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The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…

Unsupervised representation learning holds the promise of exploiting large amounts of unlabeled data to learn general representations. A promising technique for unsupervised learning is the framework of Variational Auto-encoders (VAEs).…

Time series with long-term structure arise in a variety of contexts and capturing this temporal structure is a critical challenge in time series analysis for both inference and forecasting settings. Traditionally, state space models have…

Machine learning (ML) can process large sets of data generated from complex systems, which is ideal for classification tasks as often appeared in critical phenomena. Meanwhile ML techniques have been found effective in detecting critical…

A network supporting deep unsupervised learning is presented. The network is an autoencoder with lateral shortcut connections from the encoder to decoder at each level of the hierarchy. The lateral shortcut connections allow the higher…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…

This paper develops a novel method to estimate a latent factor model for a large target panel with missing observations by optimally using the information from auxiliary panel data sets. We refer to our estimator as target-PCA. Transfer…

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…

Learning hierarchical structures in sequential data -- from simple algorithmic patterns to natural language -- in a reliable, generalizable way remains a challenging problem for neural language models. Past work has shown that recurrent…

The classical approach to non-linear regression in physics, is to take a mathematical model describing the functional dependence of the dependent variable from a set of independent variables, and then, using non-linear fitting algorithms,…

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…

We propose a method to facilitate exploration and analysis of new large data sets. In particular, we give an unsupervised deep learning approach to learning a latent representation that captures semantic similarity in the data set. The core…

Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…

Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or…

Self-supervised learning (SSL) aims to find meaningful representations from unlabeled data by encoding semantic similarities through data augmentations. Despite its current popularity, theoretical insights about SSL are still scarce. For…

Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem,…

Meta-learning synthesizes and leverages the knowledge from a given set of tasks to rapidly learn new tasks using very little data. Meta-learning of linear regression tasks, where the regressors lie in a low-dimensional subspace, is an…

Motivated by multi-task and meta-learning approaches, we consider the problem of learning structure shared by tasks or users, such as shared low-rank representations or clustered structures. While all previous works focus on well-specified…