Related papers: Forecasting and Granger Modelling with Non-linear …
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Climate projections using data driven machine learning models acting as emulators, is one of the prevailing areas of research to enable policy makers make informed decisions. Use of machine learning emulators as surrogates for…
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…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to…
This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…
Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well…
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,…
Conventional time-series forecasting methods typically aim to minimize overall prediction error, without accounting for the varying importance of different forecast ranges in downstream applications. We propose a training methodology that…
Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
Machine learning (ML) has shown significant promise in studying complex geophysical dynamical systems, including turbulence and climate processes. Such systems often display sensitive dependence on initial conditions, reflected in positive…
We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…
Forecasting based on financial time-series is a challenging task since most real-world data exhibits nonstationary property and nonlinear dependencies. In addition, different data modalities often embed different nonlinear relationships…
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…
In the 1940s, Wiener introduced a linear predictor, where the future prediction is computed by linearly combining the past data. A transformer generalizes this idea: it is a nonlinear predictor where the next-token prediction is computed by…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…