Kernel methods can learn hierarchical polynomials efficiently.
problem Learning hierarchical structure from data.
method Iteratively reweighting kernel machines using derivatives.
result Efficient learning of hierarchical polynomials.
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48 results for “Hierarchical Kernels”
We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.
A new convolutional spectral kernel network learns hierarchical and local features.
problem Lack of deep learning in non-stationary spectral kernels.
method Introduces convolutional filters and deep architectures into non-stationary spectral kernels, derives generalization error bounds, and introduces regularizers.
result Validated the effectiveness of the convolutional spectral kernel network on real-world datasets.
DHGAK aligns substructures for better graph kernel performance.
problem Limited performance of traditional graph kernels due to missing substructure similarities.
method Hierarchically aligns relational substructures in deep embedding space, assigning same feature maps in RKHS.
result DHGAK outperforms state-of-the-art graph kernels on various benchmarks.
Many real-world optimization problems require significant resources for objective function evaluations. This is a challenge to evolutionary algorithms, as it limits the number of available evaluations. One solution are surrogate models, which replace the expensive objective. A particular issue in this context are hiera…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the execution time are drastically reduced compared to standard dense linear algebra routi…
Improved outlier detection in hierarchical Gaussian Processes using Wasserstein-2 kernels.
problem Outlier detection limitations in stacked Gaussian Processes.
method Proposed a hybrid kernel combining Euclidean and Wasserstein-2 distances, emphasizing variance in Wasserstein-2 computations.
result Improved performance and enhanced out-of-distribution detection on various datasets.
We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where the Nyström method (a globally low-rank approximation) is married with a locall…
Kernel semi-implicit variational inference improves variational inference without additional optimization.
problem Intractability of hierarchical semi-implicit distributions in variational inference.
method Kernel semi-implicit variational inference (KSIVI) using kernel methods to eliminate lower-level optimization.
result KSIVI reduces variational inference to kernel Stein discrepancy (KSD) optimization, improving expressiveness and tractability.
Nowadays, hyperspectral image classification widely copes with spatial information to improve accuracy. One of the most popular way to integrate such information is to extract hierarchical features from a multiscale segmentation. In the classification context, the extracted features are commonly concatenated into a lon…
Paper analyzes consistency of Bayesian and machine learning methods for hierarchical parameter estimation.
problem Learning hierarchical parameters in complex and real-world problems.
method Empirical Bayes and Kernel Flow approaches.
result Consistency results for Matérn-like model on the torus, and comparison of algorithms.
Proposes a graph pooling method leveraging node proximity for hierarchical graph representation learning.
problem Efficiently exploiting the geometry of graph data for hierarchical representation learning.
method Combines node proximity with kernel representation of topology and node features for adaptive node signal similarities evaluation.
result Achieves state-of-the-art performance on graph classification benchmark datasets.
A new framework generates large hierarchical search spaces for neural architectures.
problem Discovering neural architectures from simple blocks is hard.
method Context-free grammars for a unified, scalable search space.
result Efficiently searches over complete architectures, outperforming existing methods.
On the Integration of Physics-Based Machine Learning with Hierarchical Bayesian Modeling Techniquesstat.ML
Combines physics-based ML with hierarchical Bayesian techniques for better model performance.
problem Lack of physical knowledge in black-box machine learning models.
method Embeds physics-based models into Gaussian Process mean function and uses kernel machines to characterize discrepancies.
result Improved model performance under blind conditions through integration of physics-based knowledge.
For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization of predictor functions by Euclidean or Hilbertian norms. In …
Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.
problem High nodal variance in BHMC trees, leading to weak separation between nodes at higher levels.
method Employing Posterior Regularization to impose max-margin constraints on nodes at every level.
result Improves cluster separation in BHMC models, enhancing overall model performance.
A new method for accurately reconstructing signals without knowing the kernel or signal regularity.
problem Recovering signals from noisy measurements without prior knowledge of the convolution kernel or signal regularity.
method Parametrizing the convolution kernel and prior length-scales, jointly estimated in the inversion procedure.
result Accurate reconstructions of signals with varying regularity and unknown kernel size.
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that these kernels are universal and that SVMs using these kernels are universally con…
Deep learning is also known as hierarchical learning, where the learner _learns_ to represent a complicated target function by decomposing it into a sequence of simpler functions to reduce sample and time complexity. This paper formally analyzes how multi-layer neural networks can perform such hierarchical learning _ef…
Sparse model for noisy datasets using hierarchical regularization.
problem Learning from large noisy datasets with sparse representations.
method Hierarchical learning strategy with projection-based penalty operators.
result Efficient sparse model reconstruction and generalizability on real datasets.
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input distribution, cross-validating for an optimal parameter requires significant computation do…
Kernel SIVI improves variational inference by avoiding lower-level optimization.
problem Intractable densities in semi-implicit variational distributions.
method Kernel SIVI-SM uses a minimax formulation and kernel tricks to avoid lower-level optimization.
result Kernel Stein discrepancy (KSD) objective is computable and leads to convergence guarantees.
Geographic object-based image analysis (GEOBIA) framework has gained increasing interest recently. Following this popular paradigm, we propose a novel multiscale classification approach operating on a hierarchical image representation built from two images at different resolutions. They capture the same scene with diff…
HKT improves sequence processing with multi-scale attention and kernel analysis.
problem Processing sequences at multiple scales with efficient attention mechanisms.
method Trainable causal downsampling and convex weights for level-specific score matrices.
result HKT achieves consistent gains over standard attention across various tasks.
Study on infinitely-wide CNNs and their adaptability to function spatial scales.
problem Understanding how CNNs efficiently learn high-dimensional functions and their adaptability to function spatial scales.
method Study infinitely-wide deep CNNs in the kernel regime, characterizing their spectrum and using generalisation bounds to prove adaptability.
result Deep CNNs adapt to the spatial scale of the target function, with error decay controlled by the effective dimensionality of function subsets.
Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the separation thus lead to various designs of the objective function in the metric …
How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96%, while other methods, especially kernel methods, fall relatively behind? Can we more provide theoretical justifications for this gap? Recently, there is an influential line of work relating neural networks to kernels in t…
Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Designcs.LG
Unified framework for modeling hierarchical spaces in design problems.
problem Challenges in modeling hierarchical, conditional, heterogeneous, or tree-structured domains.
method Unified framework combining feature modeling and graph theory, introducing meta and partially-decreed variables.
result Demonstrated effectiveness on complex system design problems, including neural networks and green-aircraft.
Free Random Projection enhances reinforcement learning by naturally incorporating hierarchical structure.
problem Improving reinforcement learning algorithms for better generalization and adaptability.
method Introduces Free Random Projection, a method that uses free probability theory to create random orthogonal matrices encoding hierarchical structure.
result Empirically shows consistent improvement in generalization over standard methods on multi-environment benchmarks.
Kernel Treeletsstat.ML
A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT), effectively substitutes the correlation coefficient matrix used in treelets with a symm…
New algorithm reduces online regression error in RKHS.
problem Online regression with time-varying functions in RKHS.
method Hierarchical Vovk-Azoury-Warmuth with discounting.
result Achieves optimal dynamic regret with regret bound.
New approach for classification using trigonometric polynomial kernels from signal processing.
problem Classifying objects in arbitrary compact metric spaces.
method Localized trigonometric polynomial kernels for separating different probability measures.
result Minimal number of queried labels for perfect classification.
Neural networks benefit from intermediate representations, reducing sample complexity.
problem Understanding how neural networks leverage intermediate representations for hierarchical learning.
method Fixed, randomly initialized neural network as a representation function, compared with raw inputs and other trainable networks.
result Neural representations can achieve improved sample complexities compared to raw inputs, especially for low-rank polynomials.
Kernelized Capsule Networksstat.ML
Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present an improvement to training capsule networks with added robustness via non-paramet…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approa…
Generalizes machine learning models using localization kernels and local means.
problem Understanding and unifying diverse machine learning models.
method Formal definition of localization method through localization kernels and local means.
result Unified theoretical lens and new methodological tools for designing flexible learning systems.
The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered trees on the basis of their subpaths, which are vertical substructures of trees resp…
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this con…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few hyperparameters or the kernel is even data dependent in a much more complicated manner. …
Random quotients of mapping class groups have rigid properties.
problem Rigidity of random quotients of mapping class groups.
method Generalization of Ivanov's theorem and use of hierarchically hyperbolic groups.
result Automorphisms and commensurators of random quotients coincide with the groups themselves.
A novel nonstationary permanental process relaxes kernel constraints and captures complex data patterns.
problem Limitations of existing permanental processes in terms of kernel types and stationarity.
method Sparse spectral representation of nonstationary kernels and hierarchical stacking of spectral feature mappings.
result Enhanced model expressiveness and reduced computational complexity.
gKRLS accelerates KRLS estimation for complex models.
problem Limited flexibility and high computation for KRLS.
method Re-formulate KRLS as a hierarchical model and implement random sketching.
result gKRLS can fit models on large datasets in minutes.
Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, [1] pointed out that the hierarchical s…
Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in…
Continuous semi-implicit models enable faster training and better performance in generative modeling.
problem Slow convergence in hierarchical semi-implicit models during training.
method CoSIM, a continuous semi-implicit model that incorporates a continuous transition kernel for efficient training.
result CoSIM achieves superior performance on image generation tasks compared to existing methods.
A new method reduces Volterra kernel complexity and uncertainty quantification.
problem Challenges in modeling nonlinear systems with Volterra series due to high model order.
method Bayesian Tensor Network Volterra kernel machines (BTN-V) using canonical polyadic decomposition.
result Competitive accuracy, enhanced uncertainty quantification, and reduced computational cost.
UNTIE learns representations of coupled categorical data.
problem Challenges in learning from unlabeled categorical data with complex couplings.
method UNTIE approach for unsupervised representation learning of heterogeneous couplings.
result UNTIE significantly improves categorical data representations on 25 diverse datasets.
Additive Gaussian Processesstat.ML
We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-expo…