Eccentricity of bivariate normal level sets
Suppose you have a bivariate normal distribution with correlation ρ where Then the level sets of the density function are ellipses, and the eccentricity e of the ellipses is related to the correlation ρ by Plots For example, suppose ρ = 0.8. Here’s a plot of the density function f(x,
Read moreGoodbye etcd, Hello PostgreSQL: Running Kubernetes with an SQL Database
How to replace etcd — the brain of a Kubernetes cluster — with PostgreSQL or any other RDBMS you wantContinue reading on Better Programming »
Read moreHow to Use LangChain’s Output Parser to Tame the Language Model Output
Photo by Digital Content Writers India on UnsplashI have been using Langchain’s output parser to structure the output of language models. I found it to be a useful tool, as it allowed me to get the output in the exact format that I wanted.In this article, I will share my experience of
Read moreBuild AI Systems Capable of Achieving Any Objective With GPT-4
Image by DALL-E 2The primary issue I’ve encountered while coaxing GPT-4 to handle tasks of increasing complexity lies in determining whether the AI’s method is correct. For instance, while tasking GPT-4 with deploying an Infrastructure as Code project, it may repetitively get entangled in setting up AWS credentials, led astray by
Read moreMemory Optimization and Garbage Collector Management in Go
Managing the garbage collector in Go, optimizing memory consumption in applications, and protecting against out-of-memory errorsHello, my name is Nina Pakshina, and I work as a Golang developer at an online grocery delivery service. In this article, I will discuss managing the garbage collector in Go, optimizing application memory consumption,
Read moreModern Software Engineering – Part 3: Documentation
“I have only made this letter longer because I have not had the time to make it shorter.” – Blaise PascalContinue reading on Better Programming »
Read moreBounds on the incomplete beta function (beta CDF)
The incomplete beta function is defined by It is called incomplete because the limit of integration doesn’t necessarily run all the way up to 1. When z = 1 the incomplete beta function is simply the beta function discussed in the previous post [1]. The incomplete beta function is proportional
Read moreUpper and lower bounds on the beta function
The beta function B(x, y) is defined by and is the normalizing constant for the beta probability distribution. It is related to the gamma function via The beta function comes up often in applications. It can be challenging to work with, however, and so estimates for the function are welcome.
Read morenth root of n!
Last week the function came up in a blog post. as the solution to the equation n! = bn. After writing that post I stumbled upon an article [1] that begins by saying, in my notation, The function b(x) … has many applications in pure and applied mathematics. The article mentions a
Read moreActivation functions and Iverson brackets
Neural network activation functions transform the output of one layer of the neural net into the input for another layer. These functions are nonlinear because the universal approximation theorem, the theorem that basically says a two-layer neural net can approximate any function, requires these functions to be nonlinear. Activation functions
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