Differential privacy is a promising approach to privacy preserving data analysis with a well-developed theory for functions. Despite recent work on implementing systems that aim to provide differential privacy, the problem of formally verifying that these systems have differential privacy has not been adequately addressed. This paper presents the first results towards automated verification of source code for differentially private interactive systems. We develop a formal probabilistic automaton model of differential privacy for systems by adapting prior work on differential privacy for functions. The main technical result of the paper is a sound proof technique based on a form of probabilistic bisimulation relation for proving that a system modeled as a probabilistic automaton satisfies differential privacy. The novelty lies in the way we track quantitative privacy leakage bounds using a relation family instead of a single relation. We illustrate the proof technique on a representative automaton motivated by PINQ, an implemented system that is intended to provide differential privacy. To make our proof technique easier to apply to realistic systems, we prove a form of refinement theorem and apply it to show that a refinement of the abstract PINQ automaton also satisfies our differential privacy definition. Finally, we begin the process of automating our proof technique by providing an algorithm for mechanically checking a restricted class of relations from the proof technique.
Much work has been done on decision algorithms for probabilistic simulation and bisimulation @cite_7 @cite_5 @cite_29 @cite_11 . Particularly relevant are the works of Baier and Hermans @cite_7 , and Cattani and Segala @cite_11 on decision algorithms for weak bisimulations. Since our unwinding relations keep track of an error bound in the form of indices in a relation family, the methods of these papers to generate relations do not readily apply to our setting. We limit ourselves to checking if a given relation family is an unwinding family rather than generating one. Extending these prior works to our setting remains as future work.
@cite_5 @cite_29 @cite_7 @cite_11
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This paper deals with probabilistic and nondeterministic processes represented by a variant of labeled transition systems where any outgoing transition of a state s is augmented with probabilities for the possible successor states. Our main contributions are algorithms for computing this bisimulation equivalence classes as introduced by Larsen and Skou (1996, Inform. and Comput.99, 1?28), and the simulation preorder a la Segala and Lynch (1995, Nordic J. Comput.2, 250?273). The algorithm for deciding bisimilarity is based on a variant of the traditional partitioning technique and runs in time O(mn(logm+logn)) where m is the number of transitions and n the number of states. The main idea for computing the simulation preorder is the reduction to maximum flow problems in suitable networks. Using the method of Cheriyan, Hagerup, and Mehlhorn, (1990, Lecture Notes in Computer Science, Vol. 443, pp. 235?248, Springer-Verlag, Berlin) for computing the maximum flow, the algorithm runs in time O((mn6+m2n3) logn). Moreover, we show that the network-based technique is also applicable to compute the simulation-like relation of Jonsson and Larsen (1991, “Proc. LICS'91” pp. 266?277) in fully probabilistic systems (a variant of ordinary labeled transition systems where the nondeterminism is totally resolved by probabilistic choices). This paper reports on a novel technique for literature indexing and searching in a mechanized library system. The notion of relevance is taken as the key concept in the theory of information retrieval and a comparative concept of relevance is explicated in terms of the theory of probability. The resulting technique called “Probabilistic Indexing,” allows a computing machine, given a request for information, to make a statistical inference and derive a number (called the “relevance number”) for each document, which is a measure of the probability that the document will satisfy the given request. The result of a search is an ordered list of those documents which satisfy the request ranked according to their probable relevance. The paper goes on to show that whereas in a conventional library system the cross-referencing (“see” and “see also”) is based solely on the “semantical closeness” between index terms, statistical measures of closeness between index terms can be defined and computed. Thus, given an arbitrary request consisting of one (or many) index term(s), a machine can elaborate on it to increase the probability of selecting relevant documents that would not otherwise have been selected. Finally, the paper suggests an interpretation of the whole library problem as one where the request is considered as a clue on the basis of which the library system makes a concatenated statistical inference in order to provide as an output an ordered list of those documents which most probably satisfy the information needs of the user. In this paper, we introduce weak bisimulation in the framework of Labeled Concurrent Markov Chains, that is, probabilistic transition systems which exhibit both probabilistic and nondeterministic behavior. By resolving the nondeterminism present, these models can be decomposed into a possibly infinite number of computation trees. We show that in order to compute weak bisimulation it is sufficient to restrict attention to only a finite number of these computations. Finally, we present an algorithm for deciding weak bisimulation which has polynomial-time complexity in the number of states of the transition system. Several recent works on relation extraction have been applying the distant supervision paradigm: instead of relying on annotated text to learn how to predict relations, they employ existing knowledge bases (KBs) as source of supervision. Crucially, these approaches are trained based on the assumption that each sentence which mentions the two related entities is an expression of the given relation. Here we argue that this leads to noisy patterns that hurt precision, in particular if the knowledge base is not directly related to the text we are working with. We present a novel approach to distant supervision that can alleviate this problem based on the following two ideas: First, we use a factor graph to explicitly model the decision whether two entities are related, and the decision whether this relation is mentioned in a given sentence; second, we apply constraint-driven semi-supervision to train this model without any knowledge about which sentences express the relations in our training KB. We apply our approach to extract relations from the New York Times corpus and use Freebase as knowledge base. When compared to a state-of-the-art approach for relation extraction under distant supervision, we achieve 31 error reduction.