Near-Optimal Bayesian Active Learning with Noisy Observations (1010.3091v2)

Abstract: We tackle the fundamental problem of Bayesian active learning with noise, where we need to adaptively select from a number of expensive tests in order to identify an unknown hypothesis sampled from a known prior distribution. In the case of noise-free observations, a greedy algorithm called generalized binary search (GBS) is known to perform near-optimally. We show that if the observations are noisy, perhaps surprisingly, GBS can perform very poorly. We develop EC2, a novel, greedy active learning algorithm and prove that it is competitive with the optimal policy, thus obtaining the first competitiveness guarantees for Bayesian active learning with noisy observations. Our bounds rely on a recently discovered diminishing returns property called adaptive submodularity, generalizing the classical notion of submodular set functions to adaptive policies. Our results hold even if the tests have non-uniform cost and their noise is correlated. We also propose EffECXtive, a particularly fast approximation of EC2, and evaluate it on a Bayesian experimental design problem involving human subjects, intended to tease apart competing economic theories of how people make decisions under uncertainty.

• The paper proposes EC2, a novel greedy algorithm providing the first competitiveness guarantees for Bayesian active learning in settings with noisy and costly observations.
• EC2 is theoretically proven to be competitive with the optimal policy even when tests have non-uniform costs and correlated noise.
• An efficient approximation, EffECXtive, demonstrates superior performance over existing heuristics and is applicable in practical areas like medical diagnosis and experimental economics.

Near-Optimal Bayesian Active Learning with Noisy Observations

The paper addresses a critical issue in Bayesian active learning: how to effectively select among noisy and costly tests to accurately determine an unknown hypothesis. The paper focuses on scenarios where observations are not noise-free, challenging the efficacy of existing algorithms such as Generalized Binary Search (GBS), which is optimal for noise-free environments.

Key Contributions

1. Algorithm Development: The authors propose a novel greedy active learning algorithm—referred to as Equivalence Class Edge Cutting (EC2)—which offers competitiveness guarantees in noisy observation settings. The algorithm is based on the notion of adaptive submodularity, a recently discovered property extending the classical submodular set functions to adaptive policies.
2. Theoretical Guarantees: EC2 is shown to be competitive with the optimal policy, providing the first competitiveness bounds for Bayesian active learning with noisy observations. This is achieved even when tests have non-uniform costs and correlated noise.
3. Efficient Approximation: The paper introduces EffECXtive, a computationally efficient approximation of EC2, which is evaluated within the context of Bayesian experimental design. This approximation is particularly useful in practical applications that involve human subjects and competing economic theories.
4. Comparative Analysis: Through simulations, EC2 and EffECXtive demonstrate superior performance over other heuristic-based criteria, including information gain, uncertainty sampling, GBS, and decision-theoretic value of information.

Implications and Future Prospects

The implications of this research are significant for both theoretical and practical dimensions of artificial intelligence and decision sciences:

• Theoretical Advancement: By establishing a theoretically sound framework for active learning with noise, this work extends the boundaries of adaptive learning algorithms and their applicability in non-ideal, real-world environments.
• Practical Applications: The methodologies developed can be applied across various domains including medical diagnosis, where tests are both costly and potentially noisy, and in experimental economics, particularly in understanding human decision-making under uncertainty.
• Speculative Directions: Future work may focus on refining these competitive guarantees, exploring different noise models, and evaluating the algorithms in more complex real-world scenarios. Moreover, integrating these algorithms with other AI systems could enhance their resilience and decision-making capabilities under uncertainty.

In conclusion, the paper makes a substantial contribution to the field of Bayesian active learning by introducing a robust framework capable of handling noisy and expensive observational scenarios. The proposed algorithms and theoretical insights are poised to influence both academic research and practical applications in fields requiring adaptive decision-making under uncertainty.