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In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional It\^o diffusion processes. To account for high-dimensional time-varying coefficients, we first estimate local (or…
The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion is often described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value.…
Recent studies found that the diffusive transport of conserved quantities in non-integrable many-body systems has an imprint on quantum entanglement: while the von Neumann entropy of a state grows linearly in time $t$ under a global quench,…
Despite the empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their generalization performance remains theoretically underexplored, especially lacking a full consideration of the shared encoder-generator…
Time series Anomaly Detection (AD) plays a crucial role for web systems. Various web systems rely on time series data to monitor and identify anomalies in real time, as well as to initiate diagnosis and remediation procedures. Variational…
Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn…
Numerous models have been developed for scanpath and saliency prediction, which are typically trained on scanpaths, which model eye movement as a sequence of discrete fixation points connected by saccades, while the rich information…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
The diffusion limited aggregation model (DLA) and the more general dielectric breakdown model (DBM) are solved exactly in a two dimensional cylindrical geometry with periodic boundary conditions of width 2. Our approach follows the exact…
The crystal diffusion variational autoencoder (CDVAE) is a machine learning model that leverages score matching to generate realistic crystal structures that preserve crystal symmetry. In this study, we leverage novel diffusion…
Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and…
Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…
Permutation patterns-based approaches, such as permutation entropy (PerEn), have been widely and successfully used to analyze data. However, these methods have two main shortcomings. First, when a series is symbolized based on permutation…
With an increasing outreach of digital platforms in our lives, researchers have taken a keen interest to study different facets of social interactions that seem to be evolving rapidly. Analysing the spread of information (aka diffusion) has…
Estimation of distribution algorithms (EDA) as one of the EAs is a stochastic optimization problem which establishes a probability model to describe the distribution of solutions and randomly samples the probability model to create…
Multivariate entropy quantification algorithms are becoming a prominent tool for the extraction of information from multi-channel physiological time-series. However, in the analysis of physiological signals from heterogeneous organ systems,…
We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous…
We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to…
Dimensional analysis (DA) pays attention to fundamental physical dimensions such as length and mass when modelling scientific and engineering systems. It goes back at least a century to Buckingham's Pi theorem, which characterizes a…
Deep generative models have made rapid progress in image, text, audio, and video generation, and are increasingly being applied to structured records. For tabular data, however, generative modeling remains difficult: a dataset may contain…