JHonaker
Joined 12 years ago
Joined 12 years ago
1. Things that are the result of a very large number of small perturbations follow a Gaussian distribution.
1a. Word embeddings are the result of millions/billions/trillions of small perturbations (i.e. gradient descent)
2. As you increase the dimension, d, of a multivariate Gaussian distribution, the actual mass of the data is increasingly concentrated in the thin spherical shell. For MVN distributions with standardized marginal dimensions, this is on the sphere of radius \sqrt{d}.
In fact when I searched "Gaussian curse of dimensionality" I got this at the top result: [1] which shows this phenomena perfectly. Or this one with pretty interactive pictures [2]
[1]: https://www.miryusupov.com/blog/posts/thin-shells/index.html
[2]: https://aseemrb.me/blog/high-dimensional-gaussians-on-a-sphe...
What exactly do you mean by this? Speed? Portability? Ease of use?
I really do think it’s a good idea to explore! Sometimes I feel crazy because I’m the only one in my department that prefers to just write SQL to deal with our DBs instead of fiddling with a python/R connector that always has its own quirks.
However, I don't see what the benefits of this are (other than having a simple DSL, but that creates the yet another DSL problme) over ggplot2. What do I gain by using this over ggplot2 in R?
The only problem, and the only reason I ever leave ggplot2 for visualizations, is how difficult it is to do anything "non-standard" that hasn't already had a geom created in the ggplot ecosystem. When you want to do something "different" it's way easier to drop into the primitive drawing operations of whatever you're using than it is to try to write the ggplot-friendly adapter.
Even wrapping common "partial specificiations" as a function (which should "just work" imo) is difficult depending on whether you're trying to wrap something that composes with the rest of the spec via `+` or via pipe (`|>`, the operator formerly known as `%>%`)
Fuck Parkinson's.
The pain points around getting a sampler/model pairing working in a reasonable timeframe is definitely a valid complaint. In my experience, inference methods in Bayesian stats are much less forgiving of poorly specified models (or said another way, don’t let you get away with ignoring important structural components of the phenomena of interest). A poorly performing model (in terms of sampler speed/mixing) is often a sign of a problem with the geometry of the parameter space. Frustratingly this can sometimes be a result of conceptually equivalent, but computationally different parameterizations (e.g. centered vs non-centered multi level effects).
The struggles are worth it IMO because it is helpful feedback that helps guide design, and the ease with which I can compute meaningful uncertainty bounds on pretty much any quantity of interest is invaluable.
I also recommend Gelman’s (one of the authors of the linked book) Regression and Other Stories as a more approachable text for this content.
Think Bayes and Bayesian Methods for Hackers are introductory books from a beginner coming from a programming background.
If you want something more from the ML world that heavily emphasizes the benefits of probabilistic (Bayesian) methods, I highly recommend Kevin Murphy’s Probabilistic Machine Learning. I have only read the first edition before he split it into two volumes and expanded it, but I’ve only heard good things about the new volumes too.
Outside of the UI/UX issues it's a great idea, and I would probably play all the levels if those were fixed.