New preprint with Fabrizio Leisen and our PhD student Zhanli Wu:
"Conformalized Regression for Bounded Outcomes"
http://arxiv.org/abs/2507.14023
#rstats #conformal #prediction
R code and data are also available at:
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response associated with a new covariate value. Most of the existing statistical and machine learning literature has focused either on point prediction of bounded outcomes or on interval prediction based on asymptotic approximations. We develop conformal prediction intervals for bounded outcomes based on transformation models and beta regression. We introduce tailored non-conformity measures based on residuals that are aligned with the underlying models, and account for the inherent heteroscedasticity in regression settings with bounded outcomes. We present a theoretical result on asymptotic marginal and conditional validity in the context of full conformal prediction, which remains valid under model misspecification. For split conformal prediction, we provide an empirical coverage analysis based on a comprehensive simulation study. The simulation study demonstrates that both methods provide valid finite-sample predictive coverage, including settings with model misspecification. Finally, we demonstrate the practical performance of the proposed conformal prediction intervals on real data and compare them with bootstrap-based alternatives.
Attention-Worthy Links for December 1st, 2024
#Internet Archive #preservation #universal access #X-59 #delta-style wingspan #conformal #cryptocurrency #FIT21 #Bitcoin Act of 2024 #$100K Bitcoin #freeze-out #freeze-in #Internet #misinformation #curated #paywalls #ARPA-E #lithium #cobalt #ammonia #OpenWrt One #copyleft #802.11ah #T-Halow #Dragon Bridge #two kilometers #Kara-Murza #Siberian penal colony #FSB #appeasement #energy #minerals #food #inadequate #pandemic
... And here Tehora Rogue
explains how we did it!
#badapple #mathart #noneuclidean #RiemannMappingTheoremInAction #conformal #newconformist
🚀 #AWS Fortuna is skyrocketing! 🚀 Just a few days, and so many GitHub stars and forks! ⭐️
Fortuna supports #ConformalPrediction, #BayesianInference and other methods for #UncertaintyQuantification in #DeepLearning.
Try it out and let us know!
https://github.com/awslabs/fortuna
In collaboration with @cedapprox, @andrewgwils and team.
#uncertainty #neuralnetworks #bayesian #conformal #calibration #jax #flax #python #opensource #library #machinelearning #ai
Bad Apple, but rendered with hyperbolic planes!
#badapple #mathart #noneuclidean #RiemannMappingTheoremInAction #conformal #newconformist
Full video: https://youtube.com/watch?v=P9EZy8ZzlVU
Vacuum Forming with 3D Printer Filament
Even if they don't have one themselves, we'd wager the average Hackaday reader is at least vaguely aware of how a vacuum former works on a fundamental level. You heat up a plastic sheet until it's soft, then use a vacuum pump to pull the ductile material down onto an object and hold it there while it cools off. It's easy to build a vacuum forming rig yourself, but small commercial units are cheap enough that it might not be worth your time. If everything goes to plan, the technique is a quick and effective way of duplicating items around the home and shop.
But we were recently tipped off to a variation of this classic technique that's certainly worth further research. As demonstrated in a recent video, [Nathan Martinez] shows how 3D printed sheets can be used in place of the 5″ x 5″ squares of thermoplastic film that his imported vacuum former was designed to use. It's easy enough to do: just model up a square with the appropriate 2D dimensions in your CAD package of choice, and extrude it to a height of about .5 mm.
A printed mesh pattern could be used to form custom shaped filters or strainers.
So what's the advantage? Well for one thing, it's cheaper. Though admittedly, not by much. Going rate on Amazon seems to be about 90 cents per sheet for the real stuff, and some back of the envelope math shows the printed version coming in at around 30 cents given nominal filament costs. Whether or not those savings are worth the extra effort is certainly debatable.
But that's not really the most interesting part. With printed sheets loaded into the vacuum former, you've got access to a much wider array of materials to work with. For example, [Nathan] shows off some very interesting flexible pieces he was able to produce using sheets of TPU. You can also experiment with different surface textures. These can not only be used to give your vacuum formed pieces a bit of interesting visual flair, but could actually have some practical applications. In the video we see how a printed mesh could be formed over a piece to create a conformal air vent or filter.
To be sure, there's some room for improvement here. Not all the pulls were successes, and [Nathan] says getting the printed sheets up to the proper temperature can be tricky. But when it works, it works quite well, and we think there could be some untapped potential in this unexpected melding of new and old methods of at-home plastic production.
[Thanks to Japanfan50 for the tip.]
#3dprinterhacks #classichacks #3dprinterfilament #conformal #mesh #vacuumforming
2次元の定曲率の幾何は局所的に
球面の非ユークリッド幾何
平面のユークリッド幾何
単位円盤もしくは上半平面の非ユークリッド幾何(負定曲率のいつもの計量を入れておく)
のどれかと同型になります。すなわち、普遍被覆(←これは基本群について習ったときに学ぶ決定的に極めて重要な概念、基本群と被覆空間の理論はGalois理論の一種！)はこれらのどれかになる。
平面を格子で割って得られるトーラスが楕円曲線です。
一般にコンパクトRiemann面は複素代数曲線になるので、代数幾何とも繋がります。
余談：2次元の場合の曲率の概念の整備はGaussさんがやってくれました。
昔風の曲面論について学べば、第一基本形式、第二基本形式、平均曲率とGauss曲率についてやって、Gauss曲率が第一基本形式(のちにRiemann計量と呼ばれるようになるもの)だけで書けること(Gauss驚愕の定理)を学びます。そして単に曲率と言えばGauss曲率を意味するようになる。
多くの数学が以上で述べたような2次元のケースの一般化になっています。
大体において $n$ が一般の場合をいきなり最初からやるのは「なまいき」過ぎることが多い。
$n=1$ の場合、$n=2$ の場合、$n=3$ の場合、……と続けて言って、詰まったら、「易しい」一般の $n$ の場合に「逃げる」という感じの方が、理解が深まる場合が多いと思います。
上で述べた長さだけを変えて、角度を変えない話(共形幾何の話)も $n$ が小さな方から順番にやってみるべきです。
$n=1$ の1次元の場合には任意の計量は座標
$x=x^1$ と取るとき、$$
ds^2 = a(x)^2 dx^2
$$と書ける。
実はその次の $n=2$ の2次元の場合は大変面白い話になります。
様々な分野が交差する多くの数学の模範とされている世界が現われます。
共形構造と複素構造の一致、共形同値な計量の中から定曲率なものを選べること、それによって2次元世界を正定曲率正・零曲率・負低曲率の3つに分類できること、コンパクトRiemann面の場合には定曲率の正負はRiemann面のトポロジーで決まることなどなど。
ƧƿѦςɛ♏ѦਹѤʞ
F. Javier Rubio
John Vaccaro (johniac)
Zeno Rogue
Gianluca Detommaso
hackaday unofficial
黒木玄 Gen Kuroki