Improved deep kernel machine achieves 94.5% test accuracy on CIFAR-10.
problem Achieving high accuracy on complex tasks like image classification.
method Stochastic kernel regularisation to add noise to learned Gram matrices.
result 94.5% test accuracy on CIFAR-10.
Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature space. We argue that linear classification in the feature space of kernels comm…
This work introduces a new quantum kernel, quantum tangent kernel, for improved performance.
problem Improving quantum machine learning performance beyond conventional methods.
method Developed a deep parameterized quantum circuit and used first-order expansion for training.
result The quantum tangent kernel outperforms conventional quantum kernel methods for ansatz-generated datasets.
Deep networks are mathematically equivalent to kernel machines learned by gradient descent.
problem Understanding the learned representations of deep learning models.
method Using gradient descent to learn deep networks, showing they are equivalent to kernel machines.
result Deep network weights are a superposition of training examples, revealing the learned function.
Deep neural-kernel models combine neural networks and kernel machines for scalable large datasets.
problem Combining neural networks and kernel machines for efficient large-scale learning.
method Hybrid neural-kernel architecture using explicit feature mapping and pooling layers.
result The deep neural-kernel models are effective and scalable on benchmark datasets.
Paper converts deep networks to flat, equivalent kernel machines.
problem Capacity control and uniform convergence in deep learning.
method Push-forward transformation from deep networks to indefinite kernel machines.
result Flat network weights are Lp-norm regularized (0<p<1).
Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. The…
Convolutional DKMs improve kernel methods on MNIST, CIFAR-10, and CIFAR-100.
problem Improving kernel methods for image classification.
method Developed a novel inter-domain inducing point approximation and introduced various techniques to extend DKMs to convolutional networks.
result Achieved state-of-the-art performance on image classification benchmarks.
In this paper, we propose a novel supervised learning method that is called Deep Embedding Kernel (DEK). DEK combines the advantages of deep learning and kernel methods in a unified framework. More specifically, DEK is a learnable kernel represented by a newly designed deep architecture. Compared with pre-defined kerne…
New kernel model scales to large datasets.
problem Challenges in scaling kernel machines to large datasets.
method Introduced EigenPro 3.0, an algorithm based on projected dual preconditioned SGD.
result Ability to scale model and data sizes independently.
Transformers are explained as infinite-dimensional kernel machines.
problem Understanding the mechanics of Transformers in AI.
method Characterized Transformers' attention mechanism as a kernel learning method on Banach spaces.
result Transformer's kernel has infinite feature dimension and can learn any binary non-Mercer reproducing kernel Banach space pair.
New theory explains deep learning's success in transforming inputs.
problem Standard theoretical approaches eliminate representation learning.
method Developed a new infinite width limit for representation learning.
result Deep Gaussian processes (DGPs) have multivariate Gaussian posteriors.
New unsupervised learning technique learns independent kernels for better machine learning tasks.
problem Improving unsupervised representation learning for machine learning tasks.
method Stacking convolutional transforms using alternating proximal minimization scheme.
result DCTL outperforms shallow version CTL on benchmark datasets.
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a framework to construct and learn a data-dependent kernel based on random features …
Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to describe the data and hence could not yield satisfactory performance. In this paper, vi…
Paper identifies how neural networks learn features.
problem Understanding how neural networks automatically select features.
method Deep Neural Feature Ansatz, implementing average gradient outer product.
result Recursive Feature Machines achieve state-of-the-art performance.
We apply a fast kernel method for mask-based single-channel speech enhancement. Specifically, our method solves a kernel regression problem associated to a non-smooth kernel function (exponential power kernel) with a highly efficient iterative method (EigenPro). Due to the simplicity of this method, its hyper-parameter…
Deep learning methods have predominantly been applied to large artificial neural networks. Despite their state-of-the-art performance, these large networks typically do not generalize well to datasets with limited sample sizes. In this paper, we take a different approach by learning multiple layers of kernels. We combi…
Graph convolutional deep kernel machine learns representations for graph tasks.
problem Limited representation learning in infinite-width neural networks.
method Developed a graph convolutional deep kernel machine as an infinite-width limit.
result Representation learning improves performance for heterophilous node classification tasks.
The paper explains generalization in kernel regression and deep neural networks using spectral bias and task-model alignment.
problem Understanding generalization in machine learning models, especially deep neural networks.
method Analytical expression for generalization error derived from statistical mechanics, applied to various kernels and data distributions.
result Spectral bias and task-model alignment explain generalization in kernel regression and deep neural networks.
Kernel density matrices simplify probabilistic deep learning.
problem Representing joint probability distributions of continuous and discrete variables.
method Extending density matrices to a reproducing kernel Hilbert space.
result Versatile representation for marginal and joint probability distributions.
Deep learning predicts drug prescriptions across global health records.
problem Predicting drug prescriptions in chronic disease patients.
method Adaptive cross-global attention graph kernel network with support vector machine.
result Model outperforms current methods in accuracy and interpretability.
DKL-KAN combines deep learning and kernel methods for scalable, expressive models.
problem Combining deep learning's depth with kernel methods' flexibility for scalable models.
method DKL-KAN uses Kolmogorov-Arnold Networks (KAN) to optimize kernel attributes within a Gaussian process framework.
result DKL-KAN outperforms DKL-MLP on datasets with a low number of observations and DKL-MLP on large datasets.
MKL-based models outperform complex multi-omics integrative approaches.
problem Integrating diverse omics data sources.
method Supervised multiple kernel learning with different kernel fusion strategies.
result MKL-based models outperform more complex architectures.
End-to-end graph SVM with graph convolutions and RKHS.
problem Graph classification with complex feature spaces.
method End-to-end training of graph convolutions, kernel function, and SVM parameters.
result Outperforms existing deep learning models on graph classification tasks.
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.
Proposes learning manifold implicitly via heat kernel.
problem Direct manifold learning methods lack flexibility for down-stream applications.
method Implicit manifold learning using heat kernel.
result Framework achieves state-of-the-art results for data generation and Bayesian inference.
This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification, statistical learning theory, and dimension independent generalization bounds. Implicit re…
In this paper, we aim at introducing a new machine learning model, namely reconciled polynomial machine, which can provide a unified representation of existing shallow and deep machine learning models. Reconciled polynomial machine predicts the output by computing the inner product of the feature kernel function and va…
A new method for disentangled representations without supervision.
problem Learning disentangled representations in unsupervised learning.
method Constr-DRKM, a deep kernel method with orthogonality constraints.
result Constr-DRKM performs similarly to β-VAE on disentanglement metrics.
New kernels boost RNN performance on non-time-series data.
problem Improving performance of RNNs on non-time-series data.
method Extended RNN kernels to complex architectures, developed fast GPU implementation.
result RNN-based classifiers outperform baselines on 90 non-time-series datasets.
New mechanism discovered for feature learning in CNNs.
problem Understanding how CNNs learn features from images.
method Proposed Convolutional Neural Feature Ansatz linking filter covariances to patch-based AGOPs.
result Deep ConvRFM algorithm learns features similar to deep CNNs, improving performance.
RKHS-SHAP uses Shapley values for kernel methods to provide feature attributions.
problem Feature attribution for kernel methods is often heuristic and not individualised.
method RKHS-SHAP uses Shapley values from coalition game theory to compute feature attributions for kernel machines efficiently.
result RKHS-SHAP can compute both Interventional and Observational Shapley values.
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence in various machine learning algorithms like generalized least squa…
Researchers develop flexible kernels for biological sequences with guaranteed reliability.
problem Challenges in applying machine learning to biological sequences, including unreliable methods.
method Theoretical analysis and development of modified kernels to ensure reliability and accuracy.
result Developed kernels that are universal, characteristic, and metrize the space of distributions for biological sequences.
Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on test data, a phenomenon not yet fully understood. The first point of our paper is t…
Scalable machine learning with path signatures for time series and graphs.
problem Challenges in real-world time series and graph data.
method Combines rough path theory with probabilistic, deep, and kernel methods.
result Scalable models for time series and graph data.
A new method uses Gaussian processes and deep kernel learning to price high-dimensional American options efficiently.
problem Challenges in pricing high-dimensional American options, especially with excessive computational costs.
method Modified Gaussian process regression with deep kernel learning and sparse variational Gaussian processes.
result The method outperforms least squares Monte Carlo in high-dimensional scenarios, especially with Merton's jump diffusion model.
Lectures on deep learning properties in infinite and large-width networks.
problem Understanding deep neural networks in extreme width conditions.
method Analysis of random deep neural networks, connections to linear models, kernels, and Gaussian processes, perturbative and non-perturbative treatments.
result Properties and behaviors of deep neural networks in the infinite-width limit and large-width regime.
A new algorithm for high-dimensional hedging problems.
problem High-dimensional, path-dependent hedging problems.
method Signature-based algorithm using operator-valued kernels and geometric rough paths.
result Theoretical guarantees on existence and uniqueness of a global minimum.
We propose a novel family of connectionist models based on kernel machines and consider the problem of learning layer-by-layer a compositional hypothesis class, i.e., a feedforward, multilayer architecture, in a supervised setting. In terms of the models, we present a principled method to "kernelize" (partly or complet…
Complex problems may require sophisticated, non-linear learning methods such as kernel machines or deep neural networks to achieve state of the art prediction accuracies. However, high prediction accuracies are not the only objective to consider when solving problems using machine learning. Instead, particular scientif…
Revisits Gaussian process model with spherical harmonics for scalable deep learning.
problem Scaling Gaussian process models to large input dimensions with high frequency learning.
method Introduces new kernels related to deep models, variational learning of spherical harmonic phases, and sparseness in eigenbasis.
result Enables scaling to larger input dimensions and learning of high frequency variations.
PDE-DKL combines NNs and GPs for high-dimensional PDE problems.
problem High-dimensional PDE problems with scarce data.
method PDE-constrained Deep Kernel Learning (PDE-DKL) framework.
result High accuracy with reduced data requirements.
Deep learning (DL) is one of the most prominent branches of machine learning. Due to the immense computational cost of DL workloads, industry and academia have developed DL libraries with highly-specialized kernels for each workload/architecture, leading to numerous, complex code-bases that strive for performance, yet …
This paper introduces a novel framework for generative models based on Restricted Kernel Machines (RKMs) with joint multi-view generation and uncorrelated feature learning, called Gen-RKM. To enable joint multi-view generation, this mechanism uses a shared representation of data from various views. Furthermore, the mod…
Robust learning method combines kernel smoothing and robust optimization.
problem Certifying robustness against distribution shifts in machine learning models.
method Adapting integral operator using supremal convolution for robustness, leveraging optimal transport.
result The method provides theoretical guarantees for certified robustness and competitive performance.
New random feature maps for Laplacian and related kernels.
problem Challenges in approximating the Laplacian kernel and its generalizations.
method Developed random feature maps for Laplacian and related kernels, providing efficient sampling schemes.
result Demonstrated the efficacy of these random feature maps on real datasets.