Graph-based active learning: A new look at expected error minimization

Abstract

In graph-based active learning, algorithms based on expected error minimization (EEM) have been popular and yield good empirical performance. The exact computation of EEM optimally balances exploration and exploitation. In practice, however, EEM-based algorithms employ various approximations due to the computational hardness of exact EEM. This can result in a lack of either exploration or exploitation, which can negatively impact the effectiveness of active learning. We propose a new algorithm TSA (Two-Step Approximation) that balances between exploration and exploitation efficiently while enjoying the same computational complexity as existing approximations. Finally, we empirically show the value of balancing between exploration and exploitation in both toy and real-world datasets where our method outperforms several state-of-the-art methods.

Data-Adaptive Active Sampling for Efficient Graph-Cognizant Classification

“…Remark 3. Existing data-adaptive sampling schemes, e.g., [13], [16], [14], often require model-retraining by examining candidate labels per unlabeled node (cf. (8)).…”

“…Interestingly, the utility in (16) leads to a form of uncertainty sampling, since (1 − µ 2 i ) is a measure of uncertainty of the model prediction for node v i , further normalized by g ii , which is the variance of the Gaussian field (cf. [10]).…”

“…Uncertainty-sampling-based criteria are also typically very lightweight requiring for instance sorting class-wise the soft labels of each node (O(log |C|N ) per sample). While uncertainty-based methods are faster and more scalable, their accuracy is typically significantly lower than that of more sophisticated methods that use G. Methods that use G such as the proposed EC algorithms in Section III, the expected-error minimization (EER) in [13], and the two-step approximation (TSA) algorithm in [16] all require O(N 2 ) to perform the update in (10). However, TSA and EER use retraining (cf.…”

“…One possible means of reducing bias is by complementing greedy active learning strategies with random sampling. Thats is, instead of selecting the index k t of the node to be sampled at the t−th iteration according to (8), one can opt for a two- [9], TSA [16] O…”

“…Such data-adaptive methods give rise to sampling schemes that are not optimal on average, but adapt to a given realization of labels on the graph. Adaptive methods include the Bayesian risk minimization [13], the information gain maximization [14], as well as the manifold preserving method of [15]; see also [16]- [18]. Finally, related works deal with selective sampling of nodes that arrive sequentially in a gradually augmented graph [19]- [21], as well as active sampling to infer the graph structure [22], [23].…”