The Analytic Garden

 If you search the web for neural net regression, you will find a number of examples. Most begin by generating some data from  a linear or sinusoidal function and adding a bit of noise. They then fit the resulting data with a neural net created with a tool such as PyTorch .  In this post, I want to try to accomplish two things: learn a bit about neural nets and explore PyTorch. Neural nets are often discussed in relation to deep learning . Deep learning typically involves large amounts of data and multiple network layers with complex architectures that are used in areas such as computer vision or speech recognition. The example we are considering isn't particularly deep, but I hope it illustrates a a few simple principles of neural nets. PyTorch is a Python machine learning toolkit developed by Facebook. Its main features are tensor computing and automatic numerical differentiation. Rather than using generated data, I want to use real data and see what happens as I u...

This post is an update to a previous post . The CDC extended the database of breakthrough cases and deaths so that it now extends from 2021_04_04 to 2021_12_12. In addition, CDC altered the format of the MMWR.week column. MMWR.week is an epidemiological date format that can be used to produce dates in R's date format. Updated code is available on GitHub . Since it now includes the beginning of the omicron phase of the pandemic, I thought it might be time to take another look. I downloaded the breakthrough data from the CDC on 2022-02-04.  First, cases and deaths for vaccinated patients vs. non-vaccinated patients. Compare these with the  previous plots . Notice the increase in cases in the later months of the plot. Fortunately, the increase in deaths is not so dramatic. Presumably, this is because it seems that omicron, more transmissible but seemingly less virulent, is replacing the delta strain in the population. Also, notice that being vaccinated provides protection agains...

 BA.2 is a sub-variant of the omicron variant of SARS-Cov-2. It has basically the same collection of mutations as BA.1, the original omicron variant with about 28 others. It was first identified in South Africa on 2021-11-17. BA.2 is more transmissible than BA.1. On 2022-01-30, I downloaded 7,623,097 records for SAR-CoV-2 sequences from GISAID . I plotted the the development of the variants of interest (VOI) and variants of concern (VOC) over time with  plot_named_variants.R available on GitHub . This messy plot show the growth of omicron (the green dots on the right) as it overtakes delta (the gold dots at the top right). The plot shows log counts of sequences in the GISAID database. Assuming GISAID data is a representative sample of COVID-19 cases, at least in developed countries, the straight line increase indicates that omicron is under going exponential grown. We can compare the growth of BA-1 and BA-2. BA_1_2 <- meta_2022_01_30 %>% filter(Pango.lineage...