arXiv subjects

Panos Toulis

Publications and source records attributed to Panos Toulis.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic Treatment on Networks

In networks, effective dynamic treatment allocation requires deciding both whom to treat and also when, so as to amplify policy impact through spillovers. An early intervention at a well-connected node can trigger cascades that change which nodes are worth targeting in the next period. Existing treatment strategies under network interference are largely static while dynamic treatment frameworks typically ignore network structure altogether. We integrate these perspectives and propose Q-Ising, a three-stage pipeline that (i) estimates network adoption dynamics via a Bayesian dynamic Ising model from a single observed panel, (ii) augments treatment adoption histories with continuous posterior latent states, and (iii) learns a dynamic policy via offline reinforcement learning. The Bayesian mechanism enables uncertainty quantification over dynamic decisions, yielding posterior ensemble policies with interpretable spillover estimates. We provide a finite-sample regret upper bound that decomposes into standard offline-RL uncertainty, network abstraction error, and first stage error in Ising state estimation. We apply our method to data from Indian village microfinance networks and synthetic stochastic block models under simulated heterogeneous susceptible-infected-susceptible (SIS) dynamics and demonstrate that adaptive targeting outperforms static centrality benchmarks.

stat.ML↗

arXiv2026

Permutation Inference under Multi-way Clustering and Missing Data

Econometric applications with multi-way clustering often feature a small number of effective clusters or heavy-tailed data, making standard cluster-robust and bootstrap inference unreliable in finite samples. In this paper, we develop a framework for finite-sample valid permutation inference in linear regression with multi-way clustering under an assumption of conditional exchangeability of the errors. Our assumption is closely related to the notion of separate exchangeability studied in earlier work, but can be more realistic in many economic settings as it imposes minimal restrictions on the covariate distribution. We construct permutation tests of significance that are valid in finite samples and establish theoretical power guarantees, in contrast to existing methods that are justified only asymptotically. We also extend our methodology to settings with missing data and derive power results that reveal phase transitions in detectability. Through simulation studies, we demonstrate that the proposed tests maintain correct size and competitive power, while standard cluster-robust and bootstrap procedures can exhibit substantial size distortions.

stat.ME↗

arXiv2025

Stabilizing Temporal Difference Learning via Implicit Stochastic Recursion

Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized algorithms. However, despite its widespread use, TD procedures are generally sensitive to step size specification. A poor choice of step size can dramatically increase variance and slow convergence in both on-policy and off-policy evaluation tasks. In practice, researchers often use trial and error to identify stable step sizes, but these approaches tend to be ad hoc and inefficient. As an alternative, we propose implicit TD algorithms that reformulate TD updates into fixed-point equations. Such updates are more stable and less sensitive to step size without sacrificing computational efficiency. Moreover, we derive almost sure convergence guarantees and finite-time error bounds (with a projection step) for the proposed implicit TD algorithms. Our results show that implicit TD algorithms are applicable to a much broader range of step sizes, and thus provide a robust and versatile framework for policy evaluation and value approximation in modern RL tasks. We demonstrate these benefits empirically through extensive numerical experiments spanning both on-policy and off-policy tasks.

cs.LG↗

arXiv2025

Randomization Inference in Two-Sided Market Experiments

Randomized experiments are increasingly employed in two-sided markets, such as buyer--seller platforms, to evaluate the effects of marketplace interventions. These experiments must reflect the underlying two-sided market structure in their design and can therefore be challenging to analyze. In this paper, we develop a randomization inference framework for outcomes from two-sided experiments, with a focus on testing and inference for two-sided spillover effects. Our approach is finite-sample valid under sharp null hypotheses. Regarding weak null hypotheses, we find that the commonly used Neyman-style studentization does not universally ensure asymptotic validity, and we document how it depends on the specific formulation of the null. We then propose a two-way variance estimator for studentization that restores asymptotic validity. We further propose methods to improve testing power by exploiting the two-sided structure of the problem, which we validate empirically. We demonstrate our methods through a series of simulation studies and an applied example from a network experiment in micro-lending.

stat.ME↗

arXiv2025

Finite-Sample Valid Randomization Tests for Monotone Spillover Effects

Randomization tests have gained popularity for causal inference under network interference because they are finite-sample valid with minimal assumptions. However, existing procedures are limited as they primarily focus on the existence of spillovers through sharp null hypotheses on potential outcomes. In this paper, we expand the scope of randomization procedures in network settings by developing new tests for the monotonicity of spillover effects. These tests offer insights into whether spillover effects increase, decrease, or exhibit ``diminishing returns'' along certain network dimensions of interest. Our approach partitions the network into multiple (possibly overlapping) parts and tests a monotone contrast hypothesis in each sub-network. The test decisions can then be aggregated in various ways depending on how each test is constructed. We demonstrate our method by re-analyzing a large-scale policing experiment in Colombia, which reveals evidence of monotonicity related to the ``crime displacement hypothesis''. Our analysis suggests that crime spillovers on a control street increase with the number of nearby streets receiving more intense policing but diminish at higher exposure levels.

stat.ME↗

arXiv2025

Gaussianized Design Optimization for Covariate Balance in Randomized Experiments

Achieving covariate balance in randomized experiments enhances the precision of treatment effect estimation. However, existing methods often require heuristic adjustments based on domain knowledge and are primarily developed for binary treatments. This paper presents Gaussianized Design Optimization, a novel framework for optimally balancing covariates in experimental design. The core idea is to Gaussianize the treatment assignments: we model treatments as transformations of random variables drawn from a multivariate Gaussian distribution, converting the design problem into a nonlinear continuous optimization over Gaussian covariance matrices. Compared to existing methods, our approach offers significant flexibility in optimizing covariate balance across a diverse range of designs and covariate types. Adapting the Burer-Monteiro approach for solving semidefinite programs, we introduce first-order local algorithms for optimizing covariate balance, improving upon several widely used designs. Furthermore, we develop inferential procedures for constructing design-based confidence intervals under Gaussianization and extend the framework to accommodate continuous treatments. Simulations demonstrate the effectiveness of Gaussianization in multiple practical scenarios.

stat.ME↗

arXiv2025

ML-assisted Randomization Tests for Detecting Treatment Effects in A/B Experiments

Experimentation is widely utilized for causal inference and data-driven decision-making across disciplines. In an A/B experiment, for example, an online business randomizes two different treatments (e.g., website designs) to their customers and then aims to infer which treatment is better. In this paper, we construct randomization tests for complex treatment effects, including heterogeneity and interference. A key feature of our approach is the use of flexible machine learning (ML) models, where the test statistic is defined as the difference between the cross-validation errors from two ML models, one including the treatment variable and the other without it. This approach combines the predictive power of modern ML tools with the finite-sample validity of randomization procedures, enabling a robust and efficient way to detect complex treatment effects in experimental settings. We demonstrate this combined benefit both theoretically and empirically through applied examples.

stat.ME↗

arXiv2024

Asymptotic Validity and Finite-Sample Properties of Approximate Randomization Tests

Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically valid under a suitable studentization of the test statistic, even if the invariance does not hold. However, practical implementation often encounters noisy data, resulting in approximate randomization tests that may not be as robust. In this paper, our key theoretical contribution is a non-asymptotic bound on the discrepancy between the size of an approximate randomization test and the size of the original randomization test using noiseless data. This allows us to derive novel conditions for the validity of approximate randomization tests under data invariances, while being able to leverage existing results based on studentization if the invariance does not hold. We illustrate our theory through several examples, including tests of significance in linear regression. Our theory can explain certain aspects of how randomization tests perform in small samples, addressing limitations of prior theoretical results.

stat.ME↗

arXiv2023

Invariance-based Inference in High-Dimensional Regression with Finite-Sample Guarantees

In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null hypothesis of significance, our test is valid in finite samples. It is also simple to implement and comes with finite-sample guarantees on statistical power. Remarkably, despite its simplicity, this testing idea has escaped the attention of earlier analytical work, which mainly concentrated on complex high-dimensional asymptotic methods. Under an additional assumption of Gaussian design, we show that this test also achieves the minimax optimal rate against certain nonsparse alternatives, a type of result that is rare in the literature. Second, for partial null hypotheses, we propose residual-based tests and derive theoretical conditions for their validity. These tests can be made powerful by constructing the test statistic in a way that, first, selects the important covariates (e.g., through Lasso) and then orthogonalizes the nuisance parameters. We illustrate our results through extensive simulations and applied examples. One consistent finding is that the strong finite-sample guarantees associated with our procedures result in added robustness when it comes to handling multicollinearity and heavy-tailed covariates.

stat.ME↗

arXiv2023

Convergence and Stability of the Stochastic Proximal Point Algorithm with Momentum

Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes with gradient noise, often leading to specific step size and momentum choices in order to guarantee convergence, set aside acceleration. Proximal point methods, on the other hand, have gained much attention due to their numerical stability and elasticity against imperfect tuning. Their stochastic accelerated variants though have received limited attention: how momentum interacts with the stability of (stochastic) proximal point methods remains largely unstudied. To address this, we focus on the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM), and show that SPPAM allows a faster linear convergence to a neighborhood compared to the stochastic proximal point algorithm (SPPA) with a better contraction factor, under proper hyperparameter tuning. In terms of stability, we show that SPPAM depends on problem constants more favorably than SGDM, allowing a wider range of step size and momentum that lead to convergence.

math.OC↗

arXiv2023

Randomization tests for peer effects in group formation experiments

Measuring the effect of peers on individuals' outcomes is a challenging problem, in part because individuals often select peers who are similar in both observable and unobservable ways. Group formation experiments avoid this problem by randomly assigning individuals to groups and observing their responses; for example, do first-year students have better grades when they are randomly assigned roommates who have stronger academic backgrounds? In this paper, we propose randomization-based permutation tests for group formation experiments, extending classical Fisher Randomization Tests to this setting. The proposed tests are justified by the randomization itself, require relatively few assumptions, and are exact in finite-samples. This approach can also complement existing strategies, such as linear-in-means models, by using a regression coefficient as the test statistic. We apply the proposed tests to two recent group formation experiments.

stat.ME↗

arXiv2021

Randomization Tests in Observational Studies with Staggered Adoption of Treatment

This paper considers the problem of inference in observational studies with time-varying adoption of treatment. In addition to an unconfoundedness assumption that the potential outcomes are independent of the times at which units adopt treatment conditional on the units' observed characteristics, our analysis assumes that the time at which each unit adopts treatment follows a Cox proportional hazards model. This assumption permits the time at which each unit adopts treatment to depend on the observed characteristics of the unit, but imposes the restriction that the probability of multiple units adopting treatment at the same time is zero. In this context, we study Fisher-style randomization tests of a null hypothesis that specifies that there is no treatment effect for all units and all time periods in a distributional sense. We first show that an infeasible test that treats the parameters of the Cox model as known has rejection probability no greater than the nominal level in finite samples. We then establish that the feasible test that replaces these parameters with consistent estimators has limiting rejection probability no greater than the nominal level. In a simulation study, we examine the practical relevance of our theoretical results, including robustness to misspecification of the model for the time at which each unit adopts treatment. Finally, we provide an empirical application of our methodology using the synthetic control-based test statistic and tobacco legislation data found in Abadie et. al. (2010).

stat.ME↗

arXiv2021

Robust Inference for High-Dimensional Linear Models via Residual Randomization

We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in settings that also include heavy-tailed covariates and errors. Moreover, our procedure can be valid under clustered errors, which is important in practice, but has been largely overlooked by earlier work. Through extensive simulations, we illustrate our method's wider range of applicability as suggested by theory. In particular, we show that our method outperforms state-of-art methods in challenging, yet more realistic, settings where the distribution of covariates is heavy-tailed or the sample size is small, while it remains competitive in standard, "well behaved" settings previously studied in the literature.

stat.ME↗

arXiv2021

Randomization Inference of Periodicity in Unequally Spaced Time Series with Application to Exoplanet Detection

The estimation of periodicity is a fundamental task in many scientific areas of study. Existing methods rely on theoretical assumptions that the observation times have equal or i.i.d. spacings, and that common estimators, such as the periodogram peak, are consistent and asymptotically normal. In practice, however, these assumptions are unrealistic as observation times usually exhibit deterministic patterns -- e.g., the nightly observation cycle in astronomy -- that imprint nuisance periodicities in the data. These nuisance signals also affect the finite-sample distribution of estimators, which can substantially deviate from normality. Here, we propose a set identification method, fusing ideas from randomization inference and partial identification. In particular, we develop a sharp test for any periodicity value, and then invert the test to build a confidence set. This approach is appropriate here because the construction of confidence sets does not rely on assumptions of regular or well-behaved asymptotics. Notably, our inference is valid in finite samples when our method is fully implemented, while it can be asymptotically valid under an approximate implementation designed to ease computation. Empirically, we validate our method in exoplanet detection using radial velocity data. In this context, our method correctly identifies the periodicity of the confirmed exoplanets in our sample. For some other, yet unconfirmed detections, we show that the statistical evidence is weak, which illustrates the failure of traditional statistical techniques. Last but not least, our method offers a constructive way to resolve these identification issues via improved observation designs. In exoplanet detection, these designs suggest meaningful improvements in identifying periodicity even when a moderate amount of randomization is introduced in scheduling radial velocity measurements.

stat.ME↗

arXiv2021

A Graph-Theoretic Approach to Randomization Tests of Causal Effects Under General Interference

Interference exists when a unit's outcome depends on another unit's treatment assignment. For example, intensive policing on one street could have a spillover effect on neighboring streets. Classical randomization tests typically break down in this setting because many null hypotheses of interest are no longer sharp under interference. A promising alternative is to instead construct a conditional randomization test on a subset of units and assignments for which a given null hypothesis is sharp. Finding these subsets is challenging, however, and existing methods are limited to special cases or have limited power. In this paper, we propose valid and easy-to-implement randomization tests for a general class of null hypotheses under arbitrary interference between units. Our key idea is to represent the hypothesis of interest as a bipartite graph between units and assignments, and to find an appropriate biclique of this graph. Importantly, the null hypothesis is sharp within this biclique, enabling conditional randomization-based tests. We also connect the size of the biclique to statistical power. Moreover, we can apply off-the-shelf graph clustering methods to find such bicliques efficiently and at scale. We illustrate our approach in settings with clustered interference and show advantages over methods designed specifically for that setting. We then apply our method to a large-scale policing experiment in Medellin, Colombia, where interference has a spatial structure.

stat.ME↗

arXiv2020

Estimation of Covid-19 Prevalence from Serology Tests: A Partial Identification Approach

We propose a partial identification method for estimating disease prevalence from serology studies. Our data are results from antibody tests in some population sample, where the test parameters, such as the true/false positive rates, are unknown. Our method scans the entire parameter space, and rejects parameter values using the joint data density as the test statistic. The proposed method is conservative for marginal inference, in general, but its key advantage over more standard approaches is that it is valid in finite samples even when the underlying model is not point identified. Moreover, our method requires only independence of serology test results, and does not rely on asymptotic arguments, normality assumptions, or other approximations. We use recent Covid-19 serology studies in the US, and show that the parameter confidence set is generally wide, and cannot support definite conclusions. Specifically, recent serology studies from California suggest a prevalence anywhere in the range 0%-2% (at the time of study), and are therefore inconclusive. However, this range could be narrowed down to 0.7%-1.5% if the actual false positive rate of the antibody test was indeed near its empirical estimate (~0.5%). In another study from New York state, Covid-19 prevalence is confidently estimated in the range 13%-17% in mid-April of 2020, which also suggests significant geographic variation in Covid-19 exposure across the US. Combining all datasets yields a 5%-8% prevalence range. Our results overall suggest that serology testing on a massive scale can give crucial information for future policy design, even when such tests are imperfect and their parameters unknown.

stat.ME↗

arXiv2020

Minimax designs for causal effects in temporal experiments with treatment habituation

Randomized experiments are the gold standard for estimating the causal effects of an intervention. In the simplest setting, each experimental unit is randomly assigned to receive treatment or control, and then the outcomes in each treatment arm are compared. In many settings, however, randomized experiments need to be executed over several time periods such that treatment assignment happens at each time period. In such temporal experiments, it has been observed that the effects of an intervention on a given unit may be large when the unit is first exposed to it, but then it often attenuates, or even vanishes, after repeated exposures. This phenomenon is typically due to units' habituation to the intervention, or some other general form of learning, such as when users gradually start to ignore repeated mails sent by a promotional campaign. This paper proposes randomized designs for estimating causal effects in temporal experiments when habituation is present. We show that our designs are minimax optimal in a large class of practical designs. Our analysis is based on the randomization framework of causal inference, and imposes no parametric modeling assumptions on the outcomes.

stat.ME↗

arXiv2020

Dynamical systems theory for causal inference with application to synthetic control methods

In this paper, we adopt results in nonlinear time series analysis for causal inference in dynamical settings.~Our motivation is policy analysis with panel data, particularly through the use of "synthetic control" methods. These methods regress pre-intervention outcomes of the treated unit to outcomes from a pool of control units, and then use the fitted regression model to estimate causal effects post-intervention. In this setting, we propose to screen out control units that have a weak dynamical relationship to the treated unit. In simulations, we show that this method can mitigate bias from "cherry-picking" of control units, which is usually an important concern. We illustrate on real-world applications, including the tobacco legislation example of \citet{Abadie2010}, and Brexit.

stat.ME↗