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Applications from finance to epidemiology and cyber-security require accurate forecasts of dynamic phenomena, which are often only partially observed. We demonstrate that a systems predictability degrades as a function of temporal sampling, regardless of the adopted forecasting model. We quantify the loss of predictability due to sampling, and show that it cannot be recovered by using external signals. We validate the generality of our theoretical findings in real-world partially observed systems representing infectious disease outbreaks, online discussions, and software development projects. On a variety of prediction tasks---forecasting new infections, the popularity of topics in online discussions, or interest in cryptocurrency projects---predictability irrecoverably decays as a function of sampling, unveiling fundamental predictability limits in partially observed systems.
Entropy-based measures are an important tool for studying human gaze behavior under various conditions. In particular, gaze transition entropy (GTE) is a popular method to quantify the predictability of fixation transitions. However, GTE does not acc
One of the most fundamental questions one can ask about a pair of random variables X and Y is the value of their mutual information. Unfortunately, this task is often stymied by the extremely large dimension of the variables. We might hope to replace
In this paper, we consider the problem of controlling a partially observed Markov decision process (POMDP) in order to actively estimate its state trajectory over a fixed horizon with minimal uncertainty. We pose a novel active smoothing problem in w
Predictive models for human mobility have important applications in many fields such as traffic control, ubiquitous computing and contextual advertisement. The predictive performance of models in literature varies quite broadly, from as high as 93% t
System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent approximat