The collection of data from a personal digital device to characterize current health conditions and behaviors that determine how an individual’s health will evolve has been called digital phenotyping. In this paper, we describe the development of and early experiences with a comprehensive digital phenotyping platform: Health Outcomes through Positive Engagement and Self-Empowerment (HOPES). HOPES is based on the open-source Beiwe platform but adds a wider range of data collection, including the integration of wearable devices and further sensor collection from smartphones. Requirements were partly derived from a concurrent clinical trial for schizophrenia that required the development of significant capabilities in HOPES for security, privacy, ease of use, and scalability, based on a careful combination of public cloud and on-premises operation. We describe new data pipelines to clean, process, present, and analyze data. This includes a set of dashboards customized to the needs of research study operations and clinical care. A test use case for HOPES was described by analyzing the digital behavior of 22 participants during the SARS-CoV-2 pandemic.
We investigate a class of feature allocation models that generalize the Indian buffet process and are parameterized by Gibbs-type random measures. Two existing classes are contained as special cases: the original two-parameter Indian buffet process, corresponding to the Dirichlet process, and the stable (or three-parameter) Indian buffet process, corresponding to the Pitman-Yor process. Asymptotic behavior of the Gibbs-type partitions, such as power laws holding for the number of latent clusters, translates into analogous characteristics for this class of Gibbs-type feature allocation models. Despite containing several different distinct subclasses, the properties of Gibbs-type partitions allow us to develop a black-box procedure for posterior inference within any subclass of models. Through numerical experiments, we compare and contrast a few of these subclasses and highlight the utility of varying power-law behaviors in the latent features.
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from conditionally-i.i.d. sequences of Bernoulli processes with a common beta process base measure, in which case the combinatorial structure is described by the Indian buffet process. Our results give a count analogue of the Indian buffet process, which we call a negative binomial Indian buffet process. As an intermediate step toward this goal, we provide a construction for the beta negative binomial process that avoids a representation of the underlying beta process base measure. We describe the key Markov kernels needed to use a NB-IBP representation in a Markov Chain Monte Carlo algorithm targeting a posterior distribution.
We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix of a multivariate time series. The Wishart and inverse Wishart processes are constructed from i.i.d. Gaussian processes, for which we apply existing black-box variational inference algorithms for approximate Gaussian process inference. These methods scale well with the length of the time series, however, they fail in the case of the Wishart process, an issue we resolve with a simple modification into an additive white noise parameterization of the model. This modification is also key to implementing a factored variant of the construction, allowing inference to additionally scale to high-dimensional covariance matrices. As with existing MCMC-based inference routines for the Wishart and inverse Wishart processes, we show that these variational alternatives significantly outperform multivariate GARCH baselines when forecasting the covariances of returns on financial instruments.
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