Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
In causal inference, it is often important to study varying treatment effects: for example, a treatment could be more effective for men than for women, or for healthy than for unhealthy patients. Suppose a study is designed to have 80% power to detect a main effect at a 95% confidence level. Further suppose that…
Numerical Optimization is one of the central techniques in Machine Learning. For many problems it is hard to figure out the best solution directly, but it is relatively easy to set up a loss function that measures how good a solution is - and then minimize the parameters of that function to find the solution.
Lambda Screen allows you to draw images using terms of pure lambda calculus. By using fixed-point combinators, you can even create infinitely detailed fractals.
See also Frequentism and Bayesianism: A Python-driven Primer , a peer-reviewed article partially based on this content.
The Game of Life is based on very simple rules, but artificial neural networks struggle to learn its rules through the classic deep learning training process.
This is a tale of two approaches to regular expression matching. One of them is in widespread use in the standard interpreters for many languages, including Perl. The other is used only in a few places, notably most implementations of awk and grep. The two approaches have wildly different performance characteristics:
Michael Gove, the UK’s Secretary of State for Education, has expressed a wish to see almost all school pupils studying mathematics in one form or another up to the age of 18. An obvious quest…
A global pandemic, apocalyptic fires, and the possible descent of the US into violent anarchy three days from now can do strange things to the soul. Bertrand Russell—and if he’d done no…
This is the first part of a series of posts on big changes for SymPy with particular focus on speed. What I am going to describe in these posts are:
At Meta, research permeates everything we do. We believe the most interesting research questions are derived from real world problems.
I have a side project to find the longest line of sight on the planet 1 using a novel Total Viewshed algorithm . At a resolution of 3 arc-seconds (~92m x 92m), the planet contains around 4.5 billion elevation samples 2 . Now obviously we don’t need to calculate the visibility between literally every single one of…
The fun of owning rural property is that knowing where your land actually starts and ends is a guess usually. Sure, you have a parcel description, and maybe even an online service with “official” GIS boundaries (for us here in New Brunswick, this is GeoNB ). However, since it’s in the middle of the forest, the odds of…
At least a familiarity with the lambda calculus, including how it is evaluated. Some base knowledge of programming languages is also assumed.
Originally developed by Aristid Lindenmayer in 1968, an L-System is a formalism to generate self-similar structures. Although, L-Systems are capable of generating famous fractals like the Sierpinski Triangle (Axiom: FXF--FF--FF, F → FF , X → --FXF++FXF++FXF-- , angle = 60 ) or the Gosper Curve (Axiom: FX, X →…
Generative Adversarial Networks refer to a family of generative models that seek to discover the underlying distribution behind a certain data generating process. This distribution is discovered through an adversarial competition between a generator and a discriminator. As we saw in an earlier introductory post on…
These remarks from “THE GENERAL AND LOGICAL THEORY OF AUTOMATA” 1947 are enormously insightful – no surprise. Von Neumann essentially predicts the emergence of the field of analysis of algorithms and algorithmic complexity. Not only does he point out the importance of understanding how many steps it will take to carry…
Note: this post was written for Lean 3; the latest version, Lean 4, is a very different language. Turn back the clock to 2009: a confused physics major newly infatuated with math and computer science, I enrolled in MATH 273: Numbers and Proofs at the University of Calgary. This wasn’t my first encounter with…
How a bit of algorithm engineering and low-level details can alter what seems like a straightforward trade-off on a blackboard.
Singular Value Decomposition (SVD) is a fundamental concept in linear algebra, and it is particularly important in the field of machine learning for tasks such as dimensionality reduction, data compression, and noise reduction.
Memories from Oxford days Mathematical Institute src Peter Neumann, Professor of Mathematics at Queen’s College, Oxford University, passed away two weeks ago. Last Monday would have been his …
In 2005 Google showed off Google Maps, which lets you drag the map around instead of reloading the page like MapQuest and others used. That’s the feature that got everyone’s attention. But what got my attention was a feature they added in 2007 where you could drag the start/end points on a route [1] , and it would…
Goodhart's Law is useless. It tells you about a phenomenon, but it doesn't tell you how to solve it. We look at how organisations actually prevent Goodhart's Law, and illustrate this with Amazon's Weekly Business Review as an example.
Optimizing a math expression parser for speed and memory.
I haven't been blogging recently because my new startup is taking up all my time, but someone needs to stand up and say the emperor has no c...
Cistercian numerals were invented by the Cistercian order of monks in the 13th century. Giuseppe Frisella explains how the notation system works: A vertical str
(I've been editing this post on and off for almost a year. I'm not really happy with it, but I suspect I never will be.)
I’m sure that some pictures are worth a thousand words, but others trigger a whole lot of puzzlement. Such was the case with the cover of a book I recently bought entitled Calculating with Tones: The Logarithmic Logic of Music:
