BackgroundRegular physical activity is known to be beneficial for people with type 2 diabetes. Nevertheless, most of the people who have diabetes lead a sedentary lifestyle. Smartphones create new possibilities for helping people to adhere to their physical activity goals through continuous monitoring and communication, coupled with personalized feedback.ObjectiveThe aim of this study was to help type 2 diabetes patients increase the level of their physical activity.MethodsWe provided 27 sedentary type 2 diabetes patients with a smartphone-based pedometer and a personal plan for physical activity. Patients were sent short message service messages to encourage physical activity between once a day and once per week. Messages were personalized through a Reinforcement Learning algorithm so as to improve each participant’s compliance with the activity regimen. The algorithm was compared with a static policy for sending messages and weekly reminders.ResultsOur results show that participants who received messages generated by the learning algorithm increased the amount of activity and pace of walking, whereas the control group patients did not. Patients assigned to the learning algorithm group experienced a superior reduction in blood glucose levels (glycated hemoglobin [HbA1c]) compared with control policies, and longer participation caused greater reductions in blood glucose levels. The learning algorithm improved gradually in predicting which messages would lead participants to exercise.ConclusionsMobile phone apps coupled with a learning algorithm can improve adherence to exercise in diabetic patients. This algorithm can be used in large populations of diabetic patients to improve health and glycemic control. Our results can be expanded to other areas where computer-led health coaching of humans may have a positive impact. Summary of a part of this manuscript has been previously published as a letter in Diabetes Care, 2016.
The Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter may be approximated by regression on a few recent observations. Surprisingly, we also show that having some process noise is essential for the exponential decay. With no process noise, it may happen that the forecast depends on all of the past uniformly, which makes forecasting more difficult.Based on this insight, we devise an on-line algorithm for improper learning of a linear dynamical system (LDS), which considers only a few most recent observations. We use our decay results to provide the first regret bounds w.r.t. to Kalman filters within learning an LDS. That is, we compare the results of our algorithm to the best, in hindsight, Kalman filter for a given signal. Also, the algorithm is practical: its per-update run-time is linear in the regression depth. arXiv:1809.05870v1 [math.ST]
Suppose that we are given a time series where consecutive samples are believed to come from a probabilistic source, that the source changes from time to time and that the total number of sources is fixed. Our objective is to estimate the distributions of the sources. A standard approach to this problem is to model the data as a hidden Markov model (HMM). However, since the data often lacks the Markov or the stationarity properties of an HMM, one can ask whether this approach is still suitable or perhaps another approach is required. In this paper we show that a maximum likelihood HMM estimator can be used to approximate the source distributions in a much larger class of models than HMMs. Specifically, we propose a natural and fairly general non-stationary model of the data, where the only restriction is that the sources do not change too often. Our main result shows that for this model, a maximum-likelihood HMM estimator produces the correct second moment of the data, and the results can be extended to higher moments.
The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis, and it has been successfully applied in a large variety of domains. One of the key reasons for this versatility is the ability of HMMs to deal with missing data. However, standard HMM learning algorithms rely crucially on the assumption that the positions of the missing observations within the observation sequence are known. In some situations where such assumptions are not feasible, a number of special algorithms have been developed. Currently, these algorithms rely strongly on specific structural assumptions of the underlying chain, such as acyclicity, and are not applicable in the general case. In particular, there are numerous domains within medicine and computational biology, where the missing observation locations are unknown and acyclicity assumptions do not hold, thus presenting a barrier for the application of HMMs in those fields. In this paper we consider a general problem of learning HMMs from data with unknown missing observation locations (i.e., only the order of the non-missing observations is known). We introduce a generative model of the location omissions and propose two learning methods for this model -a (semi) analytic approach, and a Gibbs sampler. We evaluate and compare the algorithms in a variety of scenarios, measuring their reconstruction precision and robustness under model miss-specification.
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