Category Archives: numerical linear algebra

Phase Plane plots of COVID-19 deaths with uncertainties

I. Introduction. It’s time to fulfill the promise made in “Phase plane plots of COVID-19 deaths“, a blog post from 2nd May 2020, and produce the same with uncertainty clouds about the functional trajectories(*). To begin, here are some assumptions … Continue reading

Posted in American Statistical Association, Andrew Harvey, anomaly detection, count data regression, COVID-19, dependent data, dlm package, Durbin and Koopman, dynamic linear models, epidemiology, filtering, forecasting, Kalman filter, LaTeX, model-free forecasting, Monte Carlo Statistical Methods, numerical algorithms, numerical linear algebra, population biology, population dynamics, prediction, R, R statistical programming language, regression, statistical learning, stochastic algorithms | Tagged | Leave a comment

The Johnson-Lindenstrauss Lemma, and the paradoxical power of random linear operators. Part 1.

Updated, 2018-12-04 I’ll be discussing the ramifications of: William B. Johnson and Joram Lindenstrauss, “Extensions of Lipschitz mappings into a Hilbert space, Contemporary Mathematics, 26:189–206, 1984. for several posts here. Some introduction and links to proofs and explications will be … Continue reading

Posted in clustering, data science, dimension reduction, information theoretic statistics, Johnson-Lindenstrauss Lemma, k-NN, Locality Sensitive Hashing, mathematics, maths, multivariate statistics, non-parametric model, numerical algorithms, numerical linear algebra, point pattern analysis, random projections, recommender systems, science, stochastic algorithms, stochastics, subspace projection methods | 1 Comment

When linear systems can’t be solved by linear means

Linear systems of equations and their solution form the cornerstone of much Engineering and Science. Linear algebra is a paragon of Mathematics in the sense that its theory is what mathematicians try to emulate when they develop theory for many … Continue reading

Posted in Calculus, dynamic linear models, mathematics, maths, nloptr, numerical algorithms, numerical analysis, numerical linear algebra, numerics, SVD | Leave a comment