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Irregular Time Series Data (IRTS) has shown increasing prevalence in real-world applications. We observed that IRTS can be divided into two specialized types: Natural Irregular Time Series (NIRTS) and Accidental Irregular Time Series…

Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…

Missing data imputation, where a model is trained on observed data to estimate unobserved values, is a fundamental problem in machine learning. In this paper, we rigorously formulate imputation model learning as a mean-squared error risk…

Recent state-of-the-art forecasting methods are trained on collections of time series. These methods, often referred to as global models, can capture common patterns in different time series to improve their generalization performance.…

Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be…

Transformer-based models have achieved remarkable success in multivariate time series forecasting (MTSF) by capturing long-range dependencies. However, their widespread adoption is hindered by the quadratic computational complexity of…

Unsupervised anomaly detection and segmentation methods train a model to learn the training distribution as `normal'. In the testing phase, they identify patterns that deviate from this normal distribution as `anomalies'. To learn the…

Time series analysis remains a major challenge due to its sparse characteristics, high dimensionality, and inconsistent data quality. Recent advancements in transformer-based techniques have enhanced capabilities in forecasting and…

Unsupervised/self-supervised time series representation learning is a challenging problem because of its complex dynamics and sparse annotations. Existing works mainly adopt the framework of contrastive learning with the time-based…

Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the…

This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…

Recent advances in digitization have led to the availability of multivariate time series data in various domains, enabling real-time monitoring of operations. Identifying abnormal data patterns and detecting potential failures in these…

Self-supervised learning achieves superior performance in many domains by extracting useful representations from the unlabeled data. However, most of traditional self-supervised methods mainly focus on exploring the inter-sample structure…

We present a simple yet novel time series imputation technique with the goal of constructing an irregular time series that is uniform across every sample in a data set. Specifically, we fix a grid defined by the midpoints of non-overlapping…

Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…

We propose a fully data-driven approach to designing mutual information (MI) estimators. Since any MI estimator is a function of the observed sample from two random variables, we parameterize this function with a neural network (MIST) and…

Modeling irregularly-sampled time series (ISTS) is challenging because of missing values. Most existing methods focus on handling ISTS by converting irregularly sampled data into regularly sampled data via imputation. These models assume an…

There are many time series in the literature with high dimension yet limited sample sizes, such as macroeconomic variables, and it is almost impossible to obtain efficient estimation and accurate prediction by using the corresponding…

A time series represents a set of observations collected over time. Typically, these observations are captured with a uniform sampling frequency (e.g. daily). When data points are observed in uneven time intervals the time series is…

Anomaly detection in time series data is crucial across various domains. The scarcity of labeled data for such tasks has increased the attention towards unsupervised learning methods. These approaches, often relying solely on reconstruction…