Dr. Alexander

The Silent Myjority

The FWS Scot judgement has permanently eroded my trust of the judiciary. The fact that a minority could lose their human rights without even getting to represent themselves is obscene.

My latest score, 0.0025.

I don't mean to spam this but it's a lot of fun. This is my 4th try, the previous was 0.0037. I think it's something you can improve on ?

My second try at the test, giving a score of 0.0039.

Woot!

My "∆E_OK JND" score of 0.0052. The 0.0052 is in a green-blue shade against black background; the website gives me a chance to try again.

Shades of red were easy to distinguish, it was greens where I was really getting tripped up on.

“Whosoever is born out of the Jurisdiction of the law can not [sic] have real Actions or other helps by the law.”

Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which additionally encode dependence across univariate marginals, have received less attention and pose computational and statistical challenges. In this work, we address these challenges with a new regression approach for multivariate distributional responses, in which distributions are modeled within the semiparametric nonparanormal family. By incorporating the nonparanormal transport (NPT) metric -- an efficient closed-form surrogate for the Wasserstein distance -- into the Fr\'echet regression framework, our approach decomposes the problem into separate regressions of marginal distributions and their dependence structure, facilitating both efficient estimation and granular interpretation of predictor effects. We provide theoretical justification for NPT, establishing its topological equivalence to the Wasserstein distance and proving that it mitigates the curse of dimensionality. We further prove uniform convergence guarantees for regression estimators, both when distributional responses are fully observed and when they are estimated from empirical samples, attaining fast convergence rates comparable to the univariate case. The utility of our method is demonstrated via simulations and an application to continuous glucose monitoring data.

arXiv📈🤖
Fr\'echet regression of multivariate distributions with nonparanormal transport
By Park, Gaynanova

“Then, everything changed when the Fire Nation attacked”—CNN Fire Nation affiliate station

The Willy Wonka Ground Beef Fundraising Lottery

The York reviews which uniformly found positive or neutral effects, but even contemporaneously were lied about by anti-trans cranks. But go figure they wouldn't double-dip on the lying, and instead this time simply brush it under the table.

The bombing of Iranian children is an unforgivable crime America has blood on its hands.

New in PN: The bombing of Iranian children is an unforgivable crime

"American disinterest in the lives of people abroad is a resource politicians use to justify cynical wars. It's hard to see on what moral grounds we claim a right to decide the fate of those about whom we clearly care so little."

Thank you!

I'm proud of all the work I've done. When I finish my dissertation, I'll post about that too, and will be happy to share the final document with anyone who wants to read it.

I've not prepared simulations for it yet, but I do know that my implementation of "backsolve" and "forwardsolve" (functions for solving triangular systems of equations, for upper triangular and lower triangular matrices, respectively) are faster than R's native implementations.

Comparison of Cholesky factor updates between "fastchol" R package and competing R implementations. (top left) Cholesky decomposition, in base R and Rcpp (the latter of which "fastchol" provides a wrapper for); (bottom left) triangular matrix transpose; (top middle) "cholup": rank-1 Cholesky update, i.e. the Cholesky factor of matrix M + xx', provided the Cholesky factor for M is known; (bottom middle) "choldown": rank-1 Cholesky downdate, i.e. the Cholesky factor for M - xx', provided that matrix is symmetric positive definite; (top right) "choldrop": Cholesky update after dropping the middle row/column from matrix M; (bottom right) "choladd": Cholesky update after inserting a row/column in the middle of matrix M, such that updated M is symmetric positive definite. Methods with subscript "U" utilize upper Cholesky factors, and methods with subscript "L" utilize lower Cholesky factors; "fastchol" implements both. In all cases, "fastchol" is faster than other R implementations, which include "ramcmc" package (cholup, choldown; L factor only), "fastmatrix" package (cholup; U factor only), "ukfRcpp" package (cholup, choldown; L factor only), "mgcv" package (cholup, choldown, choldrop; U factor only), and "spStack" package (cholup, choldrop; L and U factors). "fastchol" implements updates for both L and U factors for all operations, and is the only package to implement a "choladd" functionality, i.e. an inverse of "choldrop". Median run times over 50 iterations (Cholesky decomposition) or 200 iterations (everything else). All "fastchol" operations tend to be as fast as dedicated triangular matrix transpose, except for "choladd", which is as fast as naive matrix transpose. Not shown, "choladd" is faster when the index to insert the row/column is close to the first/last index, and is slowest for the middle index, as graphed. L updates are generally faster than U updates due to superior cache efficiency.

Most recently, to support my last project (on causal inference in single-cell data), I've written a package "fastchol" which implements a comprehensive, state of the art library of Cholesky operations, including low-rank updates/downdates, row/column deletion/insertion, and triangular solvers.

I also have a few R packages which I've published. The JOSS paper is about my "fastfrechet" package, which implements a faster version of what the AOAS paper describes. I also have a "distQTL" package which integrates distributional regression for eQTL finding in scRNA-seq data.

3. "distQTL: distribution quantitative trait loci identification by population-scale single-cell data", NAR GENOMICS AND BIOINFORMATICS (2025). DOI: 10.1093/nargab/lqaf155.

Link with PDF download available:
academic.oup.com/nargab/artic...

fastfrechet: An R package for fast implementation of Fréchet regression with distributional responses Coulter et al., (2025). fastfrechet: An R package for fast implementation of Fréchet regression with distributional responses. Journal of Open Source Software, 10(109), 7925, https://doi.org/10.21105/...

2. "fastfrechet: An R package for fast implementation of Fréchet regression with distributional responses", JOURNAL OF OPEN SOURCE SOFTWARE (2025). DOI: 10.21105/joss.07925.

Link with PDF download available:
joss.theoj.org/papers/10.21...

Fast variable selection for distributional regression with application to continuous glucose monitoring data With the growing prevalence of diabetes and the associated public health burden, it is crucial to identify modifiable factors that could improve patients’ glycemic control. In this work we seek to examine associations between medication usage, concurrent comorbidities, and glycemic control, utilizing data from continuous glucose monitors (CGMs). CGMs provide high-frequency interstitial glucose measurements, but reducing data to simple statistical summaries is common in clinical studies, resulting in substantial information loss. Recent advancements in the Fréchet regression framework allow to utilize more information by treating the full distributional representation of CGM data as the response, while sparsity regularization enables variable selection. However, the methodology does not scale to large datasets. Crucially, rigorous inference is not possible because the asymptotic behavior of the underlying estimates is unknown, while the application of resampling-based inference methods is computationally infeasible. We develop a new algorithm for sparse distributional regression by deriving a new explicit characterization of the gradient and Hessian of the underlying objective function, while also utilizing rotations on the sphere to perform feasible updates. The updated method is up to 10,000+ fold faster than the original approach, opening the door for applying sparse distributional regression to large-scale datasets and enabling previously unattainable resampling-based inference. We combine our algorithm with stability selection to perform variable selection inference on CGM data from patients with type 2 diabetes and obstructive sleep apnea. We find a significant association between sulfonylurea medication and glucose variability without evidence of association with glucose mean. We also find that overnight oxygen desaturation variability has a stronger association with glucose regulation than overall oxygen desaturation levels.

1. "Fast variable selection for distributional regression with application to continuous glucose monitoring data", ANNALS OF APPLIED STATISTICS (2025). DOI: 10.1214/25-AOAS2038.

Link with PDF download available:
projecteuclid.org/journals/ann...

I've published a few papers while here. I'm proud of each one, and if people want to read them, please enjoy below :)

Last week, I successfully passed my statistics PhD dissertation defense 🎉 I've got a bit more to finish writing up for my dissertation document itself, but I will be graduating in May. It's been a good time at Texas A&M, political interference from right wing agents ("regents" etc.) notwithstanding.

Basically dictating that Iran must immediately become a client state without any autonomy.

Maybe this would not disrupt some of these philosophers’ thoughts, but I’m not going to muse for them on how to understand causal idleness.

In the setting of realistic light-wave behavior, the philosophical problem would arise from boundary causal behavior on our perceptions, not on boundary causal idleness with respect to light itself. Near can causally interact with light, but it’s below our perceptive abilities.

After all the heart of the conundrum isn’t whether or not something can occlude another, or the conditions that must be satisfied to do so, but the meaning of “seeing” something when a certain form of occlusion is on the “boundary” of ray-tracing geometric frameworks.

No, but again the philosophical problem of "which do we see?" only arises in idealized non-wave settings anyway, where there is a clean sense in which things perfectly occlude others and are no larger or smaller than necessary to do that.

For the unrealistic simple case, here's my thoughts on what is perceived, and the issue with defining something "simple" when it actually requires information auxiliary to perception.
bsky.app/profile/etot...

*a visible Poisson spot

Suffice to say, including a secondary occluder Near which geometrically fits into the shadow of Far would, in fact, contribute additional interference to the diffraction pattern behind Far for real light, hence removing Near would also be perceptible.

Here's a paper that goes through the math, and also discusses why realistic objects like the Moon are not smooth enough to produce a visible sunspot. (However, the diffraction problems, i.e. that nothing is a perfect occluder, still apply.)

arxiv.org/pdf/2408.138...

This is only a philosophical problem in the unrealistic simple characterization of photons as particles which are wholly blocked, or not.