Related papers: Statistics for Differential Topological Properties…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to…
Reservoir computing is a powerful machine learning paradigm for online time series processing. It has reached state-of-the-art performance in tasks such as chaotic time series prediction and continuous speech recognition thanks to its…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
The massive data sets from today's particle physics experiments present a variety of challenges amenable to the tools developed by the statistics community. From the real-time decision of what subset of data to record on permanent storage,…
Time series forecasting plays a crucial role in many real-world applications, and numerous complex forecasting models have been proposed in recent years. Despite their architectural innovations, most state-of-the-art models report only…
Reservoir computing (RC) is attracting attention as a machine-learning technique for edge computing. In time-series classification tasks, the number of features obtained using a reservoir depends on the length of the input series.…
Reservoir computing (RC) is a computational framework known for its training efficiency, making it ideal for physical hardware implementations. However, realizing the complex interconnectivity of traditional reservoirs in physical systems…
Learning how to predict future events from patterns of past events is difficult when the set of possible event types is large. Training an unrestricted neural model might overfit to spurious patterns. To exploit domain-specific knowledge of…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Discrete-value time series are sequences of measurements where each measurement is a discrete (categorical or integer) value. These time series are widely used in various fields, and their classification and clustering are essential for…
Reservoir engineers use large-scale numerical models to predict the production performance in oil and gas fields. However, these models are constructed based on scarce and often inaccurate data, making their predictions highly uncertain. On…
The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dynamical systems for…
Condition-Based Maintenance is pivotal in enabling the early detection of potential failures in engineering systems, where precise prediction of the Remaining Useful Life is essential for effective maintenance and operation. However, a…
It is well-known in industrial data science that large values of real-life time series tend to be structured and often follow concrete and visible patterns. In this paper, we use ideas from additive combinatorics and discrete Fourier…
Statistical model checking is a class of sequential algorithms that can verify specifications of interest on an ensemble of cyber-physical systems (e.g., whether 99% of cars from a batch meet a requirement on their energy efficiency). These…
In this study, we examine if engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our…
Machine learning techniques offer an effective approach to modeling dynamical systems solely from observed data. However, without explicit structural priors -- built-in assumptions about the underlying dynamics -- these techniques typically…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…