Setting the duration of online A/B experiments

In designing an online A/B experiment, it is crucial to select a sample size and duration that ensure the resulting confidence interval (CI) for the treatment effect is the right width to detect an effect of meaningful magnitude with sufficient statistical power without wasting resources. While the relationship between sample size and CI width is well understood, the effect of experiment duration on CI width remains less clear. This paper provides an analytical formula for the width of a CI based on a ratio treatment effect estimator as a function of both sample size (N) and duration (T). The formula is derived from a mixed effects model with two variance components. One component, referred to as the temporal variance, persists over time for experiments where the same users are kept in the same experiment arm across different days. The remaining error variance component, by contrast, decays to zero as T gets large. The formula we derive introduces a key parameter that we call the user-specific temporal correlation (UTC), which quantifies the relative sizes of the two variance components and can be estimated from historical experiments. Higher UTC indicates a slower decay in CI width over time. On the other hand, when the UTC is 0 -- as for experiments where users shuffle in and out of the experiment across days -- the CI width decays at the standard parametric 1/T rate. We also study how access to pre-period data for the users in the experiment affects the CI width decay. We show our formula closely explains CI widths on real A/B experiments at YouTube.

RbX: Region-based explanations of prediction models

We introduce region-based explanations (RbX), a novel, model-agnostic method to generate local explanations of scalar outputs from a black-box prediction model using only query access. RbX is based on a greedy algorithm for building a convex polytope that approximates a region of feature space where model predictions are close to the prediction at some target point. This region is fully specified by the user on the scale of the predictions, rather than on the scale of the features. The geometry of this polytope - specifically the change in each coordinate necessary to escape the polytope - quantifies the local sensitivity of the predictions to each of the features. These "escape distances" can then be standardized to rank the features by local importance. RbX is guaranteed to satisfy a "sparsity axiom," which requires that features which do not enter into the prediction model are assigned zero importance. At the same time, real data examples and synthetic experiments show how RbX can more readily detect all locally relevant features than existing methods.