Medical researchers are coming to appreciate that many diseases are in fact complex, heterogeneous syndromes composed of subpopulations that express different variants of a related complication. Longitudinal data extracted from individual electronic health records (EHR) offer an exciting new way to study subtle differences in the way these diseases progress over time. In this paper, we focus on answering two questions that can be asked using these databases of longitudinal EHR data. First, we want to understand whether there are individuals with similar disease trajectories and whether there are a small number of degrees of freedom that account for differences in trajectories across the population. Second, we want to understand how important clinical outcomes are associated with disease trajectories. To answer these questions, we propose the Disease Trajectory Map (DTM), a novel probabilistic model that learns low-dimensional representations of sparse and irregularly sampled longitudinal data. We propose a stochastic variational inference algorithm for learning the DTM that allows the model to scale to large modern medical datasets. To demonstrate the DTM, we analyze data collected on patients with the complex autoimmune disease, scleroderma. We find that DTM learns meaningful representations of disease trajectories and that the representations are significantly associated with important clinical outcomes.

Given time series data, how can we answer questions like how did we get here?'' These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations.

This paper introduces a novel approach that leverages Large Language Models (LLMs) and Generative Agents to enhance time series forecasting by reasoning across both text and time series data. With language as a medium, our method adaptively integrates social events into forecasting models, aligning news content with time series fluctuations to provide richer insights. Specifically, we utilize LLM-based agents to iteratively filter out irrelevant news and employ human-like reasoning to evaluate predictions. This enables the model to analyze complex events, such as unexpected incidents and shifts in social behavior, and continuously refine the selection logic of news and the robustness of the agent's output. By integrating selected news events with time series data, we fine-tune a pre-trained LLM to predict sequences of digits in time series. The results demonstrate significant improvements in forecasting accuracy, suggesting a potential paradigm shift in time series forecasting through the effective utilization of unstructured news data.

Synthesizing time series data is pivotal in modern society, aiding effective decision making and ensuring privacy preservation in various scenarios. Time series are associated with various attributes, including trends, seasonality, and external information such as location. Recent research has predominantly focused on random unconditional synthesis or conditional synthesis. Nonetheless, these paradigms generate time series from scratch and are incapable of manipulating existing time series samples. This paper introduces a novel task, called Time Series Editing (TSE), to synthesize time series by manipulating existing time series.

We propose Random Projection Filter Bank (RPFB) as a generic and simple approach to extract features from time series data. RPFB is a set of randomly generated stable autoregressive filters that are convolved with the input time series to generate the features. These features can be used by any conventional machine learning algorithm for solving tasks such as time series prediction, classification with time series data, etc. Different filters in RPFB extract different aspects of the time series, and together they provide a reasonably good summary of the time series. RPFB is easy to implement, fast to compute, and parallelizable. We provide an error upper bound indicating that RPFB provides a reasonable approximation to a class of dynamical systems. The empirical results in a series of synthetic and real-world problems show that RPFB is an effective method to extract features from time series.

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent.

Multivariate time series usually contain a large number of missing values, which hinders the application of advanced analysis methods on multivariate time series data. Conventional approaches to addressing the challenge of missing values, including mean/zero imputation, case deletion, and matrix factorization-based imputation, are all incapable of modeling the temporal dependencies and the nature of complex distribution in multivariate time series. In this paper, we treat the problem of missing value imputation as data generation. Inspired by the success of Generative Adversarial Networks (GAN) in image generation, we propose to learn the overall distribution of a multivariate time series dataset with GAN, which is further used to generate the missing values for each sample. Different from the image data, the time series data are usually incomplete due to the nature of data recording process. A modified Gate Recurrent Unit is employed in GAN to model the temporal irregularity of the incomplete time series. Experiments on two multivariate time series datasets show that the proposed model outperformed the baselines in terms of accuracy of imputation. Experimental results also showed that a simple model on the imputed data can achieve state-of-the-art results on the prediction tasks, demonstrating the benefits of our model in downstream applications.

Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data.