Off-the-grid: Fast and Effective Hyperparameter Search for Kernel Clustering

• URL: http://arxiv.org/abs/2006.13567v1
• Date: Wed, 24 Jun 2020 08:58:58 GMT
• Title: Off-the-grid: Fast and Effective Hyperparameter Search for Kernel Clustering
• Authors: Bruno Ordozgoiti and Llu\'is A. Belanche Mu\~noz
• Abstract summary: We study the impact of kernel parameters on kernel $k$-means. In particular, we derive a lower bound, tight up to constant factors, below which the parameter of the RBF kernel will render kernel $k$-means meaningless.
• Score: 2.304694255100371
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Kernel functions are a powerful tool to enhance the $k$-means clustering algorithm via the kernel trick. It is known that the parameters of the chosen kernel function can have a dramatic impact on the result. In supervised settings, these can be tuned via cross-validation, but for clustering this is not straightforward and heuristics are usually employed. In this paper we study the impact of kernel parameters on kernel $k$-means. In particular, we derive a lower bound, tight up to constant factors, below which the parameter of the RBF kernel will render kernel $k$-means meaningless. We argue that grid search can be ineffective for hyperparameter search in this context and propose an alternative algorithm for this purpose. In addition, we offer an efficient implementation based on fast approximate exponentiation with provable quality guarantees. Our experimental results demonstrate the ability of our method to efficiently reveal a rich and useful set of hyperparameter values.

Related papers

• Optimal Kernel Choice for Score Function-based Causal Discovery [92.65034439889872]
  We propose a kernel selection method within the generalized score function that automatically selects the optimal kernel that best fits the data. We conduct experiments on both synthetic data and real-world benchmarks, and the results demonstrate that our proposed method outperforms kernel selection methods.
  arXiv  Detail & Related papers  (2024-07-14T09:32:20Z)
• RFFNet: Large-Scale Interpretable Kernel Methods via Random Fourier Features [3.0079490585515347]
  We introduce RFFNet, a scalable method that learns the kernel relevances' on the fly via first-order optimization. We show that our approach has a small memory footprint and run-time, low prediction error, and effectively identifies relevant features. We supply users with an efficient, PyTorch-based library, that adheres to the scikit-learn standard API and code for fully reproducing our results.
  arXiv  Detail & Related papers  (2022-11-11T18:50:34Z)
• 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)
• Taming Nonconvexity in Kernel Feature Selection---Favorable Properties of the Laplace Kernel [77.73399781313893]
  A challenge is to establish the objective function of kernel-based feature selection. The gradient-based algorithms available for non-global optimization are only able to guarantee convergence to local minima.
  arXiv  Detail & Related papers  (2021-06-17T11:05:48Z)
• 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)
• Random Features for the Neural Tangent Kernel [57.132634274795066]
  We propose an efficient feature map construction of the Neural Tangent Kernel (NTK) of fully-connected ReLU network. We show that dimension of the resulting features is much smaller than other baseline feature map constructions to achieve comparable error bounds both in theory and practice.
  arXiv  Detail & Related papers  (2021-04-03T09:08:12Z)
• Kernel k-Means, By All Means: Algorithms and Strong Consistency [21.013169939337583]
  Kernel $k$ clustering is a powerful tool for unsupervised learning of non-linear data. In this paper, we generalize results leveraging a general family of means to combat sub-optimal local solutions. Our algorithm makes use of majorization-minimization (MM) to better solve this non-linear separation problem.
  arXiv  Detail & Related papers  (2020-11-12T16:07:18Z)
• The Statistical Cost of Robust Kernel Hyperparameter Tuning [20.42751031392928]
  We study the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We provide finite-sample guarantees for the problem, characterizing how increasing the complexity of the kernel class increases the complexity of learning kernel hyper parameters.
  arXiv  Detail & Related papers  (2020-06-14T21:56:33Z)
• SimpleMKKM: Simple Multiple Kernel K-means [49.500663154085586]
  We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM) Our criterion is given by an intractable minimization-maximization problem in the kernel coefficient and clustering partition matrix. We theoretically analyze the performance of SimpleMKKM in terms of its clustering generalization error.
  arXiv  Detail & Related papers  (2020-05-11T10:06:40Z)
• Scaling up Kernel Ridge Regression via Locality Sensitive Hashing [6.704115928005158]
  We introduce a weighted version of random binning features and show that the corresponding kernel function generates smooth Gaussian processes. We show that our weighted random binning features provide a spectral approximation to the corresponding kernel matrix, leading to efficient algorithms for kernel ridge regression.
  arXiv  Detail & Related papers  (2020-03-21T21:41:16Z)

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.