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.
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Measurement invariance across items is key to the validity of instruments like a survey questionnaire or an educational test. Differential item functioning (DIF) analysis is typically conducted to assess measurement invariance at the item level. Traditional DIF analysis methods require knowing the comparison groups (reference and focal groups) and anchor items (a subset of DIF-free items). Such prior knowledge may not always be available, and psychometric methods have been proposed for DIF analysis when one piece of information is unknown. More specifically, when the comparison groups are unknown while anchor items are known, latent DIF analysis methods have been proposed that estimate the unknown groups by latent classes. When anchor items are unknown while comparison groups are known, methods have also been proposed, typically under a sparsity assumption - the number of DIF items is not too large. However, there does not exist a method for DIF analysis when both pieces of information are unknown. This paper fills the gap. In the proposed method, we model the unknown groups by latent classes and introduce item-specific DIF parameters to capture the DIF effects. Assuming the number of DIF items is relatively small, an $L_1$-regularised estimator is proposed to simultaneously identify the latent classes and the DIF items. A computationally efficient Expectation-Maximisation (EM) algorithm is developed to solve the non-smooth optimisation problem for the regularised estimator. The performance of the proposed method is evaluated by simulation studies and an application to item response data from a real-world educational test
We provide a new information-theoretic generalization error bound that is exactly tight (i.e., matching even the constant) for the canonical quadratic Gaussian mean estimation problem. Despite considerable existing efforts in deriving information-theoretic generalization error bounds, applying them to this simple setting where sample average is used as the estimate of the mean value of Gaussian data has not yielded satisfying results. In fact, most existing bounds are order-wise loose in this setting, which has raised concerns about the fundamental capability of information-theoretic bounds in reasoning the generalization behavior for machine learning. The proposed new bound adopts the individual-sample-based approach proposed by Bu et al., but also has several key new ingredients. Firstly, instead of applying the change of measure inequality on the loss function, we apply it to the generalization error function itself; secondly, the bound is derived in a conditional manner; lastly, a reference distribution, which bears a certain similarity to the prior distribution in the Bayesian setting, is introduced. The combination of these components produces a general KL-divergence-based generalization error bound. We further show that although the conditional bounding and the reference distribution can make the bound exactly tight, removing them does not significantly degrade the bound, which leads to a mutual-information-based bound that is also asymptotically tight in this setting.
Since their introduction in Abadie and Gardeazabal (2003), Synthetic Control (SC) methods have quickly become one of the leading methods for estimating causal effects in observational studies in settings with panel data. Formal discussions often motivate SC methods by the assumption that the potential outcomes were generated by a factor model. Here we study SC methods from a design-based perspective, assuming a model for the selection of the treated unit(s) and period(s). We show that the standard SC estimator is generally biased under random assignment. We propose a Modified Unbiased Synthetic Control (MUSC) estimator that guarantees unbiasedness under random assignment and derive its exact, randomization-based, finite-sample variance. We also propose an unbiased estimator for this variance. We document in settings with real data that under random assignment, SC-type estimators can have root mean-squared errors that are substantially lower than that of other common estimators. We show that such an improvement is weakly guaranteed if the treated period is similar to the other periods, for example, if the treated period was randomly selected. While our results only directly apply in settings where treatment is assigned randomly, we believe that they can complement model-based approaches even for observational studies.
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests after the experiment is completed. The purpose of this paper is to aid in the development of optimal tests for sequential experiments by analyzing their asymptotic properties. Our key finding is that the asymptotic power function of any test can be matched by a test in a limit experiment where a Gaussian process is observed for each treatment, and inference is made for the drifts of these processes. This result has important implications, including a powerful sufficiency result: any candidate test only needs to rely on a fixed set of statistics, regardless of the type of sequential experiment. These statistics are the number of times each treatment has been sampled by the end of the experiment, along with final value of the score (for parametric models) or efficient influence function (for non-parametric models) process for each treatment. We then characterize asymptotically optimal tests under various restrictions such as unbiasedness, \alpha-spending constraints etc. Finally, we apply our our results to three key classes of sequential experiments: costly sampling, group sequential trials, and bandit experiments, and show how optimal inference can be conducted in these scenarios.
Grammatical Error Correction (GEC) is the task of automatically detecting and correcting errors in text. The task not only includes the correction of grammatical errors, such as missing prepositions and mismatched subject-verb agreement, but also orthographic and semantic errors, such as misspellings and word choice errors respectively. The field has seen significant progress in the last decade, motivated in part by a series of five shared tasks, which drove the development of rule-based methods, statistical classifiers, statistical machine translation, and finally neural machine translation systems which represent the current dominant state of the art. In this survey paper, we condense the field into a single article and first outline some of the linguistic challenges of the task, introduce the most popular datasets that are available to researchers (for both English and other languages), and summarise the various methods and techniques that have been developed with a particular focus on artificial error generation. We next describe the many different approaches to evaluation as well as concerns surrounding metric reliability, especially in relation to subjective human judgements, before concluding with an overview of recent progress and suggestions for future work and remaining challenges. We hope that this survey will serve as comprehensive resource for researchers who are new to the field or who want to be kept apprised of recent developments.
Integer linear programming models a wide range of practical combinatorial optimization problems and has significant impacts in industry and management sectors. This work develops the first standalone local search solver for general integer linear programming validated on a large heterogeneous problem dataset. We propose a local search framework that switches in three modes, namely Search, Improve, and Restore modes, and design tailored operators adapted to different modes, thus improve the quality of the current solution according to different situations. For the Search and Restore modes, we propose an operator named tight move, which adaptively modifies variables' values trying to make some constraint tight. For the Improve mode, an efficient operator lift move is proposed to improve the quality of the objective function while maintaining feasibility. Putting these together, we develop a local search solver for integer linear programming called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our solver in solving large-scale hard integer linear programming problems within a reasonably short time. Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our solver establishes new records for 6 MIPLIB open instances.
To estimate causal effects, analysts performing observational studies in health settings utilize several strategies to mitigate bias due to confounding by indication. There are two broad classes of approaches for these purposes: use of confounders and instrumental variables (IVs). Because such approaches are largely characterized by untestable assumptions, analysts must operate under an indefinite paradigm that these methods will work imperfectly. In this tutorial, we formalize a set of general principles and heuristics for estimating causal effects in the two approaches when the assumptions are potentially violated. This crucially requires reframing the process of observational studies as hypothesizing potential scenarios where the estimates from one approach are less inconsistent than the other. While most of our discussion of methodology centers around the linear setting, we touch upon complexities in non-linear settings and flexible procedures such as target minimum loss-based estimation (TMLE) and double machine learning (DML). To demonstrate the application of our principles, we investigate the use of donepezil off-label for mild cognitive impairment (MCI). We compare and contrast results from confounder and IV methods, traditional and flexible, within our analysis and to a similar observational study and clinical trial.
Stratification in both the design and analysis of randomized clinical trials is common. Despite features in automated randomization systems to re-confirm the stratifying variables, incorrect values of these variables may be entered. These errors are often detected during subsequent data collection and verification. Questions remain about whether to use the mis-reported initial stratification or the corrected values in subsequent analyses. It is shown that the likelihood function resulting from the design of randomized clinical trials supports the use of the corrected values. New definitions are proposed that characterize misclassification errors as `ignorable' and `non-ignorable'. Ignorable errors may depend on the correct strata and any other modeled baseline covariates, but they are otherwise unrelated to potential treatment outcomes. Data management review suggests most misclassification errors are arbitrarily produced by distracted investigators, so they are ignorable or at most weakly dependent on measured and unmeasured baseline covariates. Ignorable misclassification errors may produce a small increase in standard errors, but other properties of the planned analyses are unchanged (e.g., unbiasedness, confidence interval coverage). It is shown that unbiased linear estimation in the absence of misclassification errors remains unbiased when there are non-ignorable misclassification errors, and the corresponding confidence intervals based on the corrected strata values are conservative.
Conditional Average Treatment Effects (CATE) estimation is one of the main challenges in causal inference with observational data. In addition to Machine Learning based-models, nonparametric estimators called meta-learners have been developed to estimate the CATE with the main advantage of not restraining the estimation to a specific supervised learning method. This task becomes, however, more complicated when the treatment is not binary as some limitations of the naive extensions emerge. This paper looks into meta-learners for estimating the heterogeneous effects of multi-valued treatments. We consider different meta-learners, and we carry out a theoretical analysis of their error upper bounds as functions of important parameters such as the number of treatment levels, showing that the naive extensions do not always provide satisfactory results. We introduce and discuss meta-learners that perform well as the number of treatments increases. We empirically confirm the strengths and weaknesses of those methods with synthetic and semi-synthetic datasets.
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
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