Efficient Optimal Reconstruction of Linear Fields and Band-powers from Cosmological Data

We present an efficient implementation of Wiener filtering of real-space linear field and optimal quadratic estimator of its power spectrum Band-powers. We first recast the field reconstruction into an optimization problem, which we solve using quasi-Newton optimization. We then recast the power spectrum estimation into the field marginalization problem, from which we obtain an expression that depends on the field reconstruction solution and a determinant term. We develop a novel simulation based method for the latter. We extend the simulations formalism to provide the covariance matrix for the power spectrum. We develop a flexible framework that can be used on a variety of cosmological fields and present results for a variety of test cases, using simulated examples of projected density fields, projected shear maps from galaxy lensing, and observed Cosmic Microwave Background (CMB) temperature anisotropies, with a wide range of map incompleteness and variable noise. For smaller cases where direct numerical inversion is possible, we show that our solution matches that created by direct Wiener Filtering at a fraction of the overall computation cost. Even more significant reduction of computational is achieved by this implementation of optimal quadratic estimator due to the fast evaluation of the Hessian matrix. This technique allows for accurate map and power spectrum reconstruction with complex masks and nontrivial noise properties.Comment: 23 pages, 14 figure

Patents Phrase to Phrase Semantic Matching Dataset

There are many general purpose benchmark datasets for Semantic Textual Similarity but none of them are focused on technical concepts found in patents and scientific publications. This work aims to fill this gap by presenting a new human rated contextual phrase to phrase matching dataset. The entire dataset contains close to $50,000$ rated phrase pairs, each with a CPC (Cooperative Patent Classification) class as a context. This paper describes the dataset and some baseline models.Comment: Presented at the SIGIR PatentSemTech 2022 Workshop. The dataset can be accessed at https://www.kaggle.com/datasets/google/google-patent-phrase-similarity-datase