Batch mode active sampling based on marginal probability distribution matching

Abstract

Active Learning is a machine learning and data mining technique that selects the most informative samples for labeling and uses them as training data; it is especially useful when there are large amount of unlabeled data and labeling them is expensive. Recently, batch-mode active learning, where a set of samples are selected concurrently for labeling, based on their collective merit, has attracted a lot of attention. The objective of batch-mode active learning is to select a set of informative samples so that a classifier learned on these samples has good generalization performance on the unlabeled data. Most of the existing batch-mode active learning methodologies try to achieve this by selecting samples based on varied criteria. In this paper we propose a novel criterion which achieves good generalization performance of a classifier by specifically selecting a set of query samples that minimizes the difference in distribution between the labeled and the unlabeled data, after annotation. We explicitly measure this difference based on all candidate subsets of the unlabeled data and select the best subset. The proposed objective is an NP-hard integer programming optimization problem. We provide two optimization techniques to solve this problem. In the first one, the problem is transformed into a convex quadratic programming problem and in the second method the problem is transformed into a linear programming problem. Our empirical studies using publicly available UCI datasets and a biomedical image dataset demonstrate the effectiveness of the proposed approach in comparison with the state-of-the-art batch-mode active learning methods. We also present two extensions of the proposed approach, which incorporate uncertainty of the predicted labels of the unlabeled data and transfer learning in the proposed formulation. Our empirical studies on UCI datasets show that incorporation of uncertainty information improves performance at later iterations while our studies on 20 Newsgroups dataset show that transfer learning improves the performance of the classifier during initial iterations.

Multi-label active learning by model guided distribution matching

“…from the same distribution [23]. Based on this, Chattopadhyay et al proposed a novel selection strategy for single-label active learning in [20], which iteratively selects a set of query samples Q from U, such that P(X, Y) represented by L ∪ Q and U\Q are similar to each other. Since the conditional probability P(Y|X) remains the same for both L and U as they are drawn from the same underlying distribution, the problem reduces to selecting Q such that the marginal probability P L∪Q (X) is similar to P U\Q (X).…”

“…Similar to [24,25], we employ maximal mean discrepancy (MMD) to empirically measure the difference between the marginal probability distributions of two sets, which has been widely used for this purpose [20,26,27]. It is a statistical test based on the fact that two distributions are different if and only if there exists at least one function in a universal reproducing kernel Hilbert space (RKHS) having different expectations on the two distributions [28].…”

“…The approaches presented in [19,20] selected those instances with minimal difference in Fisher information and Maximal Mean Discrepancy respectively between the selected and labeled datasets. In [21], a batch of queries were selected at each iteration by maximizing a mutual information criterion between the selected and labeled instances.…”

“…If we apply MMD directly into multi-label active learning scenarios, followed by [20], obviously it can only be used for instances selection. In other words, it is appropriate for single-label active learning tasks when just considering matching marginal distribution in the feature space using MMD.…”

“…If instancelabel pair (x i , y i j ) has not been queried, z i j belongs to the unlabeled dataset U, that is, z i j ∈ U, otherwise z i j ∈ L. According to the above assumption, we can infer that at the beginning of active learning, the number of unlabeled samples in U is N u = n u × C and the number of labeled samples in L is N l = n l × C. For selecting a batch Q of size b such that the distribution in the feature and label space of L ∪ Q is similar to that of U\Q, inspired by [20], we can obtain the MMD between them defined by g(Q) using Eq. (3).…”