'often' and the frequency of defecation was reduced to 1-4 times/day with a mustard yellow colour and a gruel-like consistency. The parents also rated their impression of the infants' general colic symptoms including crying behaviour as much ameliorated in 76% of the cases.</p> <p>Conclusion</p> <p>The results of the present study show that minimal acupuncture at LI4 in infantile colic is an effective and easy treatment procedure that, furthermore, is reported to be without serious side effects.</p

Differentially Private Medians and Interior Points for Non-Pathological Data

We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising negative result of Bun et al. (FOCS 2015) that showed there is no differentially private estimator with any finite sample complexity that returns any non-trivial approximation to the median of an arbitrary distribution

The limits of post-selection generalization

While statistics and machine learning offers numerous methods for ensuring generalization, these methods often fail in the presence of *post selection*---the common practice in which the choice of analysis depends on previous interactions with the same dataset. A recent line of work has introduced powerful, general purpose algorithms that ensure a property called *post hoc generalization* (Cummings et al., COLT'16), which says that no person when given the output of the algorithm should be able to find any statistic for which the data differs significantly from the population it came from. In this work we show several limitations on the power of algorithms satisfying post hoc generalization. First, we show a tight lower bound on the error of any algorithm that satisfies post hoc generalization and answers adaptively chosen statistical queries, showing a strong barrier to progress in post selection data analysis. Second, we show that post hoc generalization is not closed under composition, despite many examples of such algorithms exhibiting strong composition properties.Published versio

A thrips vector of tomato spotted wilt virus responds to tomato acylsugar chemical diversity with reduced oviposition and virus inoculation.

There is increasing evidence that acylsugars deter insect pests and plant virus vectors, including the western flower thrips (WFT), Frankliniella occidentalis (Pergande), vector of tomato spotted wilt virus (TSWV). Acylsugars are sugar-polyesters composed of saturated, un-saturated, and variously branched short and long chain fatty acids (FAs) esterified to a glucose (acylglucose) or sucrose (acylsucrose) moiety. We sought to understand how acylsucrose amount and composition of associated FA profiles interacted to mediate resistance to WFT oviposition and TSWV inoculation on tomato leaves. Towards this goal, we examined WFT oviposition and TSWV inoculation behavior on tomato lines bred to exude varying amounts of acylsucrose in association with diverse FA profiles. Our data show that as acylsucrose amounts increased, WFT egg-laying (oviposition) decreased and TSWV inoculation was suppressed. Western flower thrips also responded to FA profiles that included iC4, iC11, nC12 and nC10 FA. These findings support improving acylsugar-mediated resistance against WFT by breeding tomatoes exuding greater amounts of acylsucrose associated with specific FA profiles. We show that increasing acylsucrose amount output by type IV trichomes and selecting for particular FA profiles through advanced breeding profoundly affects WFT behavior in ways that benefit management of WFT as direct pests and as TSWV vectors