Juba Ziani

Accuracy for Sale: Aggregating Data with a Variance Constraint

We consider the problem of a data analyst who may purchase an unbiased estimate of some statistic from multiple data providers. From each provider i, the analyst has a choice: she may purchase an estimate from that provider that has variance chosen from a finite menu of options. Each level of variance has a cost associated with it, reported (possibly strategically) by the data provider. The analyst wants to choose the minimum cost set of variance levels, one from each provider, that will let her combine her purchased estimators into an aggregate estimator that has variance at most some fixed desired level. Moreover, she wants to do so in such a way that incentivizes the data providers to truthfully report their costs to the mechanism. We give a dominant strategy truthful solution to this problem that yields an estimator that has optimal expected cost, and violates the variance constraint by at most an additive term that tends to zero as the number of data providers grows large.

Joint Data Purchasing and Data Placement in a Geo-Distributed Data Market

This paper studies design challenges faced by a geo-distributed cloud data market: which data to purchase (data purchasing) and where to place/replicate the data (data placement). We show that the joint problem of data purchasing and data placement within a cloud data market is NP-hard in general. However, we give a provably optimal algorithm for the case of a data market made up of a single data center, and then generalize the structure from the single data center setting and propose Datum, a near-optimal, polynomial-time algorithm for a geo-distributed data market.

Cliques in the union of graphs

Let B and R be two simple graphs with vertex set V, and let G ( B , R ) be the simple graph with vertex set V, in which two vertices are adjacent if they are adjacent in at least one of B and R. For X ? V , we denote by B | X the subgraph of B induced by X; let R | X and G ( B , R ) | X be defined similarly. A clique in a graph is a set of pairwise adjacent vertices. A subset U ? V is obedient if U is the union of a clique of B and a clique of R. Our first result is that if B has no induced cycles of length four, and R has no induced cycles of length four or five, then every clique of G ( B , R ) is obedient. This strengthens a previous result of the second author, stating the same when B has no induced C 4 and R is chordal.The clique number of a graph is the size of its maximum clique. We say that the pair ( B , R ) is additive if for every X ? V , the sum of the clique numbers of B | X and R | X is at least the clique number of G ( B , R ) | X . Our second result is a sufficient condition for additivity of pairs of graphs.

Optimal Data Acquisition for Statistical Estimation

We consider a data analysts 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.