Recently, some posts on social media were claiming that for-sale home listings in Washington DC were spiking, presumably due to recent cuts to government and other agencies. This post investigates data from Zillow Research, both to explore the US real estate market this year in general and to determine if such a claim holds any truth.
Nonspecific: A Story About Diagnosis
It was late 2015. In a lot of ways, I felt on the top of my game and I thought I had life figured out. I was wrapping up a master’s degree in computer science. I had a 4.0 GPA. I could bench press 250 pounds. I had a girlfriend. I had my own car. I was renting a room just down the street from my school. I spent most of my time studying, at the gym, or playing music.
The Matrix-Vector Product and the SVD
The singular value decomposition (SVD) allows one to re-write a given matrix as a sum of rank one matrices. Specifically, using the SVD, one may re-write a given matrix A as follows:
where 
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Cause of Death Records in 2021
This post explores Multiple Cause-of-Death records for the year 2021, taken from the U.S. Division of Vital Statistics. Specifically, the impact of the second full year of the coronavirus pandemic is explored in more detail.
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Increases in Circulatory Death During the Coronavirus Pandemic
This post takes a closer look at Multiple Cause-of-Death records during the first year of the Coronavirus Pandemic. In this post, changes in mortality records involving the circulatory system (i.e. ICD-10 codes starting with I) are analyzed in more detail. These codes cover commonly occurring diseases like heart attacks, strokes, and other disease of the cardiovascular and, more broadly, the circulatory system.
Cause of Death in the USA: 1959-2020
This post takes another look at Mortality Multiple Cause-of-Death records from the U.S. Division of Vital Statistics. Previous posts have analyzed records for the year 2016 and also deaths due to Influenza & Pneumonia in 2017. In this post, records from 1959 to the 2020, the latest year currently available, are analyzed.
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Embedding Recipes using Kernel PCA
The previous post discusses Kernel PCA and recipes, or formulae, for deriving new kernels from known good kernels. This post applies these approaches to generate vector embeddings in a specific domain: culinary recipes. The idea is to find a low-dimensional representation of recipes such that points in the embedding space are neighbors to similar recipes.
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Kernel Recipes and Kernel PCA
One strength of kernel methods is their ability to operate directly on non-numerical objects like sets. As seen in the previous post, the Jaccard index on sets satisfies Mercer’s condition and thus is a valid kernel. The process of proving a similarity measure is a valid kernel is somewhat involved, but thankfully several theorems can be employed to get more mileage out of the set of known good kernels. This post outlines some recipes for producing new valid kernels and introduces a method for obtaining numerical representations of samples using kernel methods.
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The Jaccard Kernel and its Implied Feature Space
Kernel methods leverage the kernel trick to implicitly perform inner products in often high and even infinite dimensional feature spaces. For instance, the radial basis function (RBF) kernel can be shown to map to an infinite-dimensional feature space. In general, if a similarity function can be shown to satisfy Mercer’s Condition, one may operate on the finite-dimensional Gram matrix induced by the function, while receiving the benefit of mathematical guarantees about the implied transformation.
On The Importance of Centering in PCA
The previous post presents methods for efficiently performing principal component analysis (PCA) on certain rectangular sparse matrices. Since routines for performing the singular value decomposition (SVD) on sparse matrices are readily available (e.g. svds and TruncatedSVD), it is reasonable to investigate the influence centering has on the resulting transformation.
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