Related papers: Identifying Cointegration by Eigenanalysis
Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the…
The co-occurrence association is widely observed in many empirical data. Mining the information in co-occurrence data is essential for advancing our understanding of systems such as social networks, ecosystem, and brain network. Measuring…
We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of…
Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…
We study a CUSUM (cumulative sums) procedure for the detection of changes in the means of weakly dependent time series within an abstract Hilbert space framework. We use an empirical projection approach via a principal component…
The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range…
Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…
Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing time signals based on non-autonomous dynamical equations.…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
A central problem in unsupervised deep learning is how to find useful representations of high-dimensional data, sometimes called "disentanglement". Most approaches are heuristic and lack a proper theoretical foundation. In linear…
A method for nonlinear topology identification is proposed, based on the assumption that a collection of time series are generated in two steps: i) a vector autoregressive process in a latent space, and ii) a nonlinear, component-wise,…
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically…
Recent advances in nonlinear Independent Component Analysis (ICA) provide a principled framework for unsupervised feature learning and disentanglement. The central idea in such works is that the latent components are assumed to be…
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…
This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent…
Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…
We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…
A new portmanteau test statistic is proposed for detecting nonlinearity in time series data. In this paper, we elaborate on the Toeplitz autocorrelation matrix to the autocorrelation and cross-correlation of residuals and squared residuals…
Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…