Private hypothesis selection

We provide a differentially private algorithm for hypothesis selection. Given samples from an unknown probability distribution P and a set of m probability distributions H, the goal is to output, in a ε-differentially private manner, a distribution from H whose total variation distance to P is comparable to that of the best such distribution (which we denote by α). The sample complexity of our basic algorithm is O(log m/α^2 + log m/αε), representing a minimal cost for privacy when compared to the non-private algorithm. We also can handle infinite hypothesis classes H by relaxing to (ε, δ)-differential privacy. We apply our hypothesis selection algorithm to give learning algorithms for a number of natural distribution classes, including Gaussians, product distributions, sums of independent random variables, piecewise polynomials, and mixture classes. Our hypothesis selection procedure allows us to generically convert a cover for a class to a learning algorithm, complementing known learning lower bounds which are in terms of the size of the packing number of the class. As the covering and packing numbers are often closely related, for constant α, our algorithms achieve the optimal sample complexity for many classes of interest. Finally, we describe an application to private distribution-free PAC learning.https://arxiv.org/abs/1905.1322

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

Trader Anonymity, Price Formation and Liquidity

We analyze price formation and liquidity in a non-anonymous specialist market. Our main hypothesis is that the non-anonymity allows the specialist to assess the probability that a trader trades on the basis of private information. He uses this knowledge to price discriminate. This can be achieved by quoting a large spread and granting price improvement to traders deemed uninformed. Our empirical results confirm this view. We document that price improvement reflects lower adverse selection costs but does not lead to a reduction in the specialist's profit. We further show that the quote adjustment following transactions at the quoted prices is more pronounced than the quote adjustment after transactions at prices inside the spread. The results thus support the notion that a non-anonymous environment allows the identification of informed traders and may thus alleviate the adverse selection problem.Anonymity; specialist; bid-ask spread

Time-Honoured Management Principles of Organizing in Private Hospitals in Enugu State, Nigeria

This study focuses on the implementation of time-honoured management principles of organizing in private hospitals in Enugu State, as a way of effectively manage private hospitals and ensuring that adequate and timely health care services are provided to the citizenry of Enugu State. The study examined the organizational structures of private hospitals with a view to determining their extent of conformity with time-honoured management principles of organizing. The null hypothesis was formulated as, “there is no non-conformity of organizational structures of private hospitals with established management principles of organizing”. To achieve the objective of this study, the survey research design was adopted, where the simple random sampling technique was used in the selection of sampling units and the data collected were presented descriptively. The hypothesis statement was tested with Chi-Square test statistic, which gave chi-square result of 30.03 > X2 critical 26.296. Hence, the null hypothesis was rejected, indicating that organizational structures of private hospitals in Enugu State are being operated not in conformity with established management principles of organizing. The study concluded by pointing out the need to ensure the implementation of organizational structures that conform with established management principles of organizing, particularly the time-honoured management principle of organizing and the need to penalize defaulting hospitals, whether big or small. Keywords: Time-Honoured, Management, Private Hospitals, Nigeri

Beliefs in Decision-Making Cascades

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality.Comment: final version, to appear in IEEE Transactions on Signal Processin

The Value of Business Networks in Emerging Economies: An Analysis of Firms' External Financing Opportunities

The paper argues that networked firms are likely to have an advantage in securing external finance in countries with weak legal and judicial institutions since it helps financial institutions to minimize the underlying agency costs of lending. An analysis of recent BEEPS data from fifteen Central and Eastern European (CEE) countries lends some support to this hypothesis. Even after controlling for other factors, firms affiliated to business associations are more likely to secure bank finance. Importance of being associated with business networks is particularly evident among firms who borrow from private domestic and foreign banks, as these new banks attempt to minimize costs of adverse selection. Networking however discriminates against the small and medium sized firms' access to bank loans in the CEE regions. Results are robust in both single cross-section and panel data analyses.business networks, agency costs, external firm financing, bank loans, transition economies, endogeneity

Peer Effects and Relative Performance of Voucher Schools in Chile

The assessment of the advantages and disadvantages of vouchers has been hindered by the lack of sufficient empirical evidence. The Chilean education voucher system was established at a national scale and has data for more than 15 years. The empirical literature developed to evaluate the voucher system in Chile faced methodological and/or data limitations up until late 1999, since there was no individual data available, and papers used the school as a unit of study. Additionally, the studies lacked good information on the socioeconomic characteristics of the students. The most recent literature uses individual data and introduces the correction for selection bias, but do not take into account that some public schools receive additional resources from the government. In the first section of this paper we control for the amount of per capita funds received by the public schools from the government, and find that when public and private voucher schools receive similar per capita subsidies, the effect of treatment on the treated (where treatment is attendance to a private voucher school) is large in magnitude and statistically significant. Some fear that this result may be the consequence of sorting and peer effect, and not of the effectiveness of private voucher schools. To analyze the importance of peer effects on the previous results, in the second section we estimate new treatment parameters controlling for peer group characteristics. If the positive treatment effect estimated earlier were exclusively the result of the sorting process and peer effect, this new treatment parameter should be zero. This hypothesis is rejected. Even when we condition on peer group characteristics, we find a treatment parameter that is positive, large in magnitude and statistically significant, when public and private voucher schools receive similar per capita subsidies. Hence, papers that have asserted that positive treatment effects are due to the peer effect and/ or sorting are proved wrong