Learning from Irregularly Sampled Multivariate Time Series with Missing Values

With the rise of deep learning, researchers have explored many types of data—including
images, text, audio, graphs, and time series. Within time series, most work has focused on
regularly sampled data that is fully observed. However, in the real world, time series are
often irregular, with missing values—making them harder to model and less studied.

Irregular time series present unique challenges: data points may be unevenly spaced, many
values may be missing, and different time series may vary in length. These characteristics
make it difficult for traditional deep learning models—designed for fully observed, regularly
sampled data—to perform well. Ordinary Differential Equation (ODE)-based models have
gained popularity due to their ability to operate in continuous time, making them a natural
fit for irregular sampling. These models have been applied successfully to various supervised learning tasks, including interpolation, classification, and forecasting. However, their
performance is often subpar, and many still rely on binary masks to handle missing data.

This thesis explores an alternative paradigm: non-ODE-based models that handle IMTS
directly, without using missing-value indicators. These models are designed for a range of
supervised learning tasks—point and probabilistic forecasting, interpolation, and classification—with the core hypothesis that explicitly avoiding missingness indicators improves
learning in highly sparse scenarios. We explore different ways to represent these time series
so that no useful information is lost and no extra noise is added.

For interpolation, we introduced Tripletformer—a transformer-based model that uses a
sequence of observation-level triples to better capture irregular structure. For forecasting,
we developed GraFITi, a graph-based model that treats time points and channels as nodes
in a bipartite graph, with observations as edges.

To move beyond single-point predictions, we extended GraFITi with ProFITi, a probabilistic model that leverages normalizing flows to predict full distributions. Since ProFITi lacks
marginalization consistency, we addressed this with MOSES—a mixture of separable flows
built on top of Tripletformer—to ensure that predicted distributions match their marginals.

For classification, we proposed a channel-wise representation that allows standard models
like convolutional neural networks (CNNs) process irregular time series effectively. For
prediction tasks, we use a deep set architecture.

We evaluate all our models on real-world datasets and compare them with existing methods,
showing that our approaches consistently perform better.