A fast semi-direct least squares algorithm for hierarchically block separable matrices

We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived from asymptotically smooth radial kernels that are not too oscillatory. The algorithm is based on a recursive skeletonization procedure that exposes this sparsity and solves the dense least squares problem as a larger, equality-constrained, sparse one. It relies on a sparse QR factorization coupled with iterative weighted least squares methods. In essence, our scheme consists of a direct component, comprised of matrix compression and factorization, followed by an iterative component to enforce certain equality constraints. At most two iterations are typically required for problems that are not too ill-conditioned. For an $M \times N$ HBS matrix with $M \geq N$ having bounded off-diagonal block rank, the algorithm has optimal $\mathcal{O} (M + N)$ complexity. If the rank increases with the spatial dimension as is common for operators that are singular at the origin, then this becomes $\mathcal{O} (M + N)$ in 1D, $\mathcal{O} (M + N^{3/2})$ in 2D, and $\mathcal{O} (M + N^{2})$ in 3D. We illustrate the performance of the method on both over- and underdetermined systems in a variety of settings, with an emphasis on radial basis function approximation and efficient updating and downdating.Comment: 24 pages, 8 figures, 6 tables; to appear in SIAM J. Matrix Anal. App

Haidawood: A Social Media Approach to Indigenous Language Revitalization

British Columbia is home to 34 different Indigenous languages, most of which are in danger of losing fluency due to the combined effects of introduced diseases and assimilationist Indian Residential Schools. The Haida language, or Xaad Kil (pronounced “haad kill”), is considered critically endangered with only 9 elderly fluent speakers left. Many Haida believe that revitalizing Xaad Kil is important for keeping their culture alive: they see Xaad Kil as a cultural keystone that keeps worldview, artistic expression, food gathering, dances, stories, and songs integrated together as a unified whole. Xaad Kil also helps assert Aboriginal land rights: identification of traditional place names demonstrates use and occupation of lands since time immemorial. Xaad Kil names of medicinal plants and foods also contain important environmental information. Indigenous communities are adopting a range of strategies to revitalize their languages, including: master-apprentice programs, early childhood immersion programs, and technological approaches such as audio databases, language apps, and social media projects like Haidawood. Learning Xaad Kil can be a challenge: there are limited resources and often language learners are overwhelmed with obstacles. Haidawood helps make Haida language learning fun by bringing Haida stories to life using the power of stop motion animation and embracing an “aesthetic of accessibility” that creates beautiful art out of readily available materials, including carved puppet faces and sets made from cardboard. Haidawood seeks to help revitalize the Haida language, facilitate inter-cultural understanding, and inspire other communities to preserve and share their own stories

An Open Source Pattern Recognition Toolbox for MATLAB

Pattern recognition and machine learning are becoming integral parts of algorithms in a wide range of applications. Different algorithms and approaches for machine learning include different tradeoffs between performance and computation, so during algorithm development it is often necessary to explore a variety of different approaches to a given task. A toolbox with a unified framework across multiple pattern recognition techniques enables algorithm developers the ability to rapidly evaluate different choices prior to deployment. MATLAB is a widely used environment for algorithm development and prototyping, and although several MATLAB toolboxes for pattern recognition are currently available these are either incomplete, expensive, or restrictively licensed. In this work we describe a MATLAB toolbox for pattern recognition and machine learning known as the PRT (Pattern Recognition Toolbox), licensed under the permissive MIT license. The PRT includes many popular techniques for data preprocessing, supervised learning, clustering, regression and feature selection, as well as a methodology for combining these components using a simple, uniform syntax. The resulting algorithms can be evaluated using cross-validation and a variety of scoring metrics to ensure robust performance when the algorithm is deployed. This paper presents an overview of the PRT as well as an example of usage on Fisher's Iris dataset

Evaluating duration of response to treatment in systemic lupus erythematosus clinical trials.

ObjectiveTo evaluate response duration and identify predictors of transitioning into and out of the response state in patients with SLE receiving standard of care (SoC) in 52-week clinical trials.MethodsA multistate model (MSM) allowing for bidirectional transitions between response and non-response states was fit to data on 759 patients with SLE with active disease randomised to SoC. The probability of being in response at 52 weeks, average duration of response (sojourn time) and mean total time in response for SLE Responder Index (SRI-4, SRI-5, SRI-6) and BILAG-based Composite Lupus Assessment (BICLA) were estimated. Predictors of attainment and loss of SRI-5 response were also assessed.ResultsThe MSM estimated probability of being in response at 52 weeks ranged from 42% (SRI-6) to 61% (SRI-4). Mean duration of response ranged from 20.4 weeks (BICLA) to 31.5 weeks (SRI-4). Mean total time in response was 16.4-24.8 weeks. Baseline characteristics predictive of shorter SRI-5 response duration were African descent (p=0.005), longer history of disease (p=0.03), higher anti-dsDNA antibody titres (p=0.039), lower lymphocyte count (p=0.008) and lower haemoglobin (p=0.006). Younger age (p<0.001) and higher protein/creatinine ratio (p<0.001) were associated with higher likelihood of achieving SRI-5 but also shorter response duration.ConclusionFactors associated with disease severity were more predictive of shorter response duration than of 52-week response status. Analysing landmark response rates and response duration using MSM may be a more powerful way to distinguish effective investigational treatments from background SoC, although this remains to be evaluated in future trials

Correlation of qEEG with PET in schizophrenia

PET relative metabolism was correlated with quantitative EEG in 9 schizophrenic patients. The PET metabolic regions of interest were the frontal lobes, thalamus and basal ganglia, and right and left temporal lobes. Significant positive correlations were seen for the frontal lobes and delta EEG power, and alpha power with subcortical metabolism. The physiologic plausibility of those correlations is discussed with reference to the possible effect of neuroleptic medication