Conformal prediction for time series presents two key challenges: (1) leveraging sequential correlations in features and non-conformity scores and (2) handling multi-dimensional outcomes. We propose a novel conformal prediction method to address these two key challenges by integrating Transformer and Normalizing Flow. Specifically, the Transformer encodes the historical context of time series, and normalizing flow learns the transformation from the base distribution to the distribution of non-conformity scores conditioned on the encoded historical context. This enables the construction of prediction regions by transforming samples from the base distribution using the learned conditional flow. We ensure the marginal coverage by defining the prediction regions as sets in the transformed space that correspond to a predefined probability mass in the base distribution. The model is trained end-to-end by Flow Matching, avoiding the need for computationally intensive numerical solutions of ordinary differential equations. We demonstrate that our proposed method achieves smaller prediction regions compared to the baselines while satisfying the desired coverage through comprehensive experiments using simulated and real-world time series datasets.

Uncertainty quantification has become crucial in many scientific domains where black-box machine learning models are often used [1]. Conformal prediction has emerged as a popular and modern technique for uncertainty quantification by providing valid predictive inference for those black-box models [8, 2]. Time series prediction aims to forecast future values based on a sequence of observations sequentially ordered in time [3]. With recent advances in machine learning, numerous models have been proposed and adopted for various time series prediction tasks. The increased use of black-box machine learning models necessitates uncertainty quantification, particularly in high-stakes time series prediction tasks such as medical event prediction, stock prediction, and weather forecasting. While conformal prediction can provide valid predictive inference for uncertainty quantification, applying conformal prediction to time series is challenging since time series data often violate the exchangeability assumption.

In this work, we explored federated learning in temporal heterogeneity across clients. We observed that global model obtained by \texttt{FedAvg} trained with fixed-length sequences shows faster convergence than varying-length sequences. We proposed methods to mitigate temporal heterogeneity for efficient federated learning based on the empirical observation.

Tailoring treatment for individual patients is crucial yet challenging in order to achieve optimal healthcare outcomes. Recent advances in reinforcement learning offer promising personalized treatment recommendations; however, they rely solely on current patient observations (vital signs, demographics) as the patient's state, which may not accurately represent the true health status of the patient. This limitation hampers policy learning and evaluation, ultimately limiting treatment effectiveness. In this study, we propose the Deep Attention Q-Network for personalized treatment recommendations, utilizing the Transformer architecture within a deep reinforcement learning framework to efficiently incorporate all past patient observations. We evaluated the model on real-world sepsis and acute hypotension cohorts, demonstrating its superiority to state-of-the-art models.

Change-point detection, detecting an abrupt change in the data distribution from sequential data, is a fundamental problem in statistics and machine learning. CUSUM is a popular statistical method for online change-point detection due to its efficiency from recursive computation and constant memory requirement, and it enjoys statistical optimality. CUSUM requires knowing the precise pre- and post-change distribution. However, post-change distribution is usually unknown a priori since it represents anomaly and novelty. When there is a model mismatch with actual data, classic CUSUM can perform poorly. While likelihood ratio-based methods encounter challenges in high dimensions, neural networks have become an emerging tool for change-point detection with computational efficiency and scalability. In this paper, we introduce a neural network CUSUM (NN-CUSUM) for online change-point detection. We also present a general theoretical condition when the trained neural networks can perform change-point detection and what losses can achieve our goal. We further extend our analysis by combining it with the Neural Tangent Kernel theory to establish learning guarantees for the standard performance metrics, including the average run length (ARL) and expected detection delay (EDD). The strong performance of NN-CUSUM is demonstrated in detecting change-point in high-dimensional data using both synthetic and real-world data.