Fang Han
@johnleibniz
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Not a junior researcher fighting for the space of the Annals of Statistics any more… but hey, every acceptance still deserves a new “bound”.
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Wow, impressive!!! My morning attempt using martingale theory only...
I only knew one proof of the DKW inequality and it's not easy at all ! Nice achievement
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I put it in my book draft:
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My favorite quote of Talagrand (Probability in Banach Spaces, with Ledoux). Talagrand has the magic to turn complex things simple.
The real challenge in VC type theorems, which is usually hidden in learning theory, is the measurability requirement on the studied objects. This is a long-forsaken bug that one you noticed, is hard to get away from.
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This is a fun collaboration, for which I learnt a lot from two coauthors Peng (
@pengding00
) and Zhexiao (
@zzzxlin
). A special shout-out to Zhexiao, who just started his 2nd year PhD study (!).
We revisit the Abadie-Imbens study on nearest neighbor matching and show that, with a diverging number of nearest neighbors, matching estimators can be doubly robust and semiparametrically efficient for estimating the average treatment effect
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Hmmm... 3 AoS papers in one issue; what should I say? congrats to myself 🤪?
Random matrix theory:
Rank correlation:
Variance estimation:
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Rina, Peng (
@pengding00
), Nicole, and I are organizing an IMSI workshop aimed at forging connections between causal inference, distribution-free methods, and probability theory, within the overarching theme of "permutation".
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The dust finally settles: my students Yandi Shen () & Hongjian Shi () will join the stats departments at 𝗖𝗠𝗨 & 𝗪𝗮𝘁𝗲𝗿𝗹𝗼𝗼 as TT ass profs. They're true scholars and I feel fortunate to have worked with them.
#AcademicPride
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If you keep convoluting the same density function but deliberately keep the mean and variance stable, then it will eventually converge to a distribution with the maximum entropy under that mean/variance constraint. CLT is confirming the second law of thermodynamics.
The central limit theorem equivalently reads as the convergence of iterated convolutions.
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This Le Cam-style paper is going to appear in an upcoming issue of 𝗕𝗶𝗼𝗺𝗲𝘁𝗿𝗶𝗸𝗮. The brilliant first author, Yihui, will join stat
@Wharton
in the coming year; yes, he is still an undergrad at math
@PKU
!
Yihui He, Fang Han: On propensity score matching with a diverging number of matches
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This paper is going to appear in a future issue of the Annals of Applied Probability; it gives the limiting distribution of Chatterjee’s correlation when the data are supported over a manifold.
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The paper () now will appear in a future issue of 𝗕𝗶𝗼𝗺𝗲𝘁𝗿𝗶𝗸𝗮. The message is one-line: Chatterjee's rank correlation is root-n consistent, asymptotically normal, but 𝗶𝗿𝗿𝗲𝗴𝘂𝗹𝗮𝗿, and hence bootstrap inconsistent.
Ok, the literature review is done: Beran (1997) showed that in LAN models, bootstrap consistency is equivalent to that the estimator is regular; should be a textbook result IMHO.
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: Our holiday gift to all fans of matching methods: in strong contrast to the common belief, Abadie and Imbens's bias-corrected nearest neighbor (NN) matching actually already gives a doubly robust and semiparametrically efficient estimator of the ATE.
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In 𝗝𝗔𝗦𝗔: nonparametric Poisson mixture, nonparametric MLE, Wasserstein metric, minimax rates, random permutation, ANOVA
Motivated by single-cell genomics and approved by the expert
@weisun2013
!
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This deserves being repeatedly said: Conformal prediction gives marginal instead of conditional coverage, and it rarely works for time series prediction.
What does conformal prediction actually guarantee? I predict it’s not what you want.
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"On the power of Chatterjee's rank correlation" is currently among 𝘁𝗵𝗲 𝗺𝗼𝘀𝘁 𝗿𝗲𝗮𝗱 𝗮𝗿𝘁𝗶𝗰𝗹𝗲𝘀 𝗶𝗻 𝗕𝗶𝗼𝗺𝗲𝘁𝗿𝗶𝗸𝗮; please take a look if interested in measuring functional dependence, Le Cam's method, or rank/permutation statistics.
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Accepted to 𝗕𝗲𝗿𝗻𝗼𝘂𝗹𝗹𝗶. This is the first of a series of papers on Azadkia and Chatterjee's brilliant idea. Its real meat is a new CLT that solves their 2nd conjecture.
A complete storyline can be found in this slide deck:
Hongjian Shi, Mathias Drton, Fang Han: On Azadkia-Chatterjee's conditional dependence coefficient
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We just proved that Chatterjee's rank correlation is asymptotically normal as long as one variable is not a measurable function of the other.
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Ok, the literature review is done: Beran (1997) showed that in LAN models, bootstrap consistency is equivalent to that the estimator is regular; should be a textbook result IMHO.
Peter Bickel just pointed out to me that Hodges's estimator is another example; bootstrap fails then at mu=0 (Beran 1982). It then occurred to me that Andrea Rotnitzky also mentioned that bootstrap consistency is sth about *regular* estimators. Would be nice to see a theory!
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@bbstats
@adad8m
@octonion
@_bakshay
distance correlation is more efficient in testing independence, but is not distribution-free, is sensitive to outliers, and cannot capture perfect dependence (i.e., it is not 1 iff Y is a measurable function of X). Check my Bernoulli news article for more:
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We now improve the rate to n^{-1/2}, the obviously optimal one.
To appear in 𝗜𝗘𝗘𝗘 𝗧𝗿𝗮𝗻𝘀𝗮𝗰𝘁𝗶𝗼𝗻𝘀 𝗼𝗻 𝗜𝗻𝗳𝗼𝗿𝗺𝗮𝘁𝗶𝗼𝗻 𝗧𝗵𝗲𝗼𝗿𝘆. Do check Teh and Polyanskiy's follow-up work, which improved the rate of ours from n^{-1/10} to n^{-1/4} via a smart use of Hadamard’s three-circle theorem.
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I should have added a reference to this tweet: the super impressive Artstein-Ball-Barthe-Naor 2004 JAMS paper. Simply elegant and powerful.
If you keep convoluting the same density function but deliberately keep the mean and variance stable, then it will eventually converge to a distribution with the maximum entropy under that mean/variance constraint. CLT is confirming the second law of thermodynamics.
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The real challenge in VC type theorems, which is usually hidden in learning theory, is the measurability requirement on the studied objects. This is a long-forsaken bug that one you noticed, is hard to get away from.
@vpatryshev
Some probabilists recognized the importance of that work early on, for example Richard Dudley played a big role in spreading awareness of the VC work in the West.
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guess who is a big fan of Leibniz🤪
We are proud to announce that two of our core faculty members recently got promoted to new appointments in UW Statistics. Congratulations to Fang Han and Alex Luedtke for their accomplishments! Read about them at:
@johnleibniz
@aluedtke
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New paper in Biometrika. Nothing particularly technically challenging but, hey, only 16-page long yet with Sourav Chatterjee, Holger Dette, Jaroslav Hájek, Wassily Hoeffding, Jack Kiefer, Lucien Le Cam, Murray Rosenblatt, and many other great statisticians in😍
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Probably worth mentioning: Chatterjee's correlation coefficient is both asymptotically normal and bootstrap INCONSISTENT. I do not recall seeing a second such example except for some artifacts (Bickel&Freedman, 1981?).
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Here is the proof, executed by the magnificent
@zzzxlin
: , where discussion with
@hagmnn
and
@molivarego
on Twitter was acknowledged (and much appreciated!).
Still seeking more examples that are root-n consistent, ASN, but bootstrap inconsistent🤔
Probably worth mentioning: Chatterjee's correlation coefficient is both asymptotically normal and bootstrap INCONSISTENT. I do not recall seeing a second such example except for some artifacts (Bickel&Freedman, 1981?).
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For people that like matching, rank-based statistics, and nonparametric regression with generated covariates🤓 A collaborative work with the awesome Matias and the amazing Zhexiao
@zzzxlin
😍
Matias D. Cattaneo, Fang Han, Zhexiao Lin: On Rosenbaum's Rank-based Matching Estimator
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Here comes the great master: 𝘔𝘦𝘢𝘴𝘶𝘳𝘦𝘴 𝘰𝘧 𝘪𝘯𝘥𝘦𝘱𝘦𝘯𝘥𝘦𝘯𝘤𝘦 𝘢𝘯𝘥 𝘧𝘶𝘯𝘤𝘵𝘪𝘰𝘯𝘢𝘭 𝘥𝘦𝘱𝘦𝘯𝘥𝘦𝘯𝘤𝘦 by Peter Bickel.
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A simpler example is Kendall's tau, for which the U-statistic version is more efficient than the sample-mean version (centralize using the pop mean). However, the same observation does not apply to Pearson's correlation, for which if you know the pop mean, you should use it.
IPW with the estimated propensity score is another example. The first-stage estimation reduces the asymptotic variance, which surprises many people. A recent paper is Also, Newey&McFadden chapter 6 is about "two-step estimation"
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Handled by the fabulous AE
@mraginsky
and fresh new in the 𝗜𝗘𝗘𝗘 𝗧𝗿𝗮𝗻𝘀𝗮𝗰𝘁𝗶𝗼𝗻𝘀 𝗼𝗻 𝗜𝗻𝗳𝗼𝗿𝗺𝗮𝘁𝗶𝗼𝗻 𝗧𝗵𝗲𝗼𝗿𝘆, this paper gives the information limit of general order spline regressions. Very likely the most technical paper I will ever be able to write.
Yandi Shen, Qiyang Han, Fang Han : On a phase transition in general order spline regression
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My take on statistical reasoning (now often rebranded as “causal XXX”): NO magic, just assumptions. Statistical reasoning is, extremely unsatisfactorily to a perfectionist, entirely a play of assumptions.
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To appear in 𝗜𝗘𝗘𝗘 𝗧𝗿𝗮𝗻𝘀𝗮𝗰𝘁𝗶𝗼𝗻𝘀 𝗼𝗻 𝗜𝗻𝗳𝗼𝗿𝗺𝗮𝘁𝗶𝗼𝗻 𝗧𝗵𝗲𝗼𝗿𝘆. Do check Teh and Polyanskiy's follow-up work, which improved the rate of ours from n^{-1/10} to n^{-1/4} via a smart use of Hadamard’s three-circle theorem.
This is a fun project: we found that under the Gaussian-smoothed optimal transport distance, the estimation accuracy of the NPMLEs can be accelerated to a polynomial rate and is in sharp contrast to the \log n-type rates based on the unsmoothed Wasserstein one.
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@sp_monte_carlo
@adad8m
@gabrielpeyre
Just a plug-in estimator using knn. Berrett, Samworth, and Yuan got an impressive paper on this topic
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@daniela_witten
@Lizstuartdc
@raziehnabi
@nataliexdean
@BetsyOgburn
@analisereal
@yayyyates
I am still digesting two facts that (a) I am on the same flight with a COPSS winner and (b) she is sitting in the economic but not business class🧐
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In case you have not known yet, in this issue there is one short article written by me (!), covering some of our recent efforts to extend rank correlations to higher dimensions. Please enjoy it ☺️
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Just out!: An interview with Marc Hallin, accurately described in the abstract as "One of the most brilliant mathematical statisticians of our time". He is a role model admired by many of us.
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Peter Bickel just pointed out to me that Hodges's estimator is another example; bootstrap fails then at mu=0 (Beran 1982). It then occurred to me that Andrea Rotnitzky also mentioned that bootstrap consistency is sth about *regular* estimators. Would be nice to see a theory!
Here is the proof, executed by the magnificent
@zzzxlin
: , where discussion with
@hagmnn
and
@molivarego
on Twitter was acknowledged (and much appreciated!).
Still seeking more examples that are root-n consistent, ASN, but bootstrap inconsistent🤔
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Here comes another great master: 𝗦𝗼𝘂𝗿𝗮𝘃 𝗖𝗵𝗮𝘁𝘁𝗲𝗿𝗷𝗲𝗲 surveys recent developments in measures of association, including his own rank correlation coefficient!
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Although bootstrap could fail, m out of n bootstrap will never. Check Dette and
@k2daroll
's recent work on the validity of m out of n bootstrap for inferring Chatterjee's rank correlation. It is an elegant work.
Ok, the literature review is done: Beran (1997) showed that in LAN models, bootstrap consistency is equivalent to that the estimator is regular; should be a textbook result IMHO.
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Both "On the power of Chatterjee’s rank correlation" and "On boosting the power of Chatterjee’s rank correlation" are now among 𝘁𝗵𝗲 𝗺𝗼𝘀𝘁 𝗿𝗲𝗮𝗱 𝗮𝗿𝘁𝗶𝗰𝗹𝗲𝘀 𝗶𝗻 𝗕𝗶𝗼𝗺𝗲𝘁𝗿𝗶𝗸𝗮. Take a look!
"On the power of Chatterjee's rank correlation" is currently among 𝘁𝗵𝗲 𝗺𝗼𝘀𝘁 𝗿𝗲𝗮𝗱 𝗮𝗿𝘁𝗶𝗰𝗹𝗲𝘀 𝗶𝗻 𝗕𝗶𝗼𝗺𝗲𝘁𝗿𝗶𝗸𝗮; please take a look if interested in measuring functional dependence, Le Cam's method, or rank/permutation statistics.
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Its sister paper, "On boosting the power of Chatterjee's rank correlation", was also just 𝗮𝗰𝗰𝗲𝗽𝘁𝗲𝗱 𝘁𝗼 𝗕𝗶𝗼𝗺𝗲𝘁𝗿𝗶𝗸𝗮.
Key message: scaling up the # of nearest neighbors can boost Chatterjee's power to near parametric.
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Yup, that is true; we are hiring
The rumors are true.... UW Statistics is really hiring 2 tenure-track assistant professors!! 👩🎓👨🎓📚
Apply before 10/20 for full consideration! 📅✍️💻
PLEASE RETWEET🔊🔊🔊
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Now published in 𝗕𝗶𝗼𝗺𝗲𝘁𝗿𝗶𝗰𝘀, . Short message: 𝐭𝐚𝐤𝐢𝐧𝐠 𝐩𝐚𝐢𝐫𝐰𝐢𝐬𝐞 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞𝐬 creates symmetry (regardless of how peculiar X is, X-X' is always symmetric around, right?) and helps make statistical methods more robust.
Robust Functional Principal Component Analysis via Functional Pairwise Spatial Signs.
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For the record, ML does not replace nonparametric regression either; it needs tons of misinformation to say so.
This is a commonly held belief - that ML replaces econometrics. It’s wrong. ML only replaces nonparametric regression (including its use for forecasting). ML alone doesn’t handle most econometric issues, including identification, causality, endogeneity, selection, and attrition.
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One thing to note is that this bound no longer holds if we replace the population mean by the sample mean in centralization: the latter yields a t-statistic which is of course heavy-tailed.
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Magnificent 🤩
Graphical comparison between the standard (linear)
#correlation
and the Chatterjee's "rank correlation" recently introduced in
#statistics
#probability
@johnleibniz
@_bakshay
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so proud of Chao, best collaborator ever 😊
Dr. Chao Gao, University of Chicago, receives the 2021 IMS Tweedie Award “for groundbreaking contributions to robust statistics, including establishing connections with generative adversarial networks, network analysis, and high-dimensional statistical inference.”
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@daniela_witten
Compared to this: presenting in a median-sized workshop when the 3-year old walked in, dancing around, and insisting on your help to pee. True story 🤦♂️
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New in the 𝗔𝗻𝗻𝗮𝗹𝘀 𝗼𝗳 𝗦𝘁𝗮𝘁𝗶𝘀𝘁𝗶𝗰𝘀: shape constraint helps to estimate a piecewise constant (PC) signal. By-product: the first linear-time algorithm to compute ALL isotonic PC fits.
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This is a fun project: we found that under the Gaussian-smoothed optimal transport distance, the estimation accuracy of the NPMLEs can be accelerated to a polynomial rate and is in sharp contrast to the \log n-type rates based on the unsmoothed Wasserstein one.
Fang Han, Zhen Miao, Yandi Shen: Nonparametric mixture MLEs under Gaussian-smoothed optimal transport distance
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I am 100% endorsing this tweet... looking at the weather forecast for the next 10 days, I think I am depressed. (kidding. Seattle is super awesome. Please apply;
@UWStat
has a teaching prof position!)
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@sp_monte_carlo
Ask the right question, which is usually just about some small-dim functional but absolutely not the whole distribution.
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Sourav's comment on Lin and Han (2022, ):
Here comes another great master: 𝗦𝗼𝘂𝗿𝗮𝘃 𝗖𝗵𝗮𝘁𝘁𝗲𝗿𝗷𝗲𝗲 surveys recent developments in measures of association, including his own rank correlation coefficient!
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@maxhfarrell
@paulgp
@jt_kerwin
@causalinf
@marcfbellemare
@instrumenthull
@pedrohcgs
You are exactly right, Max! However, there is no rigorous proof about this claim until this recent paper (?). Any comment would be greatly appreciated!
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What a list!!!
@zzzxlin
first meta and now Jane street, wow🤩
Exciting news! Jane Street has announced the winner's of its first Graduate Research Fellowship:
It was a great process, and we were all deeply impressed with the quality of the applicants.
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@AngYu_soci
perhaps also worth noting: replacing a PS estimate by the *true* ps also leads to an inefficient ATE estimator; IMO this is one of the best results ever obtained in mathematical statistics.
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@ben_golub
Conditional probability (and conditional expectation) is a monster and better left to the second half (when students are expecting materials to be challenging).
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Fresh in 𝐉𝐀𝐒𝐀, with Mathias Drton
@TUM_Mathematics
and my student Hongjian Shi
@UW
. Statistical inference built on optimal-transport-induced multivariate ranks. Distribution-freeness and test consistency are simultaneously achieved.
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@daniela_witten
I thought it is model-based inference under the umbrella of (categorical) time series prediction, i.e., we observe X_t (t<=T) and accordingly build a CI for X_{T+1}. For a simple Markov chain model with three states (sun, rain, cloudy), 30% is the transition prob.
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@PreetumNakkiran
@avshrikumar
Check also this paper (of mine) for some most recent progress on Chatterjee’s rank correlation: . A literature has been quickly built up in the past two years.
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@wu_biostat
(1) Permutation uses the structure of the null hypothesis and is thus more "efficient" (Le Cam, Hajak, Bickel, Hallin). (2) Permutation usually can give "uniformly valid" inference bounds (easy?). (3) Permutation is more robust (Romano).
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If you enjoyed reading our previous Biometrika paper (), you may also like to read , where we overcome the power loss of Chattejee's original proposal by scaling up # of nearest neighbours! Technically quite challenging this time.
New paper in Biometrika. Nothing particularly technically challenging but, hey, only 16-page long yet with Sourav Chatterjee, Holger Dette, Jaroslav Hájek, Wassily Hoeffding, Jack Kiefer, Lucien Le Cam, Murray Rosenblatt, and many other great statisticians in😍
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@daniela_witten
Hmm... so can we interpret “percent chance of rain” as the conditional probability of “tomorrow is rainy” given everything obtainable until now?
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@ben_golub
In the beginning there were Pascal and Fermat, and de Moivre. They debated and debated. Then came Kolmogorov, who taught measure theory to all. Alas, we now know the conditional probability is just a Markov kernel definable over a Polish space, but does anyone still care?
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@itsbradross
@jiafengkevinc
@jt_kerwin
The exact argument was made in Abadie and Imbens' (2016, ECMA) paper, where they showed that the Donsker-type condition in the original matching outcome model can be substantially weakened by using the propensity score; at the cost of efficiency, though.
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@AngYu_soci
The high-level reason is simple: simple parametric model eliminates too much information, while a nonparametric reg with a *right* order keeps a good balance between estimation accuracy and info reservation.
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It is rare to encounter such a degree of candor on the internet.
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@paulgp
@maxhfarrell
@jt_kerwin
@causalinf
@marcfbellemare
@instrumenthull
@pedrohcgs
Check the thread here:
In short, biased-corrected matching is doing double machine learning.
: Our holiday gift to all fans of matching methods: in strong contrast to the common belief, Abadie and Imbens's bias-corrected nearest neighbor (NN) matching actually already gives a doubly robust and semiparametrically efficient estimator of the ATE.
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@hagmnn
My conjecture is that any statistic that is not asymptotically linear (=\sum g(X_i)+small order terms) will have trouble. And it just occurs to me that Abadie&Imbens 2008 is another example (ASN but bootstrap inconsistent).
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freely accessible version:
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@PreetumNakkiran
@avshrikumar
It does not matter; as long as the model is “regular”, Chatterjee’s correlation is inefficient. Chatterjee’s heuristic does not work mathematically; cf. the Biometrika paper (of mine) mentioned above.
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@ThosVarley
@adad8m
@_bakshay
Chatterjee correlation comes from the law of total variance; a Chatterjee correlation of value 0.5 means that averagely half of Var(I(Y>.)) can be explained by that conditional on X.
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@LarsvanderLaan3
Yup, I was just talking about this with Jon Wellner several days ago and was set to prove it myself. But if course, Beran got it 25 years ahead me : )
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@UnibusPluram
@kareem_carr
(1) Yes, working models are useful, and some (e.g., normal regression that leads to OLS) are super robust; (2) Parametric models can make sen from time to time; (3) nonparametric methods have their own problems, e.g., tuning parameters is a rabbit hole.
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In this department, we use it for everything that involves a faculty vote; it works like a charm.
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@pedrohcgs
@maxhfarrell
Check the thread I made here:
In short, biased-corrected matching is doing double machine learning.
: Our holiday gift to all fans of matching methods: in strong contrast to the common belief, Abadie and Imbens's bias-corrected nearest neighbor (NN) matching actually already gives a doubly robust and semiparametrically efficient estimator of the ATE.
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@analisereal
@daniela_witten
@tdietterich
@lucylgao
Define a_{k,1}, .., a_{k,k} to be the k "optimal centre points" such that M_k:=E{\min_j \| X - a_{k,j} \|^2} is minimized. My interpretation of the null hypothesis is H_0: M_k=M_{k-1}.
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@zzzxlin
, still a first-year PhD student, but already a finalist for Meta PhD fellowship🤩
Meta Research PhD Fellowship award winners for 2023 have been announced! Congratulations to all these bright minds!
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@daniela_witten
Oh yes, there is actually a widespread campus legend saying that Padelford was designed to be riot-proof; check here
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@Apoorva__Lal
@pengding00
@zzzxlin
The paper suggests a constant/rate choice for M based on the minimax theory and simulations. No idea about how to relate it to OT, though😃
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This is the tweet of the month.
i don’t know how to explain this but this is IV regression
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(b) The term K_M(i)/M above, introduced in Abadie and Imbens (2006), constitutes a consistent and efficient density ratio estimator. Even better, it is one-step, of near-linear computation complexity, and is statistically optimal, the first one to gain all three simultaneously.
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It is an amazing gathering! Thanks for putting out such a great program, Fabrizio 🤩
The 40th Linz Seminar on "
#Copulas
- Theory and Applications" ended today. Thanks to all participants and to invited speakers for brilliant talks and discussions. Many problems have been solved. Many others are still open!
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