Weaknesses: - Can we interpret the results as follows: If the TAR assumption is satisfied with positive limits, and we use MLE, then temporal interference does not cause bias. If this interpretation is correct, then it would be illuminating if the authors provide the intuitive connection between the TAR assumption and temporal interference. It is not clear if the estimations that the authors have required are feasible if the state space is large. The next natural question is how robust the results are if we use other methods for estimation. This could have been shown by providing some simulations, which is a part missing from the manuscript.

The paper studied the online experimental design problem where there are temporal dependencies between the two control policies/treatments. The novelty of the problem setup and the theoretical analysis in the paper are appreciated by all the reviewers. Although the analysis is the main contribution, the paper would be much stronger if there are meaningful experiments on toy problems to showcase the performance the online MLE-based approach vs the standard experimental design approaches.

Suppose an online platform wants to compare a treatment and control policy (e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site). Standard experimental approaches to this problem are biased (due to temporal interference between the policies), and not sample efficient. We study optimal experimental design for this setting. We view testing the two policies as the problem of estimating the steady state difference in reward between two unknown Markov chains (i.e., policies). We assume estimation of the steady state reward for each chain proceeds via nonparametric maximum likelihood, and search for consistent (i.e., asymptotically unbiased) experimental designs that are efficient (i.e., asymptotically minimum variance).

Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the latter distribution is known. However, this is not always the case, certainly when this proportion is the target variable. In this paper a maximum likelihood estimator for the true proportion of positives in data sets is suggested and tested on synthetic and real world data.

Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models by letting them either output a prediction set or abstain when the uncertainty is high. We propose training these selective prediction-set models using an uncertainty-aware loss minimization framework, which unifies ideas from decision theory and robust maximum likelihood. Moreover, since black-box methods are not guaranteed to output well-calibrated prediction sets, we show how to calculate point estimates and confidence intervals for the true coverage of any selective prediction-set model, as well as a uniform mixture of K set models obtained from K-fold sample-splitting. When applied to predicting in-hospital mortality and length-of-stay for ICU patients, our model outperforms existing approaches on both in-sample and out-of-sample age groups, and our recalibration method provides accurate inference for prediction set coverage.

In many of the possible applications as well as the theoretical models of computational social choice,the agents’ preferences are represented as partialorders. In this paper, we extend the maximum likelihood approach for defining “optimal” voting rules to this setting. We consider distributions in which the pairwise comparisons / incomparabilities between alternatives are drawn i.i.d. We call suchmodels pairwise-independentmodels and show that they correspond to a class of voting rules that we call pairwise scoring rules. This generalizes rulessuch as Kemeny and Borda. Moreover, we show that Borda is the only pairwise scoring rule that satisfies neutrality, when the outcome space is the set of all alternatives. We then study which voting rules defined for linear orders can be extended to partial orders via our MLE model. We show that any weakly neutral outcome scoring rule (includingany ranking/candidate scoring rule) based onthe weighted majority graph can be represented as the MLE of a weakly neutral pairwise-independent model. Therefore, all such rules admit natural extensionsto profiles of partial orders. Finally, we propose a specific MLE model π k for generating a set of k winning alternatives, and study the computational complexity of winner determination for the MLE of π k .