Making decisions requires information relevant to the task at hand. Many real-life decision making situations allow acquiring further relevant information at a specific cost. For example, in assessing the health status of a patient we may decide to take additional measurements such as diagnostic tests or imaging scans before making a final assessment. More information that is relevant allows for better decisions but it may be costly to acquire all of this information. How can we trade off the desire to make good decisions with the option to acquire further information at a cost? To this end, we propose a principled framework, named EDDI (Efficient Dynamic Discovery of high-value Information), based on the theory of Bayesian experimental design. In EDDI we propose a novel partial variational autoencoder (Partial VAE), to efficiently handle missing data over varying subsets of known information. EDDI combines this Partial VAE with an acquisition function that maximizes expected information gain on a set of target variables. EDDI is efficient and demonstrates that dynamic discovery of high-value information is possible; we show cost reduction at the same decision quality and improved decision quality at the same cost in benchmarks and in two health-care applications. We believe there is great potential for realizing these gains in real-world decision support systems. * This work was done during his internship at Microsoft Research Cambridge. 1 arXiv:1809.11142v3 [cs. LG] 12 Oct 2018 always associated with cost. Given a task, such as estimating the costumers' experience or assessing population health status, we dynamically decide which piece of information to acquire next. The framework is very general, and the information can be presented in any form such as answers to questions, or values of a lab test. Our contributions are: • We propose a novel efficient information acquisition framework, EDDI (Section 3). To enable EDDI, we contribute technically: 1. A partial amortized inference method with different specifications for the inference network (Section 3.2). We extend a current amortized inference method, the variational autoencoder (VAE) (Kingma & Welling, 2014; Rezende et al., 2014) , to account for partial observations. The resulting method, which we call Partial VAE, is inspired by the set formulation of the data (Qi et al., 2017; Zaheer et al., 2017) . Partial VAE, as a probabilistic framework, is highly scalable, and serves as the base for the EDDI framework. However, Partial VAE itself is generic and can be used on its own as a non-linear probabilistic framework for missing-data imputation. 2. An information theoretic acquisition function with an efficient approximation, yielding a novel variable-wise active learning method (Section 3.3). Based on the partial VAE, we select the unobserved variable which contributes most to the task, such as health assessment, evaluated using the mutual information. This acquisition function does not have an analytical solution and we derive an efficient approximation. • We demonstrate the performance of EDDI on various settings, and apply it in real-life health-care scenarios (Section 4). 1. We first show the superior performance of the Partial VAE framework on an image inpainting task (Section 4.1). 2. We then use 6 different datasets from the Machine Learning repository of University of Irvine (UCI) (Dheeru & Karra Taniskidou, 2017) to demonstrate the behavior of EDDI, comparing with multiple baseline methods (Section 4.2). 3. Finally, we evaluate EDDI on two real-life health-care applications: risk assessment in intensive care (Section 4.3) and public health assessment with national survey (Section 4.4), where traditional methods without amortized inference do not scale. EDDI shows clear improvements in these two applications.
It then computes the mutual information between the current representation and each of the available features to select the feature that minimizes this information REF .
EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE
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Mathematics Computer Science