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Mapping between two Gaussians using optimal transport and the KL-divergence
Suppose you have two multivariate Gaussian distributions \( S\) and \(T\), parameterized as \( N(\mu_S, \Sigma_S)\) and \( N(\mu_T, \Sigma_T)\). How do…
Jul 16
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Calvin McCarter
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Mapping between two Gaussians using optimal transport and the KL-divergence
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Computing the product of Gaussian distributions
Suppose you have \(K\) multivariate Gaussian distributions, each of dimensionality \(N\). It turns out that the product of these distributions, after…
Jul 16
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Calvin McCarter
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Computing the product of Gaussian distributions
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A visual exploration of the softmax function
The softmax function \(\sigma(\mathbf{z})\) maps vectors to the probability simplex, making it a useful and ubiquitous function in machine learning…
Jul 16
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Calvin McCarter
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A visual exploration of the softmax function
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Many imagine that the psychology of advertising is a modern discovery
What follows is an excerpt from Albert Jay Nock’s 1918 essay, Advertising and Liberal Literature. Nock describes how the London Mercury, founded in 1682…
Jul 2
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Calvin McCarter
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Many imagine that the psychology of advertising is a modern discovery
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June 2023
The future of AI and personal servers
A fascinating exchange happened on the latest All In podcast: the besties started talking about personal servers as the future architecture of AI…
Jun 19
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Calvin McCarter
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The future of AI and personal servers
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April 2023
The greatest hope is memory
The educated man, as some still think, is one whose existence is not isolated in the present, whose intellectual and emotional life is consciously…
Apr 30
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Calvin McCarter
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The greatest hope is memory
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March 2023
Thoughts on the future of 3d printing
I'm pretty bullish on 3d printing. This bullishness seems to be spreading, with recent articles in the Wall Street Journal and The Guardian proclaiming…
Mar 26
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Calvin McCarter
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Thoughts on the future of 3d printing
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Bailouts without the moral hazard
Nathan Tankus recently wrote about the quandary faced by central banks and regulators. The essential problem is that when the government saves the…
Mar 20
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Calvin McCarter
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Bailouts without the moral hazard
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February 2023
Leonard Cohen's Avalanche is a song about Earth
The mysterious, haunting lyrics to Avalanche by Leonard Cohen have received a variety of interpretations. The speaker of the song is said to be a…
Feb 25
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Calvin McCarter
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Leonard Cohen's Avalanche is a song about Earth
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December 2022
Peer review worsens precision but improves recall
I think Adam Mastroianni has done a fine job critiquing peer review as a barrier to entry and as a service to paper-readers, but that's not how it…
Dec 29, 2022
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Calvin McCarter
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Peer review worsens precision but improves recall
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Gradient approximations in derivative-free optimization
Most of modern ML is heavily reliant on gradient descent and its variants. We have some loss function we want to minimize; if the loss function we…
Dec 23, 2022
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Calvin McCarter
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Gradient approximations in derivative-free optimization
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Should power go to the people who want it?
In a philosophical moment after Twitterers voted for his ouster, Elon Musk tweeted, “Those who want power are the ones who least deserve it.” Musk’s…
Dec 22, 2022
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Calvin McCarter
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Should power go to the people who want it?
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