Nikhil Ravi

Sachin Kadam, Anna Scaglione, Nikhil Ravi et al.

The Differential Privacy (DP) literature often centers on meeting privacy constraints by introducing noise to the query, typically using a pre-specified parametric distribution model with one or two degrees of freedom. However, this emphasis tends to neglect the crucial considerations of response accuracy and utility, especially in the context of categorical or discrete numerical database queries, where the parameters defining the noise distribution are finite and could be chosen optimally. This paper addresses this gap by introducing a novel framework for designing an optimal noise Probability Mass Function (PMF) tailored to discrete and finite query sets. Our approach considers the modulo summation of random noise as the DP mechanism, aiming to present a tractable solution that not only satisfies privacy constraints but also minimizes query distortion. Unlike existing approaches focused solely on meeting privacy constraints, our framework seeks to optimize the noise distribution under an arbitrary $(ε, δ)$ constraint, thereby enhancing the accuracy and utility of the response. We demonstrate that the optimal PMF can be obtained through solving a Mixed-Integer Linear Program (MILP). Additionally, closed-form solutions for the optimal PMF are provided, minimizing the probability of error for two specific cases. Numerical experiments highlight the superior performance of our proposed optimal mechanisms compared to state-of-the-art methods. This paper contributes to the DP literature by presenting a clear and systematic approach to designing noise mechanisms that not only satisfy privacy requirements but also optimize query distortion. The framework introduced here opens avenues for improved privacy-preserving database queries, offering significant enhancements in response accuracy and utility.

Nikhil Ravi, Anna Scaglione, Sean Peisert

The goal of this paper is to propose and analyze a differentially private randomized mechanism for the $K$-means query. The goal is to ensure that the information received about the cluster-centroids is differentially private. The method consists in adding Gaussian noise with an optimum covariance. The main result of the paper is the analytical solution for the optimum covariance as a function of the database. Comparisons with the state of the art prove the efficacy of our approach.

Sachit Menon, Alexandru Damian, Shijia Hu et al.

The primary aim of single-image super-resolution is to construct high-resolution (HR) images from corresponding low-resolution (LR) inputs. In previous approaches, which have generally been supervised, the training objective typically measures a pixel-wise average distance between the super-resolved (SR) and HR images. Optimizing such metrics often leads to blurring, especially in high variance (detailed) regions. We propose an alternative formulation of the super-resolution problem based on creating realistic SR images that downscale correctly. We present an algorithm addressing this problem, PULSE (Photo Upsampling via Latent Space Exploration), which generates high-resolution, realistic images at resolutions previously unseen in the literature. It accomplishes this in an entirely self-supervised fashion and is not confined to a specific degradation operator used during training, unlike previous methods (which require supervised training on databases of LR-HR image pairs). Instead of starting with the LR image and slowly adding detail, PULSE traverses the high-resolution natural image manifold, searching for images that downscale to the original LR image. This is formalized through the "downscaling loss," which guides exploration through the latent space of a generative model. By leveraging properties of high-dimensional Gaussians, we restrict the search space to guarantee realistic outputs. PULSE thereby generates super-resolved images that both are realistic and downscale correctly. We show proof of concept of our approach in the domain of face super-resolution (i.e., face hallucination). We also present a discussion of the limitations and biases of the method as currently implemented with an accompanying model card with relevant metrics. Our method outperforms state-of-the-art methods in perceptual quality at higher resolutions and scale factors than previously possible.

Yijie Bei, Alex Damian, Shijia Hu et al.

This work identifies and addresses two important technical challenges in single-image super-resolution: (1) how to upsample an image without magnifying noise and (2) how to preserve large scale structure when upsampling. We summarize the techniques we developed for our second place entry in Track 1 (Bicubic Downsampling), seventh place entry in Track 2 (Realistic Adverse Conditions), and seventh place entry in Track 3 (Realistic difficult) in the 2018 NTIRE Super-Resolution Challenge. Furthermore, we present new neural network architectures that specifically address the two challenges listed above: denoising and preservation of large-scale structure.