Specifically, givenasetofmeansµ, itcanbeshownthatU in (3) belowistheoptimalmembership weightsminimizingthecostin(2) (see, e.g., [8][Theorem 11.1]). Pick , 2(0,1), and 2(0,1).

Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the flexibility ofbeing directly applicable todown-stream applications.

Sparsedeeplearning aimstoaddress thechallenge ofhugestorage consumption by deep neural networks, and to recover the sparse structure of target functions.

Causal structure learning is a key problem in many domains. Causal structures can be learnt by performing experiments on the system of interest.

Let B denote the batch size chosen for MABSplit. Note that there are at mostnB rounds in the main while loop (Line 6) of Algorithm 1 and hence at mostnmTB nmT confidence intervals computed across all arms and all steps of the algorithm. Since the mainwhile loop in the algorithm can only run nB times, the algorithm must terminate. Furthermore, if all confidence intervals throughout the algorithm are correct, itisimpossible for(f,t)tobe removed from the set ofcandidate arms. Finally, we consider the complexity of Algorithm 1. Letnused be the total number of arm pulls computed for each arm remaining in the set of candidate arms at a given point in the algorithm.

We demonstrate similar speedups when MABSplit is used across a variety of forest-based variants, such as Extremely Random Forests and Random Patches.

The SP algorithm requires the voters to predict other voters' report in the form of a full probability distribution over all rankings of alternatives.