Actively Inferring Optimal Measurement Sequences
Abstract: Measurement of a physical quantity such as light intensity is an integral part of many reconstruction and decision scenarios but can be costly in terms of acquisition time, invasion of or damage to the environment and storage. Data minimisation and compliance with data protection laws is also an important consideration. Where there are a range of measurements that can be made, some may be more informative and compliant with the overall measurement objective than others. We develop an active sequential inference algorithm that uses the low dimensional representational latent space from a variational autoencoder (VAE) to choose which measurement to make next. Our aim is to recover high dimensional data by making as few measurements as possible. We adapt the VAE encoder to map partial data measurements on to the latent space of the complete data. The algorithm draws samples from this latent space and uses the VAE decoder to generate data conditional on the partial measurements. Estimated measurements are made on the generated data and fed back through the partial VAE encoder to the latent space where they can be evaluated prior to making a measurement. Starting from no measurements and a normal prior on the latent space, we consider alternative strategies for choosing the next measurement and updating the predictive posterior prior for the next step. The algorithm is illustrated using the Fashion MNIST dataset and a novel convolutional Hadamard pattern measurement basis. We see that useful patterns are chosen within 10 steps, leading to the convergence of the guiding generative images. Compared with using stochastic variational inference to infer the parameters of the posterior distribution or each generated data point individually, the partial VAE framework can efficiently process batches of generated data and obtains superior results with minimal measurements.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: We have addressed the reviewers' suggestions and updated the text in the revised manuscript (new text in blue italics) as follows:
Introduction:Added to the definition of variational inference with new reference
Related work: Expanded this section with several more references
Equation (3): modified to improve clarity
Equation (6): corrected typo
Equation (12): added brackets to improve clarity
Figures 3 and figures 4: Added timings for methods in legend
Assigned Action Editor: ~Oleg_Arenz1
Submission Number: 3143
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