Scalable Unsupervised Segmentation via Random Fourier Feature-based Gaussian Process

• URL: http://arxiv.org/abs/2507.10632v1
• Date: Mon, 14 Jul 2025 08:41:03 GMT
• Title: Scalable Unsupervised Segmentation via Random Fourier Feature-based Gaussian Process
• Authors: Issei Saito, Masatoshi Nagano, Tomoaki Nakamura, Daichi Mochihashi, Koki Mimura,
• Abstract summary: We propose RFF-GP-HSMM to address the high computational cost of the Gaussian process hidden semi-Markov model (GP-HSMM)<n>GP-HSMM models time-series data using Gaussian processes, requiring inversion of an N times N kernel matrix during training, where N is the number of data points.<n>The proposed method approximates the Gaussian process with linear regression using RFF, preserving expressive power while eliminating the need for inversion of the kernel matrix.
• Score: 3.8214695776749013
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose RFF-GP-HSMM, a fast unsupervised time-series segmentation method that incorporates random Fourier features (RFF) to address the high computational cost of the Gaussian process hidden semi-Markov model (GP-HSMM). GP-HSMM models time-series data using Gaussian processes, requiring inversion of an N times N kernel matrix during training, where N is the number of data points. As the scale of the data increases, matrix inversion incurs a significant computational cost. To address this, the proposed method approximates the Gaussian process with linear regression using RFF, preserving expressive power while eliminating the need for inversion of the kernel matrix. Experiments on the Carnegie Mellon University (CMU) motion-capture dataset demonstrate that the proposed method achieves segmentation performance comparable to that of conventional methods, with approximately 278 times faster segmentation on time-series data comprising 39,200 frames.

Related papers

• Gaussian Processes Sampling with Sparse Grids under Additive Schwarz Preconditioner [6.408773096179187]
  We propose a scalable algorithm for sampling random realizations of the prior and posterior of GP models. The proposed algorithm leverages inducing points approximation with sparse grids, as well as additive Schwarz preconditioners.
  arXiv  Detail & Related papers  (2024-08-01T00:19:36Z)
• Compound Batch Normalization for Long-tailed Image Classification [77.42829178064807]
  We propose a compound batch normalization method based on a Gaussian mixture. It can model the feature space more comprehensively and reduce the dominance of head classes. The proposed method outperforms existing methods on long-tailed image classification.
  arXiv  Detail & Related papers  (2022-12-02T07:31:39Z)
• Efficient Dataset Distillation Using Random Feature Approximation [109.07737733329019]
  We propose a novel algorithm that uses a random feature approximation (RFA) of the Neural Network Gaussian Process (NNGP) kernel. Our algorithm provides at least a 100-fold speedup over KIP and can run on a single GPU. Our new method, termed an RFA Distillation (RFAD), performs competitively with KIP and other dataset condensation algorithms in accuracy over a range of large-scale datasets.
  arXiv  Detail & Related papers  (2022-10-21T15:56:13Z)
• FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels [82.53569355337586]
  This work offers an efficient solution to temporal point processes inference using general parametric kernels with finite support. The method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG) Results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.
  arXiv  Detail & Related papers  (2022-10-10T12:35:02Z)
• Non-Gaussian Gaussian Processes for Few-Shot Regression [71.33730039795921]
  We propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them. NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.
  arXiv  Detail & Related papers  (2021-10-26T10:45:25Z)
• Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration [63.15453821022452]
  Recent developments in approaches based on deep learning have achieved sub-second runtimes for DiffIR. We propose a simple iterative scheme that functionally composes intermediate non-stationary velocity fields. We then propose a convex optimisation model that uses a regularisation term of arbitrary order to impose smoothness on these velocity fields.
  arXiv  Detail & Related papers  (2021-09-26T19:56:45Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data [16.463077353773603]
  We develop SigGPDE, a new scalable sparse variational inference framework for Gaussian Processes (GPs) on sequential data. We show that the gradients of the GP signature kernel are solutions of a hyperbolic partial differential equation (PDE) This theoretical insight allows us to build an efficient back-propagation algorithm to optimize the ELBO.
  arXiv  Detail & Related papers  (2021-05-10T09:10:17Z)
• Sparse Algorithms for Markovian Gaussian Processes [18.999495374836584]
  Sparse Markovian processes combine the use of inducing variables with efficient Kalman filter-likes recursion. We derive a general site-based approach to approximate the non-Gaussian likelihood with local Gaussian terms, called sites. Our approach results in a suite of novel sparse extensions to algorithms from both the machine learning and signal processing, including variational inference, expectation propagation, and the classical nonlinear Kalman smoothers. The derived methods are suited to literature-temporal data, where the model has separate inducing points in both time and space.
  arXiv  Detail & Related papers  (2021-03-19T09:50:53Z)
• Faster Kernel Interpolation for Gaussian Processes [30.04235162264955]
  Key challenge in scaling Process (GP) regression to massive datasets is that exact inference requires a dense n x n kernel matrix. Structured kernel (SKI) is among the most scalable methods. We show that SKI can be reduced to O(m log m) after a single O(n) time precomputation step. We demonstrate speedups in practice for a wide range of m and n and apply the method to GP inference on a three-dimensional weather radar dataset with over 100 million points.
  arXiv  Detail & Related papers  (2021-01-28T00:09:22Z)
• Real-Time Regression with Dividing Local Gaussian Processes [62.01822866877782]
  Local Gaussian processes are a novel, computationally efficient modeling approach based on Gaussian process regression. Due to an iterative, data-driven division of the input space, they achieve a sublinear computational complexity in the total number of training points in practice. A numerical evaluation on real-world data sets shows their advantages over other state-of-the-art methods in terms of accuracy as well as prediction and update speed.
  arXiv  Detail & Related papers  (2020-06-16T18:43:31Z)
• Scalable Hybrid HMM with Gaussian Process Emission for Sequential Time-series Data Clustering [13.845932997326571]
  Hidden Markov Model (HMM) combined with Gaussian Process (GP) emission can be effectively used to estimate the hidden state. This paper proposes a scalable learning method for HMM-GPSM.
  arXiv  Detail & Related papers  (2020-01-07T07:28:21Z)

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.