Related papers: Data-Adaptive Wavelets and Multi-Scale Singular Sp…
We study the rank of the instantaneous or spot covariance matrix $\Sigma_X(t)$ of a multidimensional continuous semi-martingale $X(t)$. Given high-frequency observations $X(i/n)$, $i=0,\ldots,n$, we test the null hypothesis…
Iterative inversion of seismic, ultrasonic, and other wave data by local gradient-based optimization of mean-square data prediction error (Full Waveform Inversion or FWI) can fail to converge to useful model estimates if started from an…
The complex network framework has been successfully applied to the analysis of climatological data, providing, for example, a better understanding of the mechanisms underlying reduced predictability during El Ni\~no or La Ni\~na years.…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
Time series autoregression (AR) is a classical tool for modeling auto-correlations and periodic structures in real-world systems. We revisit this model from an interpretable machine learning perspective by introducing sparse autoregression…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Automated f ault detection and monitoring in engineering are critical but frequently difficult owing to the necessity for collecting and labeling large amounts of defective samples . We present an unsupervised method that uses the high end…
Robins (1998) introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. He established…
Abstract. Detecting anomalies in patterns of sensor data is important in many practical applications, including domestic activity monitoring for Active Assisted Living (AAL). How to represent and analyse these patterns, however, remains a…
Short-time Fourier transform (STFT) is the most common window-based approach for analyzing the spectrotemporal dynamics of time series. To mitigate the effects of high variance on the spectral estimates due to finite-length, independent…
Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
In this work, we apply multichannel singular spectrum analysis (MSSA), a data-adaptive, multivariate, non-parametric technique that simultaneously exploits the spatial and temporal correlations of the input data to extract common modes of…
Attention-based transformers have played an important role in wireless sensor network (WSN) timing anomaly detection due to their ability to capture long-term dependencies. However, there are several issues that must be addressed, such as…
Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…
The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet…
The Multiscale Fourier Transform of a seismic trace performs time-frequency analyses over a range of window lengths. The variation in window length captures local and global relative amplitudes between events, thereby allowing reflectivity…
Multiple sequences alignment (MSA) is a traditional and challenging task for time-series analyses. The MSA problem is formulated as a discrete optimization problem and is typically solved by dynamic programming. However, the computational…
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…
We use the technique of wavelet analysis to quantitatively investigate the role of solar variability in forcing terrestrial climate change on solar cycle timescales (roughly 11 years). We examine the connection between mean annual solar…