Paper:
Budgeted stream-based active learning via adaptive submodular maximization
Active learning enables us to reduce the annotation cost by adaptively selecting unlabeled instances to be labeled. For pool-based active learning, several effective methods with theoretical guarantees have been developed through maximizing some utility function satisfying adaptive submodularity. In contrast, there have been few methods for stream-based active learning based on adaptive submodularity. In this paper, we propose a new class of utility functions, policy-adaptive submodular functions, which includes many existing adaptive submodular functions appearing in real world problems. We provide a general framework based on policy-adaptive submodularity that makes it possible to convert existing poolbased methods to stream-based methods and give theoretical guarantees on their performance. In addition we empirically demonstrate their effectiveness by comparing with existing heuristics on common benchmark datasets.

Review:
This paper studies the budgeted active learning problem (as under a cardinality constraint) in the stream-based setting. The paper assumes that data arrives in a stream in a RANDOM order, and provide analysis for both the steam and secretary settings, when the objective function satisfies a notion called policy-adaptive submodularity. This property is an extension of submodularity to the adaptive setting, but stricter than adaptive submodularity (in the sense that it considers the gain of a policy as opposed to the gain of a test; however in the adaptive setting a partial realization changes not only the distribution of a test outcome, but also the structure of a policy, and this policy-adaptive submodularity imposes a stronger constraint). The authors show that several adaptive submodular objective functions in active learning also satisfies policy-adaptive submodualriy, and then proposes algorithms stream-based learning. Finally the results are backed-up by the evaluation of the stream and secretary algorithms against pool-based algorithm on UCI WDBC and MNIST dataset.
Pros:           The presentation is mostly clear. The paper shows that one can apply the proposed streaming algorithm, without changing the commonly used objective functions used in pool-based active learning setting. Proofs are sound, and experimental results show that the proposed algorithms work reasonably well in comparison with the pool-based setting.            Cons:                      The stream-based adaptive sensor placement application does not appear convincing to me.                      Is the condition $range(\pi) \subseteq V \setminus B$ in Def 3.1 necessary?                      Policy-adaptive submodularity is used for providng a lower bound on the expected gain of a policy on a random sequence of data points (Lemma B.7). It would be useful and more insightful if the authors can provide intuition in the main paper of why adaptive submodularity is not sufficient for the proof. Is policy-adaptive submodilarity (provably) necessary? or are there examples of adaptive submodular functions (which are not policy-adaptive submodular) that can not achieve the provided theoretical guarantee?                      Data arriving at a random order seems to be a strict constraint. It's a necessary assumption for the (adaptive secretary) algorithm to work provably well, because the algorithm discards the first 1/e data points in each segment, which can contain the most beneficial points in each segment. The authors point out the need of a new algorithm when the data arrives in a fixed order; it would be helpful (for completeness) to provide some very brief discussion on this (i.e., what applications fall into this category; why it's challenging; if there is any insight, or perhaps to point possible directions for solving this problem).                      Editorial issues:           Example A.6, There are two joint probabilities of P[Ya = +1, Yb = +1]. One of them should be P[Ya = +1, Yb = -1].           Ln 103, k labeled instances of the high utility --> k labeled instances of high utility           Lemma B.4, Let f: .. --> Let g: ...