Direction-Oriented Smooth Sensitivity

We propose ${\it Direction}$- ${\it Oriented \ Smooth \ Sensitivity}$ (DOSS), a novel concept that takes the direction of noise into account. By varying the amount of noise with direction, we can add perturbations more in line with reality than the original ${\it smooth \ sensitivity}$ and improve the output accuracy.

This page contains the Python codes for our experiments on accuracy and run time. We also investivated key properties regarding the TDT and $\chi^2$-statistics, which are particularly important statistics in genomic statistical analysis. This makes it easier to use our theorems for efficiently computing the value of ${\it sensitivity}$.

In "beta_evaluation" folder, the evaluation for the characteristics of the two genome statistics are provided.

In "distribution_evaluation" folder, the most advisable $(\alpha, \beta)$-admissible distribution for noise generation was investigated.

"vs SS" folder provides the comparison results between our DOSS and the original ${\it smooth \ sensitivity}$ in terms of output accuracy.

The run time of our algorithm (Algorithm 1 in our paper) was measured for reference, in "RunTime" folder.

The omitted proofs in the main paper are provided in Proofs.pdf.

Future Directions

・Conducting rigorous theoretical analysis of the influence of $(k,l)$ on the noise distributions and the exploration of the "optimal" distribution with reference to it.

・Investigating $(\alpha, \beta)$-admissible distributions on $m$-dimensional space, especially when $m$ is large.

・Are there any cases where $\alpha$ and $\beta$ in the ${\it admissible}$ property should not be represented as linear functions of $\epsilon$? / Given functions $\alpha$ and $\beta$, is it possible to find an $(\alpha, \beta)$- ${\it admissible}$ distribution?

・Developing more efficient methods for computing direction-oriented local sensitivity and smooth sensitivity.
← It might be beneficial to considering the dependency of dimensions.

Note

For details of our methods and discussion, please see our paper entitled "Direction-Oriented Smooth Sensitivity and Its Application to Genomic Statistical Analysis" (https://doi.org/10.1007/978-981-96-9101-2_4) presented at ACISP 2025.

Contact

Akito Yamamoto

Division of Medical Data Informatics, Human Genome Center,

the Institute of Medical Science, the University of Tokyo

a-ymmt@ims.u-tokyo.ac.jp