Messaggi di Rogue Scholar

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MatematicaInglese
Pubblicato in Math ∩ Programming
Autore Jeremy Kun

Last time we investigated the k-nearest-neighbors algorithm and the underlying idea that one can learn a classification rule by copying the known classification of nearby data points. This required that we view our data as sitting inside a metric space; that is, we imposed a kind of geometric structure on our data. One glaring problem is that there may be no reasonable way to do this.

MatematicaInglese
Pubblicato in Math ∩ Programming
Autore Jeremy Kun

Numberphile posted a video today describing a neat trick based on complete sequences: The mathematics here is pretty simple, but I noticed at the end of the video that Dr. Grime was constructing the cards by hand, when really this is a job for a computer program. I thought it would be a nice warmup exercise (and a treat to all of the Numberphile viewers) to write a program to construct the cards for any complete sequence.

MatematicaInglese
Pubblicato in Math ∩ Programming
Autore Jeremy Kun

Problem: Prove there are infinitely many prime numbers. Solution: First recall that an arithmetic progression with difference $ d$ is a sequence of integers $ a_n \subset \mathbb{Z}$ so that for every pair $ a_k, a_{k+1}$ the difference $ a_{k+1} – a_k = d$. We proceed be defining a topology on the set of integers by defining a basis $ B$ of unbounded (in both directions) arithmetic progressions.

MatematicaInglese
Pubblicato in Math ∩ Programming
Autore Jeremy Kun

This post comes in preparation for a post on decision trees (a specific type of tree used for classification in machine learning). While most mathematicians and programmers are familiar with trees, we have yet to discuss them on this blog. For completeness, we’ll give a brief overview of the terminology and constructions associated with trees, and describe a few common algorithms on trees.

MatematicaInglese
Pubblicato in Math ∩ Programming
Autore Jeremy Kun

The Recipe for Classification One important task in machine learning is to classify data into one of a fixed number of classes. For instance, one might want to discriminate between useful email and unsolicited spam. Or one might wish to determine the species of a beetle based on its physical attributes, such as weight, color, and mandible length.

MatematicaInglese
Pubblicato in Math ∩ Programming
Autore Jeremy Kun

A Series on Machine Learning These days an absolutely staggering amount of research and development work goes into the very coarsely defined field of “machine learning.” Part of the reason why it’s so coarsely defined is because it borrows techniques from so many different fields. Many problems in machine learning can be phrased in different but equivalent ways.

MatematicaInglese
Pubblicato in Math ∩ Programming
Autore Jeremy Kun

It’s often said that the Age of Information began on August 17, 1964 with the publication of Cooley and Tukey’s paper, “An Algorithm for the Machine Calculation of Complex Fourier Series.” They published a landmark algorithm which has since been called the Fast Fourier Transform algorithm, and has spawned countless variations.