Kobbi Nissim and Uri Stemmer. 3/2017. “

Concentration Bounds for High Sensitivity Functions Through Differential Privacy”.

arXiv PageAbstractA new line of work [6, 9, 15, 2] demonstrates how differential privacy [8] can be used as a mathematical tool for guaranteeing generalization in adaptive data analysis. Specifically, if a differentially private analysis is applied on a sample S of i.i.d. examples to select a lowsensitivity function f , then w.h.p. f (S) is close to its expectation, although f is being chosen based on the data. Very recently, Steinke and Ullman [16] observed that these generalization guarantees can be used for proving concentration bounds in the non-adaptive setting, where the low-sensitivity function is fixed beforehand. In particular, they obtain alternative proofs for classical concentration bounds for low-sensitivity functions, such as the Chernoff bound and McDiarmid’s Inequality. In this work, we set out to examine the situation for functions with high-sensitivity, for which differential privacy does not imply generalization guarantees under adaptive analysis. We show that differential privacy can be used to prove concentration bounds for such functions in the non-adaptive setting.

Ezgi Cicek, Gilles Barthe, Marco Gaboardi, Deepak Garg, and Jan Hoffmann. 1/2017. “

Relational Cost Analysis.” Symposium on the Principle of Programming Languages, ACM.

AbstractEstablishing quantitative bounds on the execution cost of programs is essential in many areas of computer science such as complexity analysis, compiler optimizations, security and privacy. Techniques based on program analysis, type systems and abstract interpretation are well-studied, but methods for analyzing how the execution costs of two programs compare to each other have not received attention. Naively combining the worst and best case execution costs of the two programs does not work well in many cases because such analysis forgets the similarities between the programs or the inputs. In this work, we propose a relational cost analysis technique that is capable of establishing precise bounds on the difference in the execution cost of two programs by making use of relational properties of programs and inputs. We develop RelCost, a refinement type and effect system for a higher-order functional language with recursion and subtyping. The key novelty of our technique is the combination of relational refinements with two modes of typing—relational typing for reasoning about similar computations/inputs and unary typing for reasoning about unrelated computations/inputs. This combination allows us to analyze the execution cost difference of two programs more precisely than a naive non-relational approach. We prove our type system sound using a semantic model based on step-indexed unary and binary logical relations accounting for non-relational and relational reasoning principles with their respective costs. We demonstrate the precision and generality of our technique through examples.

PDF Arthur Azevedo de Amorim, Marco Gaboardi, Justin Hsu, Shin-ya Katsumata, and Ikram Cherigui. 1/2017. “

A Semantic Account of Metric Preservation.” Symposium on the Principle of Programming Languages, ACM.

arXiv PageAbstractProgram sensitivity measures how robust a program is to small changes in its input, and is a fundamental notion in domains ranging from differential privacy to cyber-physical systems. A natural way to formalize program sensitivity is in terms of metrics on the input and output spaces, requiring that an r-sensitive function map inputs that are at distance d to outputs that are at distance at most r⋅d. Program sensitivity is thus an analogue of Lipschitz continuity for programs. Reed and Pierce introduced Fuzz, a functional language with a linear type system that can express program sensitivity. They show soundness operationally, in the form of a metric preservation property. Inspired by their work, we study program sensitivity and metric preservation from a denotational point of view. In particular, we introduce metric CPOs, a novel semantic structure for reasoning about computation on metric spaces, by endowing CPOs with a compatible notion of distance. This structure is useful for reasoning about metric properties of programs, and specifically about program sensitivity. We demonstrate metric CPOs by giving a model for the deterministic fragment of Fuzz.

Shiva Kasiviswanathan, Kobbi Nissim, and Hongxia Jin. 2017. “

Private Incremental Regression.” in the ACM SIGMOD/PODS Conference (PODS 2017).