arXiv subjects

Shuichi Otake

Publications and source records attributed to Shuichi Otake.

3 recordsLinked to original sources

arXiv2023

A Neighbourhood-Aware Differential Privacy Mechanism for Static Word Embeddings

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.

cs.LG↗

arXiv2018

Bezoutians and the discriminant of a certain quadrinomials

We give an explicit formula for the discriminant $Δ_f (x)$ of the quadrinomials of the form $f (x)=x^n+ t (x^2+ax+b)$. The proof uses Bezoutians of polynomials.

math.NT↗

arXiv2018

Some remarks on the non-real roots of polynomials

Let $f \in { \mathbb R} ( t) [x]$ be given by $ f(t, x) = x^n + t \cdot g(x) $ and $β_1 < \dots < β_m$ the distinct real roots of the discriminant $Δ_{(f, x)} (t)$ of $f(t, x)$ with respect to $x$. Let $γ$ be the number of real roots of $g(x)=\sum_{k=0}^s t_{s-k} x^{s-k}$. For any $ξ> | β_m |$, if $n-s$ is odd then the number of real roots of $f(ξ, x)$ is $γ+1$, and if $n-s$ is even then the number of real roots of $f(ξ, x)$ is $γ$, $γ+2$ if $t_s>0$ or $t_s < 0$ respectively. A special case of the above result is constructing a family of totally complex polynomials which are reducible over $\mathbb Q$.

math.NT↗