Kernels for time series with irregularly-spaced multivariate observations

• URL: http://arxiv.org/abs/2004.08545v1
• Date: Sat, 18 Apr 2020 07:51:54 GMT
• Title: Kernels for time series with irregularly-spaced multivariate observations
• Abstract summary: We show that a "series kernel" that is general enough to represent irregularly-spaced time series may be built out of well-known "vector kernels" We demonstrate that our series kernel may be used for the more traditional setting of time series classification, where its performance is broadly in line with alternative methods.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Time series are an interesting frontier for kernel-based methods, for the simple reason that there is no kernel designed to represent them and their unique characteristics in full generality. Existing sequential kernels ignore the time indices, with many assuming that the series must be regularly-spaced; some such kernels are not even psd. In this manuscript, we show that a "series kernel" that is general enough to represent irregularly-spaced multivariate time series may be built out of well-known "vector kernels". We also show that all series kernels constructed using our methodology are psd, and are thus widely applicable. We demonstrate this point by formulating a Gaussian process-based strategy - with our series kernel at its heart - to make predictions about test series when given a training set. We validate the strategy experimentally by estimating its generalisation error on multiple datasets and comparing it to relevant baselines. We also demonstrate that our series kernel may be used for the more traditional setting of time series classification, where its performance is broadly in line with alternative methods.

Related papers

• Feature maps for the Laplacian kernel and its generalizations [3.671202973761375]
  Unlike the Gaussian kernel, the Laplacian kernel is not separable. We provide random features for the Laplacian kernel and its two generalizations. We demonstrate the efficacy of these random feature maps on real datasets.
  arXiv  Detail & Related papers  (2025-02-21T16:36:20Z)
• Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models [61.10851158749843]
  Key insights can be obtained by discovering lead-lag relationships inherent in the data. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models.
  arXiv  Detail & Related papers  (2023-05-11T10:30:35Z)
• Consistent Interpolating Ensembles via the Manifold-Hilbert Kernel [11.759162160620678]
  We devise an ensemble classification method that simultaneously interpolates the training data, and is consistent for a broad class of data distributions. For the sphere, we show that the manifold-Hilbert kernel can be realized as a weighted random partition kernel.
  arXiv  Detail & Related papers  (2022-05-19T06:40:21Z)
• S-Rocket: Selective Random Convolution Kernels for Time Series Classification [36.9596657353794]
  Random convolution kernel transform (Rocket) is a fast, efficient, and novel approach for time series feature extraction. selection of the most important kernels and pruning the redundant and less important ones is necessary to reduce computational complexity and accelerate inference of Rocket. Population-based approach is proposed for selecting the most important kernels.
  arXiv  Detail & Related papers  (2022-03-07T15:02:12Z)
• Meta-Learning Hypothesis Spaces for Sequential Decision-making [79.73213540203389]
  We propose to meta-learn a kernel from offline data (Meta-KeL) Under mild conditions, we guarantee that our estimated RKHS yields valid confidence sets. We also empirically evaluate the effectiveness of our approach on a Bayesian optimization task.
  arXiv  Detail & Related papers  (2022-02-01T17:46:51Z)
• Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series [8.918419734720613]
  A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a kernel. Despite its previous successes, this strategy breaks down when the observed time series is not regularly sampled in time. We propose to address this problem by directly approxing the vector field of the dynamical system by incorporating time differences in the (KF) data-adapted kernels.
  arXiv  Detail & Related papers  (2021-11-25T11:45:40Z)
• Fast Sketching of Polynomial Kernels of Polynomial Degree [61.83993156683605]
  kernel is especially important as other kernels can often be approximated by the kernel via a Taylor series expansion. Recent techniques in sketching reduce the dependence in the running time on the degree oblivious $q$ of the kernel. We give a new sketch which greatly improves upon this running time, by removing the dependence on $q$ in the leading order term.
  arXiv  Detail & Related papers  (2021-08-21T02:14:55Z)
• Kernel Continual Learning [117.79080100313722]
  kernel continual learning is a simple but effective variant of continual learning to tackle catastrophic forgetting. episodic memory unit stores a subset of samples for each task to learn task-specific classifiers based on kernel ridge regression. variational random features to learn a data-driven kernel for each task.
  arXiv  Detail & Related papers  (2021-07-12T22:09:30Z)
• Kernel Identification Through Transformers [54.3795894579111]
  Kernel selection plays a central role in determining the performance of Gaussian Process (GP) models. This work addresses the challenge of constructing custom kernel functions for high-dimensional GP regression models. We introduce a novel approach named KITT: Kernel Identification Through Transformers.
  arXiv  Detail & Related papers  (2021-06-15T14:32:38Z)
• Learning Compositional Sparse Gaussian Processes with a Shrinkage Prior [26.52863547394537]
  We present a novel probabilistic algorithm to learn a kernel composition by handling the sparsity in the kernel selection with Horseshoe prior. Our model can capture characteristics of time series with significant reductions in computational time and have competitive regression performance on real-world data sets.
  arXiv  Detail & Related papers  (2020-12-21T13:41:15Z)
• Kernel learning approaches for summarising and combining posterior similarity matrices [68.8204255655161]
  We build upon the notion of the posterior similarity matrix (PSM) in order to suggest new approaches for summarising the output of MCMC algorithms for Bayesian clustering models. A key contribution of our work is the observation that PSMs are positive semi-definite, and hence can be used to define probabilistically-motivated kernel matrices.
  arXiv  Detail & Related papers  (2020-09-27T14:16:14Z)
• Generalized vec trick for fast learning of pairwise kernel models [3.867363075280544]
  We present a comprehensive review of pairwise kernels, that have been proposed for incorporating prior knowledge about the relationship between the objects. We show how all the reviewed kernels can be expressed as sums of Kronecker products, allowing the use of generalized vec trick for speeding up their computation.
  arXiv  Detail & Related papers  (2020-09-02T13:27:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.