Convolutional Neural networks (CNNs) have been found to be very effective at tasks such as facial recognition, video analysis, anomaly detections and semantic parsing. An image can be considered a graph with a very regular structure (i.e., pixel...

I always had trouble spelling Dijkstra correctly until someone pointed out “It’s just D, followed by i-j-k, then stra”. Once it was pointed out that i-j-k is represented sequentially in alphabetical order, spelling Dijkstra becomes trival - almos...

Convolutional Neural networks (CNNs) have been found to be very effective at tasks such as facial recognition, video analysis, anomaly detections and semantic parsing. An image can be considered a graph with a very regular structure (i.e., pixels...

Markov Chain Monte Carlo (MCMC) methods can be used to estimate the parameters of linear regression models. In this post, the distributional forms and algorithms associated with two Gibbs sampling approaches are outlined: the full conditionals ap...

I recently became interested in GeoHashing, and wanted to develop an understanding of the algorithm with the goal of implementing it myself. I was surprised to find it to be quite simple and intuitive. In what follows, I’ll demonstrate how to ge...

The Discrete Fourier Transform (DFT) turns a data vector into a sum of sine/cosine components. The DFT is a Fourier series on data instead of analytic functions. Why do we perform the DFT? Because the features typically of interest aren’t always...

I recently became interested in GeoHashing, and wanted to develop an understanding of the algorithm with the goal of implementing it myself. I was surprised to find it to be quite simple and intuitive. In what follows, I’ll demonstrate how to ge...

An analysis may require the ability to generate correlated random samples. For example, imagine we have monthly returns for three financial indicators over a 20 year period. We are interested in modeling these returns using parametric distributio...

Bessel’s correction is the use of instead of in the sample variance formula where is the number of observations in a sample. This method corrects the bias in the estimation of the population variance. Recall that bias is defined as: where r...

This post is intended to shed light on why the closed form solution to linear regression estimates is avoided in statistical software packages. But we start by first by deriving the solution to the normal equations within the standard multivariat...