🚨A Researcher's Guide to Empirical Risk Minimization
I put together a guide on regret theory for empirical risk minimization (ERM) as I understand it.
The goal was to compile results and proof techniques I’ve found useful in my own work. I hope people find it useful more broadly
In this sense, CP is finite sample in the same way that an empirical mean is finite sample. Averaged over randomness in the data, it’s unbiased. That doesn’t mean with sample size 3 the empirical mean is a good estimator.
Worth noting it’s double marginal coverage. Marginal over both the randomness in the test point and the training/calibration set.
New Paper: Efficient Inference for IRL & Dynamic Discrete Choice
We study reward recovery from behavior and inference in inverse RL and DDC, w/o parametric restrictions, while also simplifying optimization
A semiparametric extension of the influential Rust (1987) paper
arxiv.org/pdf/2512.24407
Lars van der Laan, Nathan Kallus
Stationary Reweighting Yields Local Convergence of Soft Fitted Q-Iteration
https://arxiv.org/abs/2512.23927
Lars van der Laan, Nathan Kallus
Fitted Q Evaluation Without Bellman Completeness via Stationary Weighting
https://arxiv.org/abs/2512.23805
link 📈🤖
Bellman Calibration for V-Learning in Offline Reinforcement Learning (Laan, Kallus) We introduce Iterated Bellman Calibration, a simple, model-agnostic, post-hoc procedure for calibrating off-policy value predictions in infinite-horizon Markov decision processes. Bellman calibration requi
He did it before Double Machine Learning
I met with professor Mark van der Laan because I think his work is pretty incredible and it sometimes feels like a secret that only a few people know about, especially in industry.
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#CausalSky #StatSky #CausalInference
What does ‘biased’ mean here? It would be biased in expectation, since if you were to repeat the experiment many times, some power users would join. If you define your estimator as the empirical mean over non-power users, then it might be unbiased.
I’d be surprised if this actually works in practice, since neural networks are often overfitting (e.g. perfectly fitting labels with double descent), which violates donsker conditions. And, the neural tangent kernel ridge approximation of neural networks has been shown to not hold empirically.
Looks like they are assuming the neural network can be approximated by ridge regression in an RKHS (which seems strong in practice). Under this approximation, plug-in efficiency follows from fairly standard results on undersmoothed ridge regression; see, e.g. arxiv.org/abs/2306.08598
I've advised 15 PhD students—10 were international students. All graduates continue advancing U.S. excellence in research and education. Cutting off this pipeline of talent would be shortsighted.
I had a hard time believing it was as simple as this until Lars taught me how to implement it - calibrate=True and you're done
github.com/apoorvalal/a...
Calibrate your outcome predictions and propensities using isotonic regression as follows:
mu_hat <- as.stepfun(isoreg(mu_hat, Y))(mu_hat)
pi_hat <- as.stepfun(isoreg(pi_hat, A))(pi_hat)
(Or use the isoreg_with_xgboost function given in the paper, which I recommend)
Had a great time presenting at #ACIC on doubly robust inference via calibration
Calibrating nuisance estimates in DML protects against model misspecification and slow convergence.
Just one line of code is all it takes.
link 📈🤖
Nonparametric Instrumental Variable Inference with Many Weak Instruments (Laan, Kallus, Bibaut) We study inference on linear functionals in the nonparametric instrumental variable (NPIV) problem with a discretely-valued instrument under a many-weak-instruments asymptotic regime, where the
I’ll be giving an oral presentation at ACIC in the Advancing Causal Inference session with ML on Wednesday!
My talk will be on Automatic Double Reinforcement Learning and long term causal inference!
I’ll discuss Markov decision processes, Q-functions, and a new form of calibration for RL!
New preprint with #Netflix out!
We study the NPIV problem with a discrete instrument under a many-weak-instruments regime.
A key application: constructing confounding-robust surrogates using past experiments as instruments.
My mentor Aurélien Bibaut will be presenting a poster at #ACIC2025!
Our work on stabilized inverse probability weighting via calibration was accepted to #CLeaR2025! I gave an oral presentation last week and was honored to receive the Best Paper Award.
I’ll be giving a related poster talk at #ACIC on calibration and DML and how it provides doubly robust inference!
Link to paper:
arxiv.org/pdf/2501.06926
This work is a result of my internship at Netflix over the summer and is joint with Aurelien Bibaut and Nathan Kallus.
I’ll be giving an oral presentation at ACIC in the Advancing Causal Inference session with ML on Wednesday!
My talk will be on Automatic Double Reinforcement Learning and long term causal inference!
I’ll discuss Markov decision processes, Q-functions, and a new form of calibration for RL!
Inference for smooth functionals of M-estimands in survival models, like regularized coxPH and the beta-geometric model (see our experiments section) are one application of this approach.
By targeting low dimensional summaries, there is no need to establish asymptotic normality of the entire infinite dimensional M-estimator (which isn’t possible in general). It allows for the use of ML and regularization to estimate it, and valid inference via a one step bias correction.
If you’re willing to consider smooth functionals of the infinite dimensional M-estimand, then there is a general theory for inference, where the sandwich variance estimator now involves the derivative of the loss and a Riesz representer of the functional.
Working paper:
arxiv.org/pdf/2501.11868
The motivation should have been something like a confounder that is somewhat predictive of both the treatment and outcome might be more important to adjust for then a variable that is super predictive of the outcome but doesn’t predict treatment. TR might help give more importance to such variables
One could have given an analogous theorem saying that E[Y | T, X] is a sufficient deconfounding score and argued that one should only adjust for features predictive of the outcome. So yeah I think it’s wrong/poorly phrased
The OP’s approach is based on the conditional probability of Y given the treatment is intervened upon and set to some value. But, they don’t seem to define what this means formally, which is exactly what potential outcomes/NPSEM achieve.
The second stage coefficients are the estimand (identifying the structural coefficients/treatment effect). The first stage coefficients are nuisances, and typically not of direct interest.
The paper "Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction" by Lars van der Laan and Ahmed Alaa introduces a comprehensive framework that extends Venn and Venn-Abers calibration methods to a broad range of prediction tasks and loss functions.
