Proving uniformity and independence by self-composition and coupling

Proof by coupling is a classical proof technique for establishing probabilistic properties of two probabilistic processes, like stochastic dominance and rapid mixing of Markov chains. More recently, couplings have been investigated as a useful abstraction for formal reasoning about relational properties of probabilistic programs, in particular for modeling reduction-based cryptographic proofs and for verifying differential privacy. In this paper, we demonstrate that probabilistic couplings can be used for verifying non-relational probabilistic properties. Specifically, we show that the program logic pRHL---whose proofs are formal versions of proofs by coupling---can be used for formalizing uniformity and probabilistic independence. We formally verify our main examples using the EasyCrypt proof assistant

Advanced Probabilistic Couplings for Differential Privacy

Differential privacy is a promising formal approach to data privacy, which provides a quantitative bound on the privacy cost of an algorithm that operates on sensitive information. Several tools have been developed for the formal verification of differentially private algorithms, including program logics and type systems. However, these tools do not capture fundamental techniques that have emerged in recent years, and cannot be used for reasoning about cutting-edge differentially private algorithms. Existing techniques fail to handle three broad classes of algorithms: 1) algorithms where privacy depends accuracy guarantees, 2) algorithms that are analyzed with the advanced composition theorem, which shows slower growth in the privacy cost, 3) algorithms that interactively accept adaptive inputs. We address these limitations with a new formalism extending apRHL, a relational program logic that has been used for proving differential privacy of non-interactive algorithms, and incorporating aHL, a (non-relational) program logic for accuracy properties. We illustrate our approach through a single running example, which exemplifies the three classes of algorithms and explores new variants of the Sparse Vector technique, a well-studied algorithm from the privacy literature. We implement our logic in EasyCrypt, and formally verify privacy. We also introduce a novel coupling technique called \emph{optimal subset coupling} that may be of independent interest

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Lee Kong Chian Fellowship, SM

Disentangling Boosted Higgs Boson Production Modes with Machine Learning

Higgs Bosons produced via gluon-gluon fusion (ggF) with large transverse momentum ($p_T$) are sensitive probes of physics beyond the Standard Model. However, high $p_T$ Higgs Boson production is contaminated by a diversity of production modes other than ggF: vector boson fusion, production of a Higgs boson in association with a vector boson, and production of a Higgs boson with a top-quark pair. Combining jet substructure and event information with modern machine learning, we demonstrate the ability to focus on particular production modes. These tools hold great discovery potential for boosted Higgs bosons produced via ggF and may also provide additional information about the Higgs Boson sector of the Standard Model in extreme phase space regions for other production modes as well.Comment: 17 pages, 9 figure