Abstract
Longitudinal data is the repeated observations of individuals through time. They often exhibit rich statistical qualities, such as skew or multimodality, that are difficult to capture using traditional parametric methods. To tackle this, we build a non-parametric Markov transition model for longitudinal data. Our approach uses kernel mean embeddings to learn a transition model that can express complex statistical features. We also propose an approximate data subsampling technique based on kernel herding and random Fourier features that allows our method to scale to large longitudinal data sets. We demonstrate our approach on two real world data sets.
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Notes
- 1.
KDE is a closely related method, but we only use positive-definite kernels. Without this requirement, we lose all the theoretical benefits discussed in this paper.
- 2.
A positive definite kernel (or just a kernel) \(k_\mathcal {X}\) defined on a measurable space \(\mathcal {X}\) satisfies \(\sum _{i=1}^n \sum _{j=1}^n c_i c_j k_\mathcal {X}(x_i, x_j) \ge 0\) for any \(n \in \mathbb {N}\), \(c_1, \dots , c_n \in \mathbb {R}\), and \(x_1, \dots , x_n \in \mathcal {X}\).
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Shen, D., Ramos, F. (2016). Kernel Embeddings of Longitudinal Data. In: Kang, B.H., Bai, Q. (eds) AI 2016: Advances in Artificial Intelligence. AI 2016. Lecture Notes in Computer Science(), vol 9992. Springer, Cham. https://doi.org/10.1007/978-3-319-50127-7_42
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DOI: https://doi.org/10.1007/978-3-319-50127-7_42
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