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Susan Holmes

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3 papers

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JBHI Journal 2022 Journal Article

Labeling Self-Tracked Menstrual Health Records With Hidden Semi-Markov Models

Laura Symul
Susan Holmes

Globally, millions of women track their menstrual cycle and fertility via smartphone-based health apps, generating multivariate time series with frequent missing data. To leverage this type of data for studies of fertility or studies of the effect of the menstrual cycle on symptoms and diseases, it is critical to have methods for identifying reproductive events, such as ovulation, pregnancy losses or births. Here, we present a hierarchical approach relying on hidden semi-Markov models that adapts to changes in tracking behavior, explicitly captures variable– and state– dependent missingness, allows for variables of different type, and quantifies uncertainty. The accuracy on simulated data reaches 98% with no missing data and 90% with realistic missingness. On our partially labeled real-world time series, the accuracy reaches 93%. Our method also accurately predicts cycle length by learning user characteristics. Its implementation is publicly available ( HiddenSemiMarkov R package) and transferable to any health time series, including self-reported symptoms and occasional tests.

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JMLR Journal 2020 Journal Article

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Nina Miolane
Nicolas Guigui
Alice Le Brigant
Johan Mathe
Benjamin Hou
Yann Thanwerdas
Stefan Heyder
Olivier Peltre

We introduce Geomstats, an open-source Python package for computations and statistics on nonlinear manifolds such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Manifolds come equipped with families of Riemannian metrics with associated exponential and logarithmic maps, geodesics, and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering, and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends---namely NumPy, PyTorch, and TensorFlow. This paper presents the package, compares it with related libraries, and provides relevant code examples. We show that Geomstats provides reliable building blocks to both foster research in differential geometry and statistics and democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at geomstats.ai. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

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NeurIPS Conference 2014 Conference Paper

Positive Curvature and Hamiltonian Monte Carlo

Christof Seiler
Simon Rubinstein-Salzedo
Susan Holmes

The Jacobi metric introduced in mathematical physics can be used to analyze Hamiltonian Monte Carlo (HMC). In a geometrical setting, each step of HMC corresponds to a geodesic on a Riemannian manifold with a Jacobi metric. Our calculation of the sectional curvature of this HMC manifold allows us to see that it is positive in cases such as sampling from a high dimensional multivariate Gaussian. We show that positive curvature can be used to prove theoretical concentration results for HMC Markov chains.

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