Marginalization Consistent Mixture of Separable Flows for Probabilistic Irregular Time Series Forecasting
Keywords: Probabilistic modelling, Normalizing flows, Marginalization consitsent
Abstract: Probabilistic forecasting models for joint distributions of targets in irregular time
series are a heavily under-researched area in machine learning with, to the best of
our knowledge, only three models researched so far: GPR, the Gaussian Process
Regression model (Dürichen et al., 2015), TACTiS, the Transformer-Attentional
Copulas for Time Series Drouin et al. (2022); Ashok et al. (2024) and ProFITi
(Yalavarthi et al., 2024b), a multivariate normalizing flow model based on invertible
attention layers. While ProFITi, thanks to using multivariate normalizing flows,
is the more expressive model with a better predictive performance, we will show
that it suffers from marginalization inconsistency: it does not guarantee that the
marginal distributions of a subset of variables in its predictive distributions coincide
with the directly predicted distributions of these variables. Also, TACTiS does not
provide any guarantees for marginalization consistency.
We develop a novel probabilistic irregular time series forecasting model, Marginal-
ization Consistent Mixtures of Separable Flows (moses), that mixes several nor-
malizing flows with (i) Gaussian Processes with full covariance matrix as source
distributions and (ii) a separable invertible transformation, aiming to combine
the expressivity of normalizing flows with the marginalization consistency of
Gaussians. In experiments on four different datasets we show that moses outper-
form other state-of-the-art marginalization consistent models, perform on par with
ProFITi, but different from ProFITi, guarantees marginalization consistency.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 1929
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