Optimal and Private Learning from Human Response Data

Item response theory (IRT) is the study of how people make probabilistic decisions, with diverse applications in education testing, recommendation systems, among others. The Rasch model of binary response data, one of the most fundamental models in IRT, remains an active area of research with important practical significance. Recently, Nguyen and Zhang (2022) proposed a new spectral estimation algorithm that is efficient and accurate. In this work, we extend their results in two important ways. Firstly, we obtain a refined entrywise error bound for the spectral algorithm, complementing the `average error' $\ell_2$ bound in their work. Notably, under mild sampling conditions, the spectral algorithm achieves the minimax optimal error bound (modulo a log factor). Building on the refined analysis, we also show that the spectral algorithm enjoys optimal sample complexity for top-$K$ recovery (e.g., identifying the best $K$ items from approval/disapproval response data), explaining the empirical findings in the previous work. Our second contribution addresses an important but understudied topic in IRT: privacy. Despite the human-centric applications of IRT, there has not been any proposed privacy-preserving mechanism in the literature. We develop a private extension of the spectral algorithm, leveraging its unique Markov chain formulation and the discrete Gaussian mechanism (Canonne et al., 2020). Experiments show that our approach is significantly more accurate than the baselines in the low-to-moderate privacy regime.Comment: International Conference on Artificial Intelligence and Statistics (AISTATS) 202

Structural origins of the properties of rare earth nickelate superlattices

NiO6 octahedral tilts in the LaNiO3/SrTiO3 superlattices are quantified using position averaged convergent beam electron diffraction in scanning transmission electron microscopy. It is shown that maintaining oxygen octahedra connectivity across the interface controls the octahedral tilts in the LaNiO3 layers, their lattice parameters and their transport properties. Unlike films and layers that are connected on one side to the substrate, subsequent LaNiO3 layers in the superlattice exhibit a relaxation of octahedral tilts towards bulk values. This relaxation is facilitated by correlated tilts in SrTiO3 layers and is correlated with the conductivity enhancement of the LaNiO3 layers in the superlattices relative to individual films.Comment: Accepted for publication in Physical Review B (Rapid Communication

Optimality of Spectral Clustering in the Gaussian Mixture Model

Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been fully understood. In this paper, we show that spectral clustering is minimax optimal in the Gaussian Mixture Model with isotropic covariance matrix, when the number of clusters is fixed and the signal-to-noise ratio is large enough. Spectral gap conditions are widely assumed in the literature to analyze spectral clustering. On the contrary, these conditions are not needed to establish optimality of spectral clustering in this paper