Near-optimal Bayesian active learning with correlated and noisy tests

We consider the Bayesian active learning and experimental design problem, where the goal is to learn the value of some unknown target variable through a sequence of informative, noisy tests. In contrast to prior work, we focus on the challenging, yet practically relevant setting where test outcomes can be conditionally dependent given the hidden target variable. Under such assumptions, common heuristics, such as greedily performing tests that maximize the reduction in uncertainty of the target, often perform poorly. We propose ECED, a novel, efficient active learning algorithm, and prove strong theoretical guarantees that hold with correlated, noisy tests. Rather than directly optimizing the prediction error, at each step, ECED picks the test that maximizes the gain in a surrogate objective, which takes into account the dependencies between tests. Our analysis relies on an information-theoretic auxiliary function to track the progress of ECED, and utilizes adaptive submodularity to attain the approximation bound. We demonstrate strong empirical performance of ECED on three problem instances, including a Bayesian experimental design task intended to distinguish among economic theories of how people make risky decisions, an active preference learning task via pairwise comparisons, and a third application on pool-based active learning

Leveraging Crowdsourcing Data For Deep Active Learning - An Application: Learning Intents in Alexa

This paper presents a generic Bayesian framework that enables any deep learning model to actively learn from targeted crowds. Our framework inherits from recent advances in Bayesian deep learning, and extends existing work by considering the targeted crowdsourcing approach, where multiple annotators with unknown expertise contribute an uncontrolled amount (often limited) of annotations. Our framework leverages the low-rank structure in annotations to learn individual annotator expertise, which then helps to infer the true labels from noisy and sparse annotations. It provides a unified Bayesian model to simultaneously infer the true labels and train the deep learning model in order to reach an optimal learning efficacy. Finally, our framework exploits the uncertainty of the deep learning model during prediction as well as the annotators' estimated expertise to minimize the number of required annotations and annotators for optimally training the deep learning model. We evaluate the effectiveness of our framework for intent classification in Alexa (Amazon's personal assistant), using both synthetic and real-world datasets. Experiments show that our framework can accurately learn annotator expertise, infer true labels, and effectively reduce the amount of annotations in model training as compared to state-of-the-art approaches. We further discuss the potential of our proposed framework in bridging machine learning and crowdsourcing towards improved human-in-the-loop systems

Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy.Comment: 23 pages, 13 figure

Active inference and oculomotor pursuit: the dynamic causal modelling of eye movements.

This paper introduces a new paradigm that allows one to quantify the Bayesian beliefs evidenced by subjects during oculomotor pursuit. Subjects' eye tracking responses to a partially occluded sinusoidal target were recorded non-invasively and averaged. These response averages were then analysed using dynamic causal modelling (DCM). In DCM, observed responses are modelled using biologically plausible generative or forward models - usually biophysical models of neuronal activity