Optimal Data Acquisition for Statistical Estimation

We consider a data analyst's problem of purchasing data from strategic agents to compute an unbiased estimate of a statistic of interest. Agents incur private costs to reveal their data and the costs can be arbitrarily correlated with their data. Once revealed, data are verifiable. This paper focuses on linear unbiased estimators. We design an individually rational and incentive compatible mechanism that optimizes the worst-case mean-squared error of the estimation, where the worst-case is over the unknown correlation between costs and data, subject to a budget constraint in expectation. We characterize the form of the optimal mechanism in closed-form. We further extend our results to acquiring data for estimating a parameter in regression analysis, where private costs can correlate with the values of the dependent variable but not with the values of the independent variables

Geometric Inference for General High-Dimensional Linear Inverse Problems

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize the local estimation rate of convergence and to provide statistical inference guarantees. Our results are built based on the local conic geometry and duality. The difficulty of statistical inference is captured by the geometric characterization of the local tangent cone through the Gaussian width and Sudakov minoration estimate.Comment: 39 pages, 6 figure

Bit-Vector Model Counting using Statistical Estimation

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms

Statistical Reliability Estimation of Microprocessor-Based Systems

What is the probability that the execution state of a given microprocessor running a given application is correct, in a certain working environment with a given soft-error rate? Trying to answer this question using fault injection can be very expensive and time consuming. This paper proposes the baseline for a new methodology, based on microprocessor error probability profiling, that aims at estimating fault injection results without the need of a typical fault injection setup. The proposed methodology is based on two main ideas: a one-time fault-injection analysis of the microprocessor architecture to characterize the probability of successful execution of each of its instructions in presence of a soft-error, and a static and very fast analysis of the control and data flow of the target software application to compute its probability of success. The presented work goes beyond the dependability evaluation problem; it also has the potential to become the backbone for new tools able to help engineers to choose the best hardware and software architecture to structurally maximize the probability of a correct execution of the target softwar

Optimum Statistical Estimation with Strategic Data Sources

We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and estimation error is minimized. The mechanism applies to a broad range of estimators, including linear and polynomial regression, kernel regression, and, under some additional assumptions, ridge regression. It also generalizes to several objectives, including minimizing estimation error subject to budget constraints. Besides our concrete results for regression problems, we contribute a mechanism design framework through which to design and analyze statistical estimators whose examples are supplied by workers with cost for labeling said examples

Statistical Estimation of Quantum Tomography Protocols Quality

A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a-priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography