Related papers: Fourier Feature Methods for Nonlinear Causal Disco…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and…
Robust feature selection is vital for creating reliable and interpretable Machine Learning (ML) models. When designing statistical prediction models in cases where domain knowledge is limited and underlying interactions are unknown,…
Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model.…
Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations…
Oscillatory processes are central for the understanding of the neural bases of cognition and behaviour. To analyse these processes, time-frequency (TF) decomposition methods are applied and non-parametric cluster-based statistical procedure…
The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive…
The Fast Fourier Transform (FFT), as a core computation in a wide range of scientific applications, is increasingly threatened by reliability issues. In this paper, we introduce TurboFFT, a high-performance FFT implementation equipped with…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
Causal discovery is central to inferring causal relationships from observational data. In the presence of latent confounding, algorithms such as Fast Causal Inference (FCI) learn a Partial Ancestral Graph (PAG) representing the true model's…
Score-based causal discovery methods can effectively identify causal relationships by evaluating candidate graphs and selecting the one with the highest score. One popular class of scores is kernel-based generalized score functions, which…
In this paper, a novel sensor fault detection, isolation and identification (FDII) strategy is proposed by using the multiple model (MM) approach. The scheme is based on multiple hybrid Kalman filters (HKF) which represents an integration…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
The growth of data today poses a challenge in management and inference. While feature extraction methods are capable of reducing the size of the data for inference, they do not help in minimizing the cost of data storage. On the other hand,…
Portfolio managers rely on correlation-based analysis and heuristic methods that fail to capture true causal relationships driving performance. We present a hybrid framework that integrates statistical causal discovery algorithms with…
Constraint-based causal discovery methods require a large number of conditional independence (CI) tests, which severely limits their practical applicability due to high computational complexity. Therefore, it is crucial to design an…
We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error.…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…
Causal learning is a beneficial approach to analyze the cause and effect relationships among variables in a dataset. A causal graph can be generated from a dataset using a particular causal algorithm, for instance, the PC algorithm or Fast…