Lihua Lei Profile picture
Mar 2 6 tweets 3 min read
🚨Job talk thread🚨

Title: What Can *Conformal Inference* Offer to Statistics?

Slides: lihualei71.github.io/Job_Talk_Lihua…

Main points:
(1) Conformal Inference can be made applicable in many #stats problems
(2) There are lots of misconceptions about Conformal Inference
(3) Try it!

1/n
Conformal Inference was designed for generating prediction intervals with guaranteed coverage in standard #ML problems.

Nevertheless, it can be modified to be applicable in

✔️Causal inference
✔️Survival analysis
✔️Election night model
✔️Outlier detection
✔️Risk calibration

2/n
Misconceptions about conformal inference:

❌ Conformal intervals only have marginal coverage and tend to be wide
✔️ Conformal intervals w/ proper conformity scores achieve conditional coverage & efficiency (short length) if the model is correctly specified

3/n
Misconceptions about conformal inference:

❌ Conformal inference is slow
✔️ Split conformal inference incurs almost negligible computational overhead (nearly as fast as the algorithm it wraps around)

4/n
Misconceptions about conformal inference:

❌ Conformal inference can’t be used with Bayesian procedures
✔️ Conformal inference can not only wrap around Bayesian methods, but also achieve the validity (w/ a simple adjustment) in both Bayesian and Frequentist sense.

5/n
I’m so proud that my job talk convinced many folks to read more about Conformal Inference. There are tons of exciting methodological questions (distribution shifts, dependence, conditional coverage, …) and real-world applications.

It’s a very🔥area now! Come and join us!

6/6

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More from @lihua_lei_stat

Feb 14
A thread on BUE & BLUE🔥

Gauss-Markov condition:
1) y=Xβ+ε
2) E[ε|X]=0
3) Cov(ε|X)=σ^2Σ

Standard GM:
4) Σ=I

The GM thm shows that OLS/GLS is BL(inear)UE.

Hansen (’20) shows it holds for all unbiased est (inc. nonlinear) w/ an elegant proof (tilted density + Cramer-Rao)

1/n
Call F_2 & F_2^0 the classes of dists satisfying 1-3 & 1-4.
Hansen proves if \hat{β} is unbiased under F_2 for all Σ, then GLS (OLS) is BUE under F_2 (F_2^0).

An intriguing Q. raised by @jmwooldridge & @CavaliereGiu is

Does there exist nonlinear unbiased est under F_2?

2/n Image
Turns out no nonlinear est can be unbiased under F_2!

This can be proved using a deep result by Koopmann (’82) and restated in Gnot et al. (’92)

tandfonline.com/doi/abs/10.108…

Roughly speaking, an estimator that is unbiased under F_2 w/ a fixed Σ must be linear+quadratic.

3/n Image
Read 6 tweets

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