1021
Machine Learning 101: What Is Regularization?
Posts and writings by Datanice
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
1022
When gradient descent is a kernel method
Suppose that we sample a large number N N N of independent random functions f i : R → R f_i \colon \R \to \R f i : R → R from a certain distribution F \Fc F and propose to solve a regression problem by choosing a linear combination f ˉ = ∑ i λ i f i . \bar{f} = \sum_i \lambda_i f_i. f ˉ = i ∑ λ i f i . For…
1023
Writing a Faster Sorting Algorithm
These days it’s a pretty bold claim if you say that you invented a sorting algorithm that’s 30% faster than state of the art. Unfortunately I have to make a far bolder claim: I wrote a …
1024
1025
Introduction to the Fourier transform for image processing (2001)
The definitons of the transform (to expansion coefficients) and the inverse transform are given below:
1026
How many floating-point numbers are in the interval [0,1]?
Most commodity processors support single-precision IEEE 754 floating-point numbers. Though they are ubiquitous, they are often misunderstood. One of my readers left a comment suggesting that picking an integer in [0,232) at random and dividing it by 232, was equivalent to picking a number at random in [0,1). I am not…
1027
Why Y? Deriving the Y Combinator in JavaScript
In this essay, after a brief review of the work we’ve already done on the Mockingbird, we’ll derive the Why Bird, known most famously as the Y Combinator . The why bird provides all the benefits of the mockingbird, but allows us to write more idiomatic JavaScript. We’ll see that one of the benefits of writing…
1028
Game Theory Reveals the Future of Deep Learning
If you’ve been following my articles up to now, you’ll begin to perceive, what’s apparent to many advanced practitioners of Deep Learning…
1029
Is there such a thing as half a derivative?
The original question was: Another one of those questions of the type “does this make sense”. You have first derivatives and second derivatives. f'(x), f”(x) or sometimes dy/dx …
1030
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Graph Isomorphism update: quasipolynomial claim restored
On January 4 I announced that Harald Helfgott pointed out an error in the analysis of my Graph Isomorphism test. The error invalidated my previous claim of quasipolynomial efficiency. The text of the announcement is appended below.
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1035
The Minsky circle algorithm
Consider the following pseudocode: x <- 32; y <- 0; while(true){ x <- x – floor((1/8) * y); y <- y + floor((1/8) * x); plotPointAt(x, y); } x and y are always integers. This draws…
1036
Solving Wordle in 3.64 guesses on average, 99.4% of the time
Hey all, I’ve been enjoying wordle, the puzzle game recently but also wondered how a program might do at it.
1037
Is every game of Slay the Spire winnable?
There is a lot of randomness in a game of Slay the Spire. From the cards and relics offered, to the potions dropped, to the map layouts and random encounters, very little remains the same between two playthroughs. This is part of the beauty of the game, forcing you to adapt and make the most out of the resources you…
1038
Lewis Carroll – computing the day of the week for any given date (1887)
A letter from Lewis Carroll to Nature, March 31, 1887: Having hit upon the following method of mentally computing the day of the week for any given date, I send it you in the hope that it may interest some of your readers. I am not a rapid computer myself, and as I find my average time for doing any such question is…
1039
The New XOR Problem
In 1969, Marvin Minsky and Seymour Papert published Perceptrons: An Introduction to Computational Geometry. In it, they showed that a single-layer perceptron cannot compute the XOR function. The main argument relies on linear separability: Perceptrons are linear classifiers, which essentially means drawing a line to…
1040
Tetris is capable of universal computation
This text presents a method for embedding a programmable, general-purpose, digital computer into Tetris. It describes the capabilities and performance of an implementation that runs Tetris on Tetris.
1041
Reminder of Complexity
An impressive poster summarizing biochemical pathways reminds us how complex life is, and how interconnected the world is.
1042
Modern Image Processing Algorithms Implementation in C
Learn how modern image analysis and processing algorithms works under the hood with their C/C++ implementation on PixLab's APIs & FACEIO, facial recognition framework using the SOD Embedded Computer Vision Library.
1043
A Beginner’s Guide to Eigenvectors, Covariance, PCA and Entropy
The Eclipse Deeplearning4j Project. Eclipse Deeplearning4j has 5 repositories available. Follow their code on GitHub.
1044
Gridlock vs. Bottlenecks: A visual explanation
"Emails show [Chris Cristie]'s aides did plan bridge gridlock," says Salon . To a transportation engineer, the aides are innocent: bridges can't have gridlock. While we often say "gridlock" to mean "bad traffic," it has a technical meaning.
1045
The Mystery of 355/113 (2010)
Today's date is a good excuse to memorize a few more digits of 3.1415926 53589793 23846264 33832795....
1046
The Dying Art of Mental Math Tricks
Mathematics, applications of mathematics to life in general, and my life as a mathematician.
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1048
There Are Magic Hexagons of Every Order
What is so special about the number 19?
1049
Modern Portfolio Theory: A Case Study on Turnips
And how having friends makes the stalk market a lot more profitable.
1050
They say that stocks go down during the day and up at night
Prompted by your blog post this morning, I attach a plot from Figure 3 of They Still Haven’t Told You showing overnight and intraday returns to AIG (with logarithmic vertical scale, updated with data through the end of October).