We develop a Bayesian model for decision-making under time pressure with endogenous information acquisition. In our model, the decision-maker decides when to observe (costly) information by sampling an underlying continuoustime stochastic process (time series) that conveys information about the potential occurrence/non-occurrence of an adverse event which will terminate the decisionmaking process. In her attempt to predict the occurrence of the adverse event, the decision-maker follows a policy that determines when to acquire information from the time series (continuation), and when to stop acquiring information and make a final prediction (stopping). We show that the optimal policy has a "rendezvous" structure, i.e. a structure in which whenever a new information sample is gathered from the time series, the optimal "date" for acquiring the next sample becomes computable. The optimal interval between two information samples balances a trade-off between the decision maker's "surprise", i.e. the drift in her posterior belief after observing new information, and "suspense", i.e. the probability that the adverse event occurs in the time interval between two information samples. Moreover, we characterize the continuation and stopping regions in the decisionmaker's state-space, and show that they depend not only on the decision-maker's beliefs, but also on the "context", i.e. the current realization of the time series.

Understanding the predictions of a machine learning model can be as crucial as the model's accuracy in many application domains. However, the black-box nature of most highly-accurate (complex) models is a major hindrance to their interpretability. To address this issue, we introduce the symbolic metamodeling framework -- a general methodology for interpreting predictions by converting "black-box" models into "white-box" functions that are understandable to human subjects. A symbolic metamodel is a model of a model, i.e., a surrogate model of a trained (machine learning) model expressed through a succinct symbolic expression that comprises familiar mathematical functions and can be subjected to symbolic manipulation. We parameterize metamodels using Meijer G-functions -- a class of complex-valued contour integrals that depend on real-valued parameters, and whose solutions reduce to familiar algebraic, analytic and closed-form functions for different parameter settings. This parameterization enables efficient optimization of metamodels via gradient descent, and allows discovering the functional forms learned by a model with minimal a priori assumptions. We show that symbolic metamodeling provides a generalized framework for model interpretation -- many common forms of model explanation can be analytically derived from a symbolic metamodel.

Models of disease progression are instrumental for predicting patient outcomes and understanding disease dynamics. Existing models provide the patient with pragmatic (supervised) predictions of risk, but do not provide the clinician with intelligible (unsupervised) representations of disease pathology. In this paper, we develop the attentive state-space model, a deep probabilistic model that learns accurate and interpretable structured representations for disease trajectories. Unlike Markovian state-space models, in which state dynamics are memoryless, our model uses an attention mechanism to create "memoryful" dynamics, whereby attention weights determine the dependence of future disease states on past medical history. To learn the model parameters from medical records, we develop an inference algorithm that jointly learns a compiled inference network and the model parameters, leveraging the attentive representation to construct a variational approximation of the posterior state distribution. Experiments on data from the UK Cystic Fibrosis registry show that our model demonstrates superior predictive accuracy, in addition to providing insights into disease progression dynamic.

Models of disease progression are instrumental for predicting patient outcomes and understanding disease dynamics. Existing models provide the patient with pragmatic (supervised) predictions of risk, but do not provide the clinician with intelligible (unsupervised) representations of disease pathology. In this paper, we develop the attentive state-space model, a deep probabilistic model that learns accurate and interpretable structured representations for disease trajectories. Unlike Markovian state-space models, in which state dynamics are memoryless, our model uses an attention mechanism to create "memoryful" dynamics, whereby attention weights determine the dependence of future disease states on past medical history. To learn the model parameters from medical records, we develop an inference algorithm that jointly learns a compiled inference network and the model parameters, leveraging the attentive representation to construct a variational approximation of the posterior state distribution. Experiments on data from the UK Cystic Fibrosis registry show that our model demonstrates superior predictive accuracy, in addition to providing insights into disease progression dynamic.

Neural Information Processing Systems http://nips.cc/