arXiv subjects

Jonas M. Mikhaeil

Publications and source records attributed to Jonas M. Mikhaeil.

7 recordsLinked to original sources

arXiv2026

Valid Inference when Testing Violations of Parallel Trends for Difference-in-Differences

The difference-in-differences (DID) research design is a key identification strategy which allows researchers to estimate causal effects under the parallel trends assumption. While the parallel trends assumption is counterfactual and cannot be tested directly, researchers often examine pre-treatment periods to check whether the time trends are parallel before treatment is administered. A recent literature has shown that existing preliminary tests have adverse effects on conventional statistical methods for estimation and inference, including low power, bias, and undercoverage. In this paper, we describe simple preliminary tests and corresponding confidence intervals for the causal effect which overcome these issues. Under mild separation conditions, the preliminary test is shown to be consistent and the confidence intervals for the causal effect have valid coverage conditional on passing the test. Our results hold under what we refer to as the conditional extrapolation assumption, which posits a relationship between the unidentified post-treatment violation of parallel trends and the identified pre-treatment violations. We view the conditional extrapolation assumption as one formalization of the assumption which is implicitly held when conducting a preliminary test for parallel trends. To illustrate the performance of the proposed methods, we use synthetic data as well as data on recentralization of public services in Vietnam and right-to-carry laws in Virginia.

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arXiv2025

The Sequential Nature of Science: Quantifying Learning from a Sequence of Studies

Scientific progress is inherently sequential: collective knowledge is updated as new studies enter the literature. We propose the sequential meta-analysis research trace (SMART), which quantifies the influence of each study at the time it enters the literature. In contrast to classical meta-analysis, our method can capture how new studies may cast doubt on previously held beliefs, increasing collective uncertainty. For example, a new study may present a methodological critique of prior work and propose a superior method. Even small studies, which may not materially affect a retrospective meta-analysis, can be influential at the time they appeared. To contrast SMART with classical meta-analysis, we re-analyze two meta-analysis datasets, from psychology and labor economics. One assembles studies using a single methodology; the other contains studies that predate or follow an important methodological innovation. Our formalization of sequential learning highlights the importance of methodological innovation that might otherwise be overlooked by classical meta-analysis.

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arXiv2025

Russian roulette: The need for stochastic potential outcomes when utilities depend on counterfactuals

It has been proposed in medical decision analysis to express the ``first do no harm'' principle as an asymmetric utility function in which the loss from killing a patient would count more than the gain from saving a life. Such a utility depends on unrealized potential outcomes, and we show how this yields a paradoxical decision recommendation in a simple hypothetical example involving games of Russian roulette. The problem is resolved if we abandon the stable unit treatment value assumption (SUTVA) and allow the potential outcomes to be random variables. This leads us to conclude that, if you are interested in this sort of asymmetric utility function, you need to move to the stochastic potential outcome framework. We discuss the implications of the choice of parameterization in this setting.

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arXiv2025

Sharp Bounds on the Variance of General Regression Adjustment in Randomized Experiments

A growing statistical literature focuses on causal inference in the context of experiments where the target of inference is the average treatment effect in a finite population and random assignment determines which subjects are allocated to one of the experimental conditions. In this framework, variances of average treatment effect estimators remain unidentified because they depend on the covariance between treated and untreated potential outcomes, which are never jointly observed. Conventional variance estimators are upwardly biased. Aronow, Green and Lee [Ann. Statist. 42(3): 850-871 (June 2014)] provide an estimator for the variance of the difference-in-means estimator that is asymptotically sharp. In practice, researchers often use some form of covariate adjustment, such as linear regression, when estimating the average treatment effect. Adapting propositions from empirical process theory, we extend the result in (Aronow et al., 2014), providing asymptotically sharp variance bounds for general regression adjustment. We apply these results to linear regression adjustment and show benefits both in a simulation and in three empirical applications drawn from different disciplines.

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arXiv2025

Quantifying How Much Has Been Learned from a Research Study

How much does a research study contribute to a scientific literature? We propose a learning metric to quantify how much a research community learns from a given study. To do so, we adopt a Bayesian perspective and assess changes in the community's beliefs once updated with a new study's evidence. We recommend the Wasserstein-2 distance as a way to describe how the research community's prior beliefs change to incorporate a study's findings. We illustrate this approach through stylized examples and empirical applications, showing how it differs from more traditional evaluative standards, such as statistical significance. We then extend the framework to the prospective setting, offering a way for decision-makers to evaluate the expected amount of learning from a proposed study. While assessments about what has or could be learned from a research program are often expressed informally, our learning metric provides a principled tool for judging scientific contributions. By formalizing these judgments, our measure has the potential to allow for more transparent assessments of past and prospective research contributions.

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arXiv2022

On the difficulty of learning chaotic dynamics with RNNs

Recurrent neural networks (RNNs) are wide-spread machine learning tools for modeling sequential and time series data. They are notoriously hard to train because their loss gradients backpropagated in time tend to saturate or diverge during training. This is known as the exploding and vanishing gradient problem. Previous solutions to this issue either built on rather complicated, purpose-engineered architectures with gated memory buffers, or - more recently - imposed constraints that ensure convergence to a fixed point or restrict (the eigenspectrum of) the recurrence matrix. Such constraints, however, convey severe limitations on the expressivity of the RNN. Essential intrinsic dynamics such as multistability or chaos are disabled. This is inherently at disaccord with the chaotic nature of many, if not most, time series encountered in nature and society. It is particularly problematic in scientific applications where one aims to reconstruct the underlying dynamical system. Here we offer a comprehensive theoretical treatment of this problem by relating the loss gradients during RNN training to the Lyapunov spectrum of RNN-generated orbits. We mathematically prove that RNNs producing stable equilibrium or cyclic behavior have bounded gradients, whereas the gradients of RNNs with chaotic dynamics always diverge. Based on these analyses and insights we suggest ways of how to optimize the training process on chaotic data according to the system's Lyapunov spectrum, regardless of the employed RNN architecture.

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arXiv2022

Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems

In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward this goal often suffered from a lack of interpretability and tractability. In particular, the high-dimensional latent spaces often required for a faithful embedding, even when the underlying dynamics lives on a lower-dimensional manifold, can hamper theoretical analysis. Motivated by the emerging principles of dendritic computation, we augment a dynamically interpretable and mathematically tractable piecewise-linear (PL) recurrent neural network (RNN) by a linear spline basis expansion. We show that this approach retains all the theoretically appealing properties of the simple PLRNN, yet boosts its capacity for approximating arbitrary nonlinear dynamical systems in comparatively low dimensions. We employ two frameworks for training the system, one combining back-propagation-through-time (BPTT) with teacher forcing, and another based on fast and scalable variational inference. We show that the dendritically expanded PLRNN achieves better reconstructions with fewer parameters and dimensions on various dynamical systems benchmarks and compares favorably to other methods, while retaining a tractable and interpretable structure.

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