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 this paper, we explore penalizing by sparsity-inducing norms such as the l1-norm or the block l1-norm. We assume that the kernel decomposes into a large sum of individual basis kernels which can be embedded in a directed acyclic graph; we show that it is then possible to perform kernel selection through a hierarchical multiple kernel learning framework, in polynomial time in the number of selected kernels. This framework is naturally applied to non linear variable selection; our extensive simulations on synthetic datasets and datasets from the UCI repository show that efficiently exploring the large feature space through sparsity-inducing norms leads to state-of-the-art predictive performance.
Universität Stuttgart（斯图加特大学）；Bosch Healthcare Solutions（博世医疗解决方案）
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 consistent. We further describe a parameter optimization method for the kernel parameters and empirically compare this method to SVMs, random forests, a multiple kernel learning approach, and to some deep neural networks.
IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Tel Aviv University（特拉维夫大学）；Google Brain, NYC（谷歌大脑（纽约））
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 locally lossless approximation in a hierarchical fashion. The kernel maintains (strict) positive-definiteness. The corresponding kernel matrix admits a recursively off-diagonal low-rank structure, which allows for fast linear algebra computations. Suppressing the factor of data dimensi…
University of Michigan（密歇根大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
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 routines. We consider both the general $\mathcal{H}$ matrix hierarchical format as well as Hierarchically Semi-Separable (HSS) matrices. Furthermore, we investigate the impact of several preprocessing and clustering techniques on the hierarchical matrix compression. Effective clusteri…
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 learning model. One classical metric is the Mahalanobis distance, where a linear transformation matrix is designed and applied on the original dataset to obtain a new subspace equipped with the Euclidean norm. The kernelized version has also been developed, followed by Multiple-K…
Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络空间安全学院）
Recently, non-stationary spectral kernels have drawn much attention, owing to its powerful feature representation ability in revealing long-range correlations and input-dependent characteristics. However, non-stationary spectral kernels are still shallow models, thus they are deficient to learn both hierarchical features and local interdependence. In this paper, to obtain hierarchical and local knowledge, we build an interpretable convolutional spectral kernel network (\texttt{CSKN}) based on the inverse Fourier transform, where we introduce deep architectures and convolutional filters into no…
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-parametric kernel methods. The representations learned through the capsule network are used to construct covariance kernels for Gaussian processes (GPs). We demonstrate that this approach achieves comparable prediction performance to Capsule Networks while improving robustness to advers…
KU Leuven（鲁汶大学）；Telecom Paris（巴黎电信学院）；London School of Economics（伦敦政治经济学院）
The focus of the paper is functional output regression (FOR) with convoluted losses. While most existing work consider the square loss setting, we leverage extensions of the Huber and the $ε$-insensitive loss (induced by infimal convolution) and propose a flexible framework capable of handling various forms of outliers and sparsity in the FOR family. We derive computationally tractable algorithms relying on duality to tackle the resulting tasks in the context of vector-valued reproducing kernel Hilbert spaces. The efficiency of the approach is demonstrated and contrasted with the classical squ…
University of California Santa Barbara（加州大学圣巴巴拉分校）
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 symmetric, positive semi-definite matrix efficiently constructed from a kernel function. Unlike most clustering methods, which require data sets to be numeric, KT can be applied to more general data and yield a multi-resolution sequence of basis on the data directly in feature space.…
In this paper, we propose a novel approach for unsupervised domain adaptation, that relates notions of optimal transport, learning probability measures and unsupervised learning. The proposed approach, HOT-DA, is based on a hierarchical formulation of optimal transport, that leverages beyond the geometrical information captured by the ground metric, richer structural information in the source and target domains. The additional information in the labeled source domain is formed instinctively by grouping samples into structures according to their class labels. While exploring hidden structures i…
Graduate School of Information Science and Technology, The University of Tokyo（东京大学信息科学与技术研究生院）
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 responsible for hierarchical information in them. Their kernel exhibits practically good performance in terms of accuracy and speed; however, linear-time computation is not guaranteed theoretically, unlike the case of the other unordered tree kernel proposed by Vishwanathan and Smola…
Microsoft Research AI（微软研究院人工智能部门）；Stanford University（斯坦福大学）
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 the over-parameterized regime, proving they can learn certain concept class that is also learnable by kernels with similar test error. Yet, can neural networks provably learn some concept class BETTER than kernels? We answer this positively in the distribution-free setting. We pro…
Prominently used in support vector machines and logistic regressions, kernel functions (kernels) can implicitly map data points into high dimensional spaces and make it easier to learn complex decision boundaries. In this work, by replacing the inner product function in the softmax layer, we explore the use of kernels for contextual word classification. In order to compare the individual kernels, experiments are conducted on standard language modeling and machine translation tasks. We observe a wide range of performances across different kernel settings. Extending the results, we look at the g…
Imperial College London（帝国理工学院）；University College London（伦敦大学学院）
Stacking Gaussian Processes severely diminishes the model's ability to detect outliers, which when combined with non-zero mean functions, further extrapolates low non-parametric variance to low training data density regions. We propose a hybrid kernel inspired from Varifold theory, operating in both Euclidean and Wasserstein space. We posit that directly taking into account the variance in the computation of Wasserstein-2 distances is of key importance towards maintaining outlier status throughout the hierarchy. We show improved performance on medium and large scale datasets and enhanced out-o…
Beijing Normal University（北京师范大学）；Central University of Finance and Economics（中央财经大学）；Zhejiang Normal University（浙江师范大学）；University of York（约克大学）
In this work, we propose a family of novel quantum kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed graphs. Different from most existing classical graph kernels, the proposed HAQJSK kernels can incorporate hierarchical aligned structure information between graphs and transform graphs of random sizes into fixed-sized aligned graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of vertices and the Hierarchical Transitive Aligned Density Matrix of the Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the r…
Central University of Finance and Economics（中央财经大学）；University of York（约克大学）
In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing state-of-the-art graph kernels, the proposed kernel has three theoretical advantages. First, it incorporates the locational correspondence information between graphs into the kernel computation, and thus overcomes the shortcoming of ignoring structural correspondences arising in most R-convolution kernels. Second, it guarantees the transitivity between the correspondenc…
Joint modeling of language and vision has been drawing increasing interest. A multimodal data representation allowing for bidirectional retrieval of images by sentences and vice versa is a key aspect. In this paper we present three contributions in canonical correlation analysis (CCA) based multimodal retrieval. Firstly, we show that an asymmetric weighting of the canonical weights, while achieving a cross view mapping from the search to the query space, improves the retrieval performance. Secondly, we devise a computationally efficient model selection, crucial to generalization and stability,…
Department of Computer Science and Technology（计算机科学与技术系）；MIIT Key Laboratory of Pattern Analysis and Machine Intelligence（工业和信息化部模式分析与机器智能重点实验室）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Jiangsu Province（江苏省）
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph hierarchical structure information, we propose pyramid graph kernel based on optimal transport (OT). Each graph is embedded into hierarchical structures of the pyramid. Then, the OT distance is utilized to measure the similarity between graphs in hierarchical structures. We also utilize the OT distance to measure the similarity between subgraphs and propose sub…
The Hong Kong University of Science and Technology（香港科技大学）；University of Thessaly（色萨利大学）
Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of black-box models is that they underperform under blind conditions since no physical knowledge is incorporated. Physics-based ML aims to address this problem by retaining the mathematical flexibility of ML techniques while incorporating physics. In accord, this paper proposes to embed mechanics-based models into the mean function of a Gaussian Process (GP) model an…
INRIA（法国国家信息与自动化研究所）；Laboratoire d’Informatique de l’Ecole Normale Supérieure（巴黎高等师范学院计算机实验室）；CNRS（法国国家科学研究中心）；ENS（巴黎高等师范学院）
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that characterize non-linear interactions between the original variables. To select efficiently from these many kernels, we use the natural hierarchical structure of the problem to extend the multiple kernel learning framework to kernels that can be embedded in a directed acyclic graph; we show that it is then possible to perform kernel selection through a graph-adapted sp…
University of Oulu（奥卢大学）；Lappeenranta-Lahti University of Technology（拉彭兰塔-拉赫蒂工业大学）；University College London（伦敦大学学院）
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the convolution kernel to recover an accurate reconstruction and additionally prior assumptions on the regularity of the signal are needed. To overcome these limitations, we parametrise the convolution kernel and prior length-scales, which are then jointly estimated in the inversion procedure. The proposed framework of blind hierarchical deconvolution enables accurat…
High-order parametric models that include terms for feature interactions are applied to various data mining tasks, where ground truth depends on interactions of features. However, with sparse data, the high- dimensional parameters for feature interactions often face three issues: expensive computation, difficulty in parameter estimation and lack of structure. Previous work has proposed approaches which can partially re- solve the three issues. In particular, models with factorized parameters (e.g. Factorization Machines) and sparse learning algorithms (e.g. FTRL-Proximal) can tackle the first …
Shanghai Jiao Tong University（上海交通大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Graph neural networks have attracted wide attentions to enable representation learning of graph data in recent works. In complement to graph convolution operators, graph pooling is crucial for extracting hierarchical representation of graph data. However, most recent graph pooling methods still fail to efficiently exploit the geometry of graph data. In this paper, we propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Node proximity is obtained by harmonizing the kernel representat…
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 long vector (also called stacked vector), on which is applied a conventional vector-based machine learning technique (e.g. SVM with Gaussian kernel). In this paper, we rather propose to use a sequence structured kernel: the spectrum kernel. We show that the conventional stacked vect…
Center for Brains Minds and Machines, Massachusetts Institute of Technology（麻省理工学院脑、心智与机器中心）；Laboratory for Computational Learning, Istituto Italiano di Tecnologia（意大利理工学院计算学习实验室）；Massachusetts Institute of Technology（麻省理工学院）；DIBRIS, Universitá degli studi di Genova（热那亚大学DIBRIS）；Institute for Infocomm Research（信息通信研究院）
In i-theory a typical layer of a hierarchical architecture consists of HW modules pooling the dot products of the inputs to the layer with the transformations of a few templates under a group. Such layers include as special cases the convolutional layers of Deep Convolutional Networks (DCNs) as well as the non-convolutional layers (when the group contains only the identity). Rectifying nonlinearities -- which are used by present-day DCNs -- are one of the several nonlinearities admitted by i-theory for the HW module. We discuss here the equivalence between group averages of linear combinations…
The University of Electro-Communications（电气通信大学）；Nanjing University（南京大学）；Nanjing University of Science and Technology（南京理工大学）
Recently, the application of deep learning models to diagnose neuropsychiatric diseases from brain imaging data has received more and more attention. However, in practice, exploring interactions in brain functional connectivity based on operational magnetic resonance imaging data is critical for studying mental illness. Since Attention-Deficit and Hyperactivity Disorder (ADHD) is a type of chronic disease that is very difficult to diagnose in the early stages, it is necessary to improve the diagnosis accuracy of such illness using machine learning models treating patients before the critical c…
Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class of priors would represent weights compactly, capture correlations between weights, facilitate calibrated reasoning about uncertainty, and allow inclusion of prior knowledge about the function space such as periodicity or dependence on contexts such as inputs. To this end, this paper introduces two innovations: (i) a Gaussian process-based hierarchical model…
Zhejiang University（浙江大学）；Alibaba-Zhejiang University Joint Institute of Frontier Technologies（阿里巴巴-浙江大学前沿技术联合研究院）；Innovation Center of Yangtze River Delta（长三角创新中心）；Microsoft Research Asia（微软亚洲研究院）
Although deep learning has revolutionized music generation, existing methods for structured melody generation follow an end-to-end left-to-right note-by-note generative paradigm and treat each note equally. Here, we present WuYun, a knowledge-enhanced deep learning architecture for improving the structure of generated melodies, which first generates the most structurally important notes to construct a melodic skeleton and subsequently infills it with dynamically decorative notes into a full-fledged melody. Specifically, we use music domain knowledge to extract melodic skeletons and employ sequ…
Exploring Hierarchical Molecular Graph Representation in Multimodal LLMs
National University of Singapore（新加坡国立大学）；Institute of High-Performance Computing, Agency for Science, Technology and Research（新加坡科技研究局高性能计算研究所）；Centre for Frontier AI Research, Agency for Science, Technology and Research（新加坡科技研究局前沿人工智能研究中心）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
Kernel PCA is a powerful feature extractor which recently has seen a reformulation in the context of Restricted Kernel Machines (RKMs). These RKMs allow for a representation of kernel PCA in terms of hidden and visible units similar to Restricted Boltzmann Machines. This connection has led to insights on how to use kernel PCA in a generative procedure, called generative kernel PCA. In this paper, the use of generative kernel PCA for exploring latent spaces of datasets is investigated. New points can be generated by gradually moving in the latent space, which allows for an interpretation of the…
Reinforcement learning (RL) is currently a popular research topic in control engineering and has the potential to make its way to industrial and commercial applications. Corresponding RL controllers are trained in direct interaction with the controlled system, rendering them data-driven and performance-oriented solutions. The best practice of exploring starts (ES) is used by default to support the learning process via randomly picked initial states. However, this method might deliver strongly biased results if the system's dynamic and constraints lead to unfavorable sample distributions in the…
Bosch Center for Artificial Intelligence（博世人工智能中心）
Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior. Machine learning methods that are used to produce the surrogate model should therefore address these problems by providing a scheme to keep the number of queries small, e.g. by using active learning and be able to capture the nonlinear and nonstationary properties of the system. One way of modeling the nonstationarity is to induce input-partitioning, a principle t…
The recent 3D medical ViTs (e.g., SwinUNETR) achieve the state-of-the-art performances on several 3D volumetric data benchmarks, including 3D medical image segmentation. Hierarchical transformers (e.g., Swin Transformers) reintroduced several ConvNet priors and further enhanced the practical viability of adapting volumetric segmentation in 3D medical datasets. The effectiveness of hybrid approaches is largely credited to the large receptive field for non-local self-attention and the large number of model parameters. In this work, we propose a lightweight volumetric ConvNet, termed 3D UX-Net, w…
Exploring the Energy Landscape of RBMs: Reciprocal Space Insights into Bosons, Hierarchical Learning and Symmetry Breaking
TRIUMF；Perimeter Institute for Theoretical Physics（佩里米特理论物理研究所）；University of Virginia（弗吉尼亚大学）；Computer Science and Biocomplexity Institute（计算机科学与生物复杂性研究所）；Department of Physics and Astronomy（物理与天文学系）；University of Waterloo（滑铁卢大学）
In recent times, using small data to train networks has become a hot topic in the field of deep learning. Reusing pre-trained parameters is one of the most important strategies to address the issue of semi-supervised and transfer learning. However, the fundamental reason for the success of these methods is still unclear. In this paper, we propose a solution that can not only judge whether a given network is reusable or not based on the performance of reusing convolution kernels but also judge which layers' parameters of the given network can be reused, based on the performance of reusing corre…
Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success, but a framework for deep principal component analysis is still lacking. Here we develop a deep kernel PCA methodology (DKPCA) to extract multiple levels of the most informative components of the data. Our scheme can effectively identify new hierarchical variables, called deep principal components, capturing the main characteristics of high-dimensional data th…
Exploring the Boundaries of On-Device Inference: When Tiny Falls Short, Go Hierarchical
KTH Royal Institute of Technology（瑞典皇家理工学院）；University of Helsinki（赫尔辛基大学）；IMDEA Networks Institute（IMDEA网络研究所）；EURECOM（欧洲通信学院）；University of Victoria（维多利亚大学）
Discovering relational structure between input features in sequence labeling models has shown to improve their accuracy in several problem settings. However, the search space of relational features is exponential in the number of basic input features. Consequently, approaches that learn relational features, tend to follow a greedy search strategy. In this paper, we study the possibility of optimally learning and applying discriminative relational features for sequence labeling. For learning features derived from inputs at a particular sequence position, we propose a Hierarchical Kernels-based …
