Oran Looney's personal blog about math, programming, machine learning, and data visualization.
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Here’s a fact: GPT-4o charges 170 tokens to process each 512x512 tile used in high-res mode. At ~0.75 tokens/word, this suggests a picture is worth about 227 words—only a factor of four off from the traditional saying. (There’s also an 85 tokens charge for a low-res ‘master thumbnail’ of each picture and higher…
To kick off this series, will start with something simple yet foundational: linear regression via ordinary least squares. While not particularly exciting, linear regression finds widespread use both as a standalone learning algorithm and as a building block in more advanced learning algorithms.
In this second installment of the machine learning from scratch we switch the point of view from regression to classification: instead of estimating a number, we will be trying to guess which of 2 possible classes a given input belongs to. A modern example is looking at a photo and deciding if its a cat or a dog.
In the previous article in this series we distinguished between two kinds of unsupervised learning (cluster analysis and dimensionality reduction) and discussed the former in some detail. In this installment we turn our attention to the later. In dimensionality reduction we seek a function $f : \mathbb{R}^n \mapsto…