conjugate

I am not willing to sit through a 49 minute video, but skimming through it suggests that the idea is to have some sort of class that represents a word and autogenerate methods to conjugate the words. I think.

Keep track of your gradient changes when using either gradient descent or conjugate gradient. Plot your filters, visualize what each neuron is learning.

A teacher ought to be able to, at minimum conjugate "to be" correctly, especially when addressing a public meeting! A complete embarrassment.

Nowadays you whippersnappers complain when scipy doesn't have a built in heat equation solver, and you are forced to manually write conjugate gradient."

This idiom is common in mathematics, where it's called a conjugate. Any time you have an element, y, of a group, the action of pre-composing with any other element, x, and post-composing with x's inverse to get xyx^{-1} is called conjugating, and the result is a called a conjugate of y.

Teaching kids about how to conjugate Latin verbs or some other rote activity always seemed pointless to me. Perhaps I'm preaching to the choir, but learning about entrepreneurship or practicing selling things would have been much more useful to me than many of the things I learned in high school or undergrad.

The gamma distribution is the first choice of distribution because it is the conjugate prior for the exponential distribution. For the Pareto/NBD it means that we can write the likelihood function without having to use quadrature to solve the integral.

It's easier in many respects to romance languages because when conjugating verbs you don't have to also conjugate possessive personal pronouns which you do with most other languages of European origin. And yet, in my opinion, it is more expressive than languages such as Chinese which don't have proper pronouns at all.

You can often work around that with a carefully chosen pre-conditioner, but you're rapidly going down a rabbit hole that takes you away from the extreme simplicity of conjugate-gradient.

If you're interested in some techniques people have been using, I highly suggested you read up on optimization methods such as conjugate gradient and hessian-free optimization. I did this recently [0] and have a brief write-up, but honestly the original Martens paper may be more understandable [1].

If you combine this property with a bayesian analysis, and put a conjugate prior on the parameters of an exponential family distribution, then the posterior distribution, and the marginal likelihood depend upon on the data only through these sufficient statistics and everything else is easily computed. in this form, one of the sufficient statistics often has an interpretation as a "pseudo-count"; how many effective samples are encoded in your prior?

Saying "conjugate prior" or "shape parameter" is going to put you out of reach of anyone who isn't a practiced statistician. I'd aim somewhere in the middle. Technical people who aren't afraid of following a well-outlined, mathematical description of a problem they encounter regularly. "Why a gamma distribution?" would be a good footnote, for example, linking to a paper or another blog post of yours that explains it in more detail. I find the articles that do the best are ones which take a somewhat-complicated topic and explain it, step-by-step, to an intelligent, technical audience. Pretend you were giving a lecture to a room full of HN members -- all technical and versed in basic mathematics, but not practiced statisticians. Write something that is not just a one-off, but could serve as reference material months and years from now. I'm probably at the upper-end of this target audience in terms of mathematical maturity, in the sense that when you say "conjugate prior" I know what you mean but can't remember the definition off the top of my head. However, I could look it up and understand it instantly. I'd have a harder time understanding why being the conjugate prior of the exponential distribution implies that the gamma distribution is well-suited for modeling customer behavior on an e-commerce site.