Related papers: Joint Characterization of Spatiotemporal Data Mani…

The sea surface temperature (SST), a key environmental parameter, is crucial to optimizing production planning, making its accurate prediction a vital research topic. However, the inherent nonlinearity of the marine dynamic system presents…

The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…

Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…

This paper presents a principled approach for detecting out-of-distribution (OOD) samples in deep neural networks (DNN). Modeling probability distributions on deep features has recently emerged as an effective, yet computationally cheap…

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…

Traffic prediction plays an important role in the realization of traffic control and scheduling tasks in intelligent transportation systems. With the diversification of data sources, reasonably using rich traffic data to model the complex…

Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…

Low-rank tensor representation (LRTR) has emerged as a powerful tool for multi-dimensional data processing. However, classical LRTR-based methods face two critical limitations: (1) they typically assume that the holistic data is low-rank,…

This paper presents a fast, principled approach for detecting anomalous and out-of-distribution (OOD) samples in deep neural networks (DNN). We propose the application of linear statistical dimensionality reduction techniques on the…

Unsupervised/self-supervised time series representation learning is a challenging problem because of its complex dynamics and sparse annotations. Existing works mainly adopt the framework of contrastive learning with the time-based…

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…

We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…

Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be…

Data-dependent superimposed training (DDST) scheme has shown the potential to achieve high bandwidth efficiency, while encounters symbol misidentification caused by hardware imperfection. To tackle these challenges, a joint model and data…

Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and…

We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural…

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…

Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…

In recent years, hyperspectral imaging, also known as imaging spectroscopy, has been paid an increasing interest in geoscience and remote sensing community. Hyperspectral imagery is characterized by very rich spectral information, which…

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…