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Randomized A/B tests within online learning platforms represent an exciting direction in learning sciences. With minimal assumptions, they allow causal effect estimation without confounding bias and exact statistical inference even in small samples. However, often experimental samples and/or treatment effects are small, A/B tests are underpowered, and effect estimates are overly imprecise. Recent methodological advances have shown that power and statistical precision can be substantially boosted by coupling design-based causal estimation to machine-learning models of rich log data from historical users who were not in the experiment. Estimates using these techniques remain unbiased and inference remains exact without any additional assumptions. This paper reviews those methods and applies them to a new dataset including over 250 randomized A/B comparisons conducted within ASSISTments, an online learning platform. We compare results across experiments using four novel deep-learning models of auxiliary data and show that incorporating auxiliary data into causal estimates is roughly equivalent to increasing the sample size by 20% on average, or as much as 50-80% in some cases, relative to t-tests, and by about 10% on average, or as much as 30-50%, compared to cutting-edge machine learning unbiased estimates that use only data from the experiments. We show that the gains can be even larger for estimating subgroup effects, hold even when the remnant is unrepresentative of the A/B test sample, and extend to post-stratification population effects estimators. 

Randomized controlled trials (RCTs) admit unconfounded design-based inference – randomization largely justifies the assumptions underlying statistical effect estimates – but often have limited sample sizes. However, researchers may have access to big observational data on covariates and outcomes from RCT nonparticipants. For example, data from A/B tests conducted within an educational technology platform exist alongside historical observational data drawn from student logs. We outline a design-based approach to using such observational data for variance reduction in RCTs. First, we use the observational data to train a machine learning algorithm predicting potential outcomes using covariates and then use that algorithm to generate predictions for RCT participants. Then, we use those predictions, perhaps alongside other covariates, to adjust causal effect estimates with a flexible, design-based covariate-adjustment routine. In this way, there is no danger of biases from the observational data leaking into the experimental estimates, which are guaranteed to be exactly unbiased regardless of whether the machine learning models are “correct” in any sense or whether the observational samples closely resemble RCT samples. We demonstrate the method in analyzing 33 randomized A/B tests and show that it decreases standard errors relative to other estimators, sometimes substantially.

 

Summary Genomic data sets contain the effects of various unobserved biological variables in addition to the variable of primary interest. These latent variables often affect a large number of features (e.g., genes), giving rise to dense latent variation. This latent variation presents both challenges and opportunities for classification. While some of these latent variables may be partially correlated with the phenotype of interest and thus helpful, others may be uncorrelated and merely contribute additional noise. Moreover, whether potentially helpful or not, these latent variables may obscure weaker effects that impact only a small number of features but more directly capture the signal of primary interest. To address these challenges, we propose the cross-residualization classifier (CRC). Through an adjustment and ensemble procedure, the CRC estimates and residualizes out the latent variation, trains a classifier on the residuals, and then reintegrates the latent variation in a final ensemble classifier. Thus, the latent variables are accounted for without discarding any potentially predictive information. We apply the method to simulated data and a variety of genomic data sets from multiple platforms. In general, we find that the CRC performs well relative to existing classifiers and sometimes offers substantial gains. 

There is interest in using social media content to supplement or even substitute for survey data. In one of the first studies to test the feasibility of this idea, O’Connor, Balasubramanyan, Routledge, and Smith report reasonably high correlations between the sentiment of tweets containing the word “jobs” and survey-based measures of consumer confidence in 2008–2009. Other researchers report a similar relationship through 2011, but after that time it is no longer observed, suggesting such tweets may not be as promising an alternative to survey responses as originally hoped. But, it’s possible that with the right analytic techniques, the sentiment of “jobs” tweets might still be an acceptable alternative. To explore this, we first classify “jobs” tweets into categories whose content is either related to employment or not, to see whether sentiment of the former correlates more highly with a survey-based measure of consumer sentiment. We then compare the relationship when sentiment is determined with traditional dictionary-based methods versus newer machine learning-based tools developed for Twitter-like texts. We calculated daily sentiment in three different ways and used a measure of association less sensitive to outliers than correlation. None of these approaches improved the size of the relationship in the original or more recent data. We found that the many micro-decisions these analyses require, such as the size of the smoothing interval and the length of the lag between the two series, can significantly affect the outcomes. In the end, despite the earlier promise of tweets as an alternative to survey responses, we find no evidence that the original relationship in these data was more than a chance occurrence.