Privacy and the price of data

Several important application areas in data science involve assigning numbers to (possibly randomized) algorithms. In the case of statistical privacy, it is important to quantify the amount of information leaked by a data processing algorithm. In the case of data marketplaces, it is important to properly set the prices for data queries (which, in general, can be specified by arbitrary algorithms). In both cases, it is also important to quantify application-specific utility of the outputs of an algorithm or query. For example, if a user has a choice of purchasing some combination of query answers, the user's decision should be guided by the consideration of a utility/price trade-off. These numbers cannot be assigned to algorithms in an arbitrary manner - there are common-sense restrictions that must be enforced. For example, the answer to an expensive query should not be derivable from a much cheaper query. Each application has its own set of restrictions but when they are formulated mathematically, common patterns emerge. Thus technical results from one area can often be ported to the others.