arXiv subjects

Michael Lindon

Publications and source records attributed to Michael Lindon.

9 recordsLinked to original sources

arXiv2026

Design-Based Anytime-Valid Inference for Randomized Experiments with Delayed Outcomes and Staggered Entry

Delayed outcomes are ubiquitous in online experimentation: treatment can affect whether an outcome occurs, when it occurs, and its realized value. To accommodate staggered entry while remaining robust to environmental nonstationarity and unit-level heterogeneity, we adopt a design-based perspective and target the sample cumulative reward in each arm as a function of calendar time. Our confidence sequences allow practitioners to continuously monitor the counterfactual incremental reward, such as revenue, that would have been realized by calendar time $t$ had all entered units been assigned to treatment rather than control. The main technical challenge is the choice of design-based filtration, complicated by the presence of asynchronous potential outcome times. We show that the IPW treatment-effect estimation error is not a martingale with respect to any filtration, while each arm-specific IPW estimation error is a martingale with respect to a carefully chosen arm-specific event-time filtration. We therefore construct a confidence sequence for the treatment effect by combining two arm-level confidence sequences with a union bound, and further demonstrate that this can outperform the traditional design-based variance upper bound. Finally, we characterize the class of augmentations for which the per-arm AIPW estimation error remains a martingale.

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arXiv2024

Anytime-Valid Continuous-Time Confidence Processes for Inhomogeneous Poisson Processes

Motivated by monitoring the arrival of incoming adverse events such as customer support calls or crash reports from users exposed to an experimental product change, we consider sequential hypothesis testing of continuous-time inhomogeneous Poisson point processes. Specifically, we provide an interval-valued confidence process $C^\alpha(t)$ over continuous time $t$ for the cumulative arrival rate $\Lambda(t) = \int_0^t \lambda(s) \mathrm{d}s$ with a continuous-time anytime-valid coverage guarantee $\mathbb{P}[\Lambda(t) \in C^\alpha(t) \, \forall t >0] \geq 1-\alpha$. We extend our results to compare two independent arrival processes by constructing multivariate confidence processes and a closed-form $e$-process for testing the equality of rates with a time-uniform Type-I error guarantee at a nominal $\alpha$. We characterize the asymptotic growth rate of the proposed $e$-process under the alternative and show that it has power 1 when the average rates of the two Poisson process differ in the limit. We also observe a complementary relationship between our multivariate confidence process and the universal inference $e$-process for testing composite null hypotheses.

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arXiv2023

Design-Based Inference for Multi-arm Bandits

Multi-arm bandits are gaining popularity as they enable real-world sequential decision-making across application areas, including clinical trials, recommender systems, and online decision-making. Consequently, there is an increased desire to use the available adaptively collected datasets to distinguish whether one arm was more effective than the other, e.g., which product or treatment was more effective. Unfortunately, existing tools fail to provide valid inference when data is collected adaptively or require many untestable and technical assumptions, e.g., stationarity, iid rewards, bounded random variables, etc. Our paper introduces the design-based approach to inference for multi-arm bandits, where we condition the full set of potential outcomes and perform inference on the obtained sample. Our paper constructs valid confidence intervals for both the reward mean of any arm and the mean reward difference between any arms in an assumption-light manner, allowing the rewards to be arbitrarily distributed, non-iid, and from non-stationary distributions. In addition to confidence intervals, we also provide valid design-based confidence sequences, sequences of confidence intervals that have uniform type-1 error guarantees over time. Confidence sequences allow the agent to perform a hypothesis test as the data arrives sequentially and stop the experiment as soon as the agent is satisfied with the inference, e.g., the mean reward of an arm is statistically significantly higher than a desired threshold.

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arXiv2022

Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations

Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential tests that under-cover in practice or concentration-bound-based sequences that over-cover and have suboptimal rejection times. In this work, we consider classic delayed-start normal-mixture sequential probability ratio tests, and we provide the first asymptotic type-I-error and expected-rejection-time guarantees under general non-parametric data generating processes, where the asymptotics are indexed by the test's burn-in time. The type-I-error results primarily leverage a martingale strong invariance principle and establish that these tests (and their implied confidence sequences) have type-I error rates asymptotically equivalent to the desired (possibly varying) $\alpha$-level. The expected-rejection-time results primarily leverage an identity inspired by It\^o's lemma and imply that, in certain asymptotic regimes, the expected rejection time is asymptotically equivalent to the minimum possible among $\alpha$-level tests. We show how to apply our results to sequential inference on parameters defined by estimating equations, such as average treatment effects. Together, our results establish these (ostensibly parametric) tests as general-purpose, non-parametric, and near-optimal. We illustrate this via numerical simulations and a real-data application to A/B testing at Netflix.

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arXiv2022

Anytime-Valid Linear Models and Regression Adjusted Causal Inference in Randomized Experiments

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable for sequential settings such as online A/B testing. We develop an anytime-valid theory of inference for the linear model, introducing sequential analogues of classical tests and confidence sets that provide Type-I error control and coverage guarantees uniformly over all sample sizes. Our construction is based on likelihood ratios of invariantly sufficient statistics, yielding simple closed-form expressions of ordinary least squares estimators and standard errors. The resulting tests are optimal in the GROW/REGROW sense for both frequentist and Bayesian alternative hypotheses. We then relax the linear model assumptions to provide heteroskedasticity-robust asymptotic sequential tests and confidence sequences, which enable sequential regression-adjusted inference for causal estimands in randomized controlled experiments. This formally allows experiments to be continuously monitored for significance, stopped early, and safeguards against statistical malpractices in data collection. We demonstrate the practical utility of our approach through simulations and applications to real A/B test data from Netflix.

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arXiv2022

Design-Based Confidence Sequences: A General Approach to Risk Mitigation in Panel Experiments

Randomized experiments have become the standard method for companies to evaluate the performance of new products or services. Beyond aiding managerial decision-making, experiments mitigate risk by limiting the proportion of customers exposed to innovations. Since many experiments are conducted sequentially over time, an emerging strategy to further derisk the process is to allow managers to ``peek'' at the results as new data become available and stop the test if the results are statistically significant. The class of statistical methods that allow managers to peek and still provide valid inference are often called anytime-valid since they maintain proper uniform type-1 error guarantees. In this paper, we extend existing anytime-valid approaches to accommodate the more complex yet standard settings in time series, switchback, and panel experiments. To achieve this, we leverage the design-based approach to focus on assumption-light and managerial relevant finite-sample estimands defined on the study participants as a direct measure of the risks incurred by companies. As a special case, our (asymptotic) results also provide a robust method for achieving always-valid inference in A/B tests. We further provide a variance reduction technique incorporating modeling assumptions and covariates. Finally, we demonstrate the effectiveness of our proposed approach through a simulation study and three real-world applications from Netflix. Our results show that using our confidence sequence, harmful experiments could be stopped after only observing a handful of units; for instance, our method would have stopped a 30,000 person Netflix experiment after the first 100 people.

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arXiv2022

Rapid Regression Detection in Software Deployments through Sequential Testing

The practice of continuous deployment has enabled companies to reduce time-to-market by increasing the rate at which software can be deployed. However, deploying more frequently bears the risk that occasionally defective changes are released. For Internet companies, this has the potential to degrade the user experience and increase user abandonment. Therefore, quality control gates are an important component of the software delivery process. These are used to build confidence in the reliability of a release or change. Towards this end, a common approach is to perform a canary test to evaluate new software under production workloads. Detecting defects as early as possible is necessary to reduce exposure and to provide immediate feedback to the developer. We present a statistical framework for rapidly detecting regressions in software deployments. Our approach is based on sequential tests of stochastic order and of equality in distribution. This enables canary tests to be continuously monitored, permitting regressions to be rapidly detected while strictly controlling the false detection probability throughout. The utility of this approach is demonstrated based on two case studies at Netflix.

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arXiv2020

Anytime-Valid Inference for Multinomial Count Data

Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary experiments. Observations typically arrive in data streams and practitioners wish to continuously monitor their experiments, sequentially testing hypotheses while maintaining Type I error probabilities under optional stopping and continuation. These goals are frequently complicated in practice by non-stationary time dynamics. We provide practical solutions through sequential tests of multinomial hypotheses, hypotheses about many inhomogeneous Bernoulli processes and hypotheses about many time-inhomogeneous Poisson counting processes. For estimation, we further provide confidence sequences for multinomial probability vectors, all contrasts among probabilities of inhomogeneous Bernoulli processes and all contrasts among intensities of time-inhomogeneous Poisson counting processes. Together, these provide an "anytime-valid" inference framework for a wide variety of experiments dealing with count outcomes, which we illustrate with a number of industry applications.

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arXiv2019

Adaptive Variable Selection for Sequential Prediction in Multivariate Dynamic Models

We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant models. Based on formal Bayesian decision-theoretic reasoning, we develop a time-adaptive approach to exploring, weighting, combining and selecting models that differ in terms of predictive variables included. The adaptivity allows for changes in the sets of favored models over time, and is guided by the specific forecasting goals. A synthetic example illustrates how decision-guided variable selection differs from traditional Bayesian model uncertainty analysis and standard model averaging. An applied study in one motivating application of long-term macroeconomic forecasting highlights the utility of the new approach in terms of improving predictions as well as its ability to identify and interpret different sets of relevant models over time with respect to specific, defined forecasting goals.

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