Feedback has a powerful influence on learning, but it is also expensive to provide. In large classes it may even be impossible for instructors to provide individualized feedback. Peer assessment is one way to provide personalized feedback that scales to large classes. Besides these obvious logistical benefits, it has been conjectured that students also learn from the practice of peer assessment. However, this has never been conclusively demonstrated. Using an online educational platform that we developed, we conducted an in-class matched-set, randomized crossover experiment with high power to detect small effects. We establish that peer assessment causes a small but significant gain in student achievement. Our study also demonstrates the potential of web-based platforms to facilitate the design of high-quality experiments to identify small effects that were previously not detectable.

LazySorted is a Python C extension implementing a partially and lazily sorted list data structure. It solves a common problem faced by programmers, in which they need just part of a sorted list, like its middle element (the median), but sort the entire list to get it. LazySorted presents them with the abstraction that they are working with a fully sorted list, while actually only sorting the list partially with quicksort partitions to return the requested sub-elements. This enables programmers to use naive "sort first" algorithms but nonetheless attain linear run-times when possible. LazySorted may serve as a drop-in replacement for the built-in sorted function in most cases, and can sometimes achieve run-times more than 7 times faster.

A new line of research [5] on the lasso [8] exploits the beautiful geometric fact that the lasso fit is the residual from projecting the response vector y onto a certain convex polytope [10]. This geometric picture also allows an exact geometric description of the set of accessible lasso models for a given design matrix, that is, which configurations of the signs of the coefficients it is possible to realize with some choice of y. In particular, the accessible lasso models are those that correspond to a face of the convex hull of all the feature vectors together with their negations. This convex hull representation then permits the enumeration and bounding of the number of accessible lasso models, which in turn provides a direct proof of model selection inconsistency when the size of the true model is greater than half the number of observations. Primary 62J07; secondary 52B12.