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We propose a Neighbourhood-Aware Differential Privacy (NADP) mechanism considering the neighbourhood of a word in a pretrained static word embedding space to determine the minimal amount of noise required to guarantee a specified privacy level. We first construct a nearest neighbour graph over the words using their embeddings, and factorise it into a set of connected components (i.e. neighbourhoods). We then separately apply different levels of Gaussian noise to the words in each neighbourhood, determined by the set of words in that neighbourhood. Experiments show that our proposed NADP mechanism consistently outperforms multiple previously proposed DP mechanisms such as Laplacian, Gaussian, and Mahalanobis in multiple downstream tasks, while guaranteeing higher levels of privacy., Comment: Accepted to IJCNLP-AACL 2023

We propose a method to protect the privacy of search engine users by decomposing the queries using semantically \emph{related} and unrelated \emph{distractor} terms. Instead of a single query, the search engine receives multiple decomposed query terms. Next, we reconstruct the search results relevant to the original query term by aggregating the search results retrieved for the decomposed query terms. We show that the word embeddings learnt using a distributed representation learning method can be used to find semantically related and distractor query terms. We derive the relationship between the \emph{obfuscity} achieved through the proposed query anonymisation method and the \emph{reconstructability} of the original search results using the decomposed queries. We analytically study the risk of discovering the search engine users' information intents under the proposed query obfuscation method, and empirically evaluate its robustness against clustering-based attacks. Our experimental results show that the proposed method can accurately reconstruct the search results for user queries, without compromising the privacy of the search engine users., Comment: Accepted to Language Resources and Evaluation (LREC-2022)

We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademacher sums arise. In the course of its proof, we also obtain a transformation formula for elliptic Dedekind-Rademacher sums. When a complex parameter $¥tau$ tends to $i ¥infty$, these represent some classical results which include the reciprocity formula for Apostol-Dedekind sums.

In this paper we introduce an elliptic analogue of the generalized Dedekind-Rademacher sums which satisfy reciprocity laws. In these sums, Kronecker's double series play a role of elliptic Bernoulli functions. This paper gives an answer to the problem of S. Fukuhara and N. Yui concerning the elliptic Apostol-Dedekind sums. We also mention a relation between the generating function of Kronecker's double series and that of the (Debye) elliptic polylogarithms studied by A. Levin.

Closed expressions are obtained for sums of products of Kronecker's double series. Corresponding results are derived for functions which are an elliptic analogue of the periodic Euler polynomials. As corollaries, we reproduce the formulas for sums of products of Bernoulli numbers, Bernoulli polynomials, Euler numbers, and Euler polynomials, which were given by K. Dilcher.

Let $\theta (x)$ denote Jacobi's theta function. We show that the function $F_\xi (x) = (\theta '(0) \theta (x+\xi) )/ (\theta (x) \theta (\xi))$ satisfies functional equations, which is a generalization of the harmonic relations for multiple zeta values.

We introduce an elliptic analogue of the Bernoulli functions, which we call elliptic Bernoulli functions. They are defined by using the modified generating function of the elliptic polylogarithms. By degeneration of the elliptic Bernoulli functions, we obtain standard properties and new identities for the Bernoulli functions.