Cory McCartan

@corymccartan

Asst. Prof. of Statistics & Political Science at Penn State. I study stats methods, gerrymandering, & elections. Founder of UGSDW and proud alum of HGSU-UAW L. 5118. 🏳️‍🌈 corymccartan.com

266 Siguiendo678 Seguidores222 Publicaciones

Bluesky

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Cory McCartan@corymccartan· 9d

We also show random tree features have similar uncertainty quantification to full BART, despite not learning the tree structure

Cory McCartan@corymccartan· 9d

Enough theory—does this work in practice? We show random tree features are competitive with full BART, random forests, and xgboost, and lie along the Pareto frontier of accuracy & computation

Cory McCartan@corymccartan· 9d

Turns out (with some conditions) you only need n^(1/3) trees to achieve the optimal learning rate! Notably this rate is faster than existing rates for BART theory, which suffer from the curse of dimensionality* *not quite this simple, but basically

Cory McCartan@corymccartan· 9d

OK, but this is for infinitely many trees, right? What do we do in practice? We propose "random tree features," which are a BART model where the tree structure isn't learned

Cory McCartan@corymccartan· 9d

We can characterize the RKHS (function space) that BART's kernel corresponds to. It lies in between a weak class (just requiring 1 derivative; slow learning rates) and a smooth class (p derivatives; fast-ish rates), and has a nice minimax learning rate that depends only logarithmically on dimension!

Cory McCartan@corymccartan· 9d

The BART kernel is anisotropic, a.k.a. not rotation invariant, which means intuitively it prioritizes main effects over interactions (more about this below)

Cory McCartan@corymccartan· 9d

In fact, we show formally for the first time that as the # trees grows, BART converges to a Gaussian Process with a kernel we can describe in closed form! This means (a) no tree learning happens in the limit, and (b) we can study the kernel to learn things about the types of functions BART learns

Cory McCartan@corymccartan· 9d

We first try knocking out different parts of the BART model to see what matters most. Turns out, at least when you have many trees, it's (mostly) not being Bayesian, nor learning the tree structures, nor even the flexible part of trees per se

Cory McCartan@corymccartan· 9d

New WP w/@melodyyhuang.bsky.social studying the success of BART models, which regularly win causal inference competitions! We argue that BART should be thought of as a random features approximation to a limiting GP. This view helps understand BART & apply it in more places arxiv.org/abs/2607.28844

Seeing the Forest for the Trees: The Gaussian Process Limit of BART

Cory McCartan & Melody Huang

Abstract:
Bayesian Additive Regression Trees (BART) have shown state-of-the-art performance in both prediction and causal inference problems. Previous theoretical work has attempted to explain BART’s superior performance by establishing posterior contraction rates for standard BART models, but these rates depend strongly on the number of covariates. Here, we take a different approach and study the behavior of BART as the number of trees grows towards infinity. We show that in this regime, BART converges to a Gaussian process (GP) with a particular kernel. The kernel and its corresponding reproducing kernel Hilbert space (RKHS) have favorable inferential properties that help explain BART’s excellent performance. We introduce random tree features as an approximation to this limiting GP, and establish minimax-optimal learning rates for ridge
regression on these random features that depend only logarithmically on dimension. In addition to providing insight into the empirical success of BART, random tree features offer a computational benefit over traditional MCMC estimation. The random-features approximation also allows
practitioners to easily incorporate BART into any model which has a linear predictor, expanding the applicability and flexibility of BART.

Cory McCartan@corymccartan· 12d

Out today in the APSR: our paper studying which gerrymandering reforms work! Long story short, do what Michigan does! Slightly longer story: we project these different complex reforms onto a 1-dimensional "partisan leeway" axis, and do continuous-trt DiDiD there. doi.org/10.1017/S000...

Cory McCartan@corymccartan· Jun 22

Had a great time presenting Shiro Kuriwaki's and my new EI methods to EPSS in Belfast on Saturday! Our R package implementing all these methods (as well as partial ID bounds) is also now on CRAN! corymccartan.com/seine/

Cory McCartan@corymccartan· Jun 11

New R package on CRAN! ONNX is a runtime & file format for ML models. 'onnxr' lets you load & run models in about 2 lines of code! E.g. image detection running in ms from a pretrained model. Perfect for embeddings, smaller models, etc. And lots of .onnx available online! corymccartan.com/onnxr/

R code snippet:
library(onnxr)
model = onnx_model(model_path)
res = onnx_run(model, img, simplify = TRUE)

Vermeer's "The Milkmaid" with person, bowls, dining table detected by ML model running via onnxr

Cory McCartan@corymccartan· Jun 3

Roberts court: "the mere fact of racially polarized voting is not relevant to proving racially polarized voting patterns"

The District Court also failed to follow our instruction in Callais that the mere fact that voters of differ-ent races vote for different parties is not relevant to proving racially polarized voting patterns. See id., at ___ (slip op., at 30).

Cory McCartan@corymccartan· May 29

Newly updated simple congressional model (tinyurl.com/cmchousemodel), now with LA map & recalibrated election model fit only to 2026-2024 data! Ds have lost 4 seats on avg to redistricting, but the loss grows to 5.6 seats in a D+6 environment. Ds 98% to win house in a D+6 environment, though

Cory McCartan@corymccartan· Apr 29

The NYT calls it a 'blow' to the VRA, but Thomas and Gorsuch are clear on what the effects of the decision will be: "an end" to the "misadventure" of "roughly proportional representation" for minority groups.

Cory McCartan@corymccartan· Apr 29

The egregious decision in Rucho now lets SCOTUS punch a massive loophole for VRA §2: partisan goals can justify disparate racial impacts. This is about districting, but the same logic would let states resurrect literacy tests, etc. as long as the stated goal was partisan discrimination.

plaintiffs’ illustrative maps must satisfy two conditions: Plaintiffs can-not use race as a districting criterion in drawing illustrative maps, and
illustrative maps must meet all the State’s legitimate districting ob-jectives, including traditional districting criteria and the State’s spec-ified political goals.

Cory McCartan@corymccartan· Apr 22

Time to plug my simple congressional model again, which I've updated with the new VA plan: tinyurl.com/cmchousemodel. Net effect of re-redistricting is D+1.5 seats in tied environment, growing to D+2 seats in a D+10 environment. Bit more competitive map, too.

Cory McCartan@corymccartan· Mar 24

New WP! Philip O'Sullivan, Kosuke Imai, and I generalize an earlier SMC sampler for redistricting plans, allowing it to scale better & be applied to multi-member districts, too, like the Dáil Éireann (Irish parliament) below. Look for a new 'redist' version soon(ish)! arxiv.org/abs/2603.22188

Cory McCartan@corymccartan· Feb 27

v0.2 of `bases` is up on CRAN! `bases` brings nonparametrics into your favorite modeling functions—using random Fourier features is as easy as sticking `b_rff()` into your formula. v0.2 brings graph Fourier & random convolutional features, `mgcv` integration, & more! corymccartan.com/bases/

Example graph Fourier feature on a large lattice graph

Cory McCartan@corymccartan· Feb 13

these people are sick

Cory McCartan@corymccartan· Jan 13

Last fall I shared new methods research with @shirokuriwaki.bsky.social on ecological inference—inferring individual relationships from aggregate data. Our new review WP frames past EI methods as linear models, and argues credible EI requires controlling for covariates arxiv.org/abs/2601.07668

The Role of Confounders and Linearity in Ecological Inference: A Reassessment

Abstract: Estimating conditional means using only the marginal means available from aggregate data is commonly known as the ecological inference problem (EI). We provide a reassessment of EI, including a new formalization of identification conditions and a demonstration of how these conditions fail to hold in common cases. The identification conditions reveal that, similar to causal inference, credible ecological inference requires controlling for confounders. The aggregation process itself creates additional structure to assist in estimation by restricting the conditional expectation function to be linear in the predictor variable. A linear model perspective also clarifies the differences between the EI methods commonly used in the literature, and when they lead to ecological fallacies. We provide an overview of new methodology which builds on both the identification and linearity results to flexibly control for confounders and yield improved ecological inferences. Finally, using datasets for common EI problems in which the ground truth is fortuitously observed, we show that, while covariates can help, all methods are prone to overestimating both racial polarization and nationalized partisan voting.

Cory McCartan@corymccartan· Dec 3

Interestingly, the TX gerrymander doesn't have any net impact in a D+12 environment Plots below show new effect of redistricting this cycle—cf left with the changes vs right if the 3-judge ruling holds

Cory McCartan@corymccartan· Dec 3

Davidson/Nashville swinging D+25 is wild Most swing districts next year won't look the way TN-07 does, with mainly rural counties that are shifting D by less

Cory McCartan@corymccartan· Dec 3

D+10-15 national environment would mean Dems end up ~100 seats over Rs in the House tinyurl.com/cmchousemodel

Cory McCartan@corymccartan· Nov 18

IF it holds, this would net Dems 1.6 seats, on average, due to mid-decade redistricting (D+1 seat in a Dem-favoring environment)

Cory McCartan@corymccartan· Nov 17

Net change in avg. Dem seats by state:

Cory McCartan@corymccartan· Nov 17

D+8.5 (±2) would be 245 Dem seats on average

table showing an average outcome of 245 to 190 under an 8.5 point Dem national environment (tinyurl.com/cmchousemodel)

Cory McCartan@corymccartan· Nov 17

Have updated my simple House model spreadsheet with currently enacted districting plans. Net effect is R+0.4 seats on average (!), with actually a _Dem_ advantage past a D+8 national environment. Copy, edit, & explore for yourself: tinyurl.com/cmchousemodel

Cory McCartan@corymccartan· Nov 5

NYC precinct map: Mamdani now vs the primary Purple = relative improvement vs primary Orange = relative loss vs primary (e.g. GOP voters) Takeaway? Mamdani improved significantly with Black voters since June! We see this in EI estimates as well: Mamdani likely won Black voters ~ 52/43 vs Cuomo

Cory McCartan@corymccartan· Nov 5

Precinct-level NYC data: Mamdani exceeded our voterfile-based expectations, Cuomo slightly exceeded them; Sliwa fell way behind, especially in places he was expected to do well!