[Paper Review] Bayesian Batch Active Learning as Sparse Subset Approximation

Robert Pinsler, Jonathan Gordon+2 more|arXiv (Cornell University)|Aug 6, 2019

Machine Learning and AlgorithmsComputer Science45 references43 citations

TL;DR

Introduces ACS-FW, a Bayesian batch active learning method that constructs diverse, informative batches by approximating the full data posterior with a sparse subset using Frank-Wolfe optimization and random projections.

ABSTRACT

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the most informative data points to be labeled. However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change. In this paper, we introduce a novel Bayesian batch active learning approach that mitigates these issues. Our approach is motivated by approximating the complete data posterior of the model parameters. While naive batch construction methods result in correlated queries, our algorithm produces diverse batches that enable efficient active learning at scale. We derive interpretable closed-form solutions akin to existing active learning procedures for linear models, and generalize to arbitrary models using random projections. We demonstrate the benefits of our approach on several large-scale regression and classification tasks.

Motivation & Objective

• Leverage大量 unlabeled data to improve supervised models under high labeling costs.
• Prevent highly correlated batch queries and enable scalable batch active learning.
• Provide closed-form insights for linear and probit models and a generalizable approach for arbitrary models via projections.

Proposed method

• Formulate batch construction as a sparse subset approximation to the expected complete data log posterior.
• Relax the 0-1 batch selection to a non-negative weight vector with a budget constraint and solve via Frank-Wolfe in a Hilbert space.
• Define L_m(θ) as the per-point log-likelihood contribution plus entropy term and optimize the weighted sum to approximate the full pool contribution.
• Use inner products to encode similarity between data points, with two concrete choices: weighted Fisher inner product and weighted Euclidean inner product.
• Provide analytic closed-form solutions for linear and probit regression in the weighted Fisher inner product setting.
• Extend to non-linear models with random feature projections to keep computations scalable to large pool sizes.

Experimental results

Research questions

• RQ1 Does the proposed ACS-FW method avoid highly correlated batch queries typical of standard batch AL strategies?
• RQ2 Is ACS-FW competitive with greedy batch AL methods in small-data regimes?
• RQ3 Can ACS-FW scale to large datasets and complex models while maintaining or improving performance?

Key findings

• ACS-FW yields diverse batches that cover the data manifold, reducing query redundancy.
• In small-data regimes, ACS-FW outperforms random batching and is competitive with MaxEnt-based approaches.
• With larger datasets and models, projection-based ACS-FW scales to hundreds of thousands of examples and outperforms random and non-probabilistic baselines, while matching or surpassing competitive batch AL methods.
• Analytic expressions for linear and probit models reveal connections to existing AL methods and intuitive leverage-like quantities.
• Random projections enable a model-agnostic, scalable approximation of batch construction for any tractable likelihood.
• Empirical results on regression and classification tasks show data-efficient learning and scalable runtime performance.