Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers unreliable. We propose a principled, model-based framework that embeds discriminant analysis within state-space models to obtain nonstationary linear discriminant analysis (NSLDA) and nonstationary quadratic discriminant analysis (NSQDA). For linear-Gaussian dynamics, we adapt Kalman smoothing to handle multiple samples per time step and develop two practical extensions: (i) an expectation-maximization (EM) approach that jointly estimates unknown system parameters, and (ii) a Gaussian mixture model (GMM)-Kalman method that simultaneously recovers unobserved time labels and parameters, a scenario common in practice. To address nonlinear or non-Gaussian drift, we employ particle smoothing to estimate time-varying class centroids, yielding fully nonstationary discriminant rules. Extensive simulations demonstrate consistent improvements over stationary linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and support vector machine (SVM) baselines, with robustness to noise, missing data, and class imbalance. This paper establishes a unified and data-efficient foundation for discriminant analysis under temporal distribution shift.

In many real-world scenarios, such as single-cell RNA sequencing, data are observed only as discrete-time snapshots spanning finite time intervals and subject to noisy timestamps, with no continuous trajectories available. Recovering the underlying continuous-time dynamics from these snapshots with coarse and noisy observation times is a critical and challenging task. We propose Continuous-Time Optimal Transport Flow (CT-OT Flow), which first infers high-resolution time labels via partial optimal transport and then reconstructs a continuous-time data distribution through a temporal kernel smoothing. This reconstruction enables accurate training of dynamics models such as ODEs and SDEs. CT-OT Flow consistently outperforms state-of-the-art methods on synthetic benchmarks and achieves lower reconstruction errors on real scRNA-seq and typhoon-track datasets. Our results highlight the benefits of explicitly modeling temporal discretization and timestamp uncertainty, offering an accurate and general framework for bridging discrete snapshots and continuous-time processes.

In this paper, we study the method to reconstruct dynamical systems from data without time labels. Data without time labels appear in many applications, such as molecular dynamics, single-cell RNA sequencing etc. Reconstruction of dynamical system from time sequence data has been studied extensively. However, these methods do not apply if time labels are unknown. Without time labels, sequence data becomes distribution data. Based on this observation, we propose to treat the data as samples from a probability distribution and try to reconstruct the underlying dynamical system by minimizing the distribution loss, sliced Wasserstein distance more specifically. Extensive experiment results demonstrate the effectiveness of the proposed method.

Tasks are a fundamental unit of work in the daily lives of people, who are increasingly using digital means to keep track of, organize, triage and act on them. These digital tools -- such as task management applications -- provide a unique opportunity to study and understand tasks and their connection to the real world, and through intelligent assistance, help people be more productive. By logging signals such as text, timestamp information, and social connectivity graphs, an increasingly rich and detailed picture of how tasks are created and organized, what makes them important, and who acts on them, can be progressively developed. Yet the context around actual task completion remains fuzzy, due to the basic disconnect between actions taken in the real world and telemetry recorded in the digital world. Thus, in this paper we compile and release a novel, real-life, large-scale dataset called MS-LaTTE that captures two core aspects of the context surrounding task completion: location and time. We describe our annotation framework and conduct a number of analyses on the data that were collected, demonstrating that it captures intuitive contextual properties for common tasks. Finally, we test the dataset on the two problems of predicting spatial and temporal task co-occurrence, concluding that predictors for co-location and co-time are both learnable, with a BERT fine-tuned model outperforming several other baselines. The MS-LaTTE dataset provides an opportunity to tackle many new modeling challenges in contextual task understanding and we hope that its release will spur future research in task intelligence more broadly.

The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded applications. In this paper we extend the approach to deal with temporal information. We introduce a notion of temporal decision tree, which is designed to make use of relevant information as long as it is acquired, and we present an algorithm for compiling such trees from a model-based reasoning system.

The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded applications. In this paper we extend the approach to deal with temporal information. We introduce a notion of temporal decision tree, which is designed to make use of relevant information as long as it is acquired, and we present an algorithm for compiling such trees from a model-based reasoning system.