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Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about the true probability distribution of random variables of interest. This makes them a key element in data-driven robust optimization by exploiting…
The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…
Time irreversibility (temporal asymmetry) is one of fundamental properties that characterize the nonlinearity of complex dynamical processes, and our brain is a typical complex dynamical system manifested with nonlinearity. Two…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
Anomaly detection for time-series data has been an important research field for a long time. Seminal work on anomaly detection methods has been focussing on statistical approaches. In recent years an increasing number of machine learning…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal…
Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture…
Several techniques for multivariate time series anomaly detection have been proposed recently, but a systematic comparison on a common set of datasets and metrics is lacking. This paper presents a systematic and comprehensive evaluation of…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
The training algorithms for AI systems all introduce far-from-equilibrium dynamical processes, and understanding the irreversibility of these algorithms is a fundamental step towards understanding the learning dynamics of modern AI systems.…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
We propose a retrodictive forecasting paradigm for time series: instead of predicting the future from the past, we identify the future that best explains the observed present via inverse MAP optimization over a Conditional Variational…
We investigate the statistical arrow of time for a quantum system being monitored by a sequence of measurements. For a continuous qubit measurement example, we demonstrate that time-reversed evolution is always physically possible, provided…
The analysis of a timeseries can provide many new perspectives if it is accompanied by the assumption that the timeseries is generated from an underlying dynamical system. For example, statistical properties of the data can be related to…
This paper addresses the issue of detecting change-points in multivariate time series. The proposed approach differs from existing counterparts by making only weak assumptions on both the change-points structure across series, and the…
Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…
Multivariate time series is a very active topic in the research community and many machine learning tasks are being used in order to extract information from this type of data. However, in real-world problems data has missing values, which…
Time series data from real-world systems often display non-stationary behavior, indicating varying statistical characteristics over time. This inherent variability poses significant challenges in deciphering the underlying structural…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…