We introduce squared neural Poisson point processes (SNEPPPs) by parameterising the intensity function by the squared norm of a two layer neural network. When the hidden layer is fixed and the second layer has a single neuron, our approach resembles previous uses of squared Gaussian process or kernel methods, but allowing the hidden layer to be learnt allows for additional flexibility. In many cases of interest, the integrated intensity function admits a closed form and can be computed in quadratic time in the number of hidden neurons. We enumerate a far more extensive number of such cases than has previously been discussed. Our approach is more memory and time efficient than naive implementations of squared or exponentiated kernel methods or Gaussian processes. Maximum likelihood and maximum a posteriori estimates in a reparameterisation of the final layer of the intensity function can be obtained by solving a (strongly) convex optimisation problem using projected gradient descent. We demonstrate SNEPPPs on real, and synthetic benchmarks, and provide a software implementation.
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This paper studies robust nonparametric regression, in which an adversarial attacker can modify the values of up to q samples from a training dataset of size N. Our initial solution is an M-estimator based on Huber loss minimization. Compared with simple kernel regression, i.e. the Nadaraya-Watson estimator, this method can significantly weaken the impact of malicious samples on the regression performance. We provide the convergence rate as well as the corresponding minimax lower bound. The result shows that, with proper bandwidth selection, supremum error is minimax optimal. The L2 error is optimal with relatively small q, but is suboptimal with larger q. The reason is that this estimator is vulnerable if there are many attacked samples concentrating in a small region. To address this issue, we propose a correction method by projecting the initial estimate to the space of Lipschitz functions. The final estimate is nearly minimax optimal for arbitrary q, up to a logarithmic factor.
Incomplete Multiple Kernel Clustering algorithms, which aim to learn a common latent representation from pre-constructed incomplete multiple kernels from the original data, followed by k-means for clustering. They have attracted intensive attention due to their high computational efficiency. However, our observation reveals that the imputation of these approaches for each kernel ignores the influence of other incomplete kernels. In light of this, we present a novel method called Low-Rank Kernel Tensor Learning for Incomplete Multiple Views Clustering (LRKT-IMVC) to address the above issue. Specifically, LRKT-IMVC first introduces the concept of kernel tensor to explore the inter-view correlations, and then the low-rank kernel tensor constraint is used to further capture the consistency information to impute missing kernel elements, thereby improving the quality of clustering. Moreover, we carefully design an alternative optimization method with promising convergence to solve the resulting optimization problem. The proposed method is compared with recent advances in experiments with different missing ratios on seven well-known datasets, demonstrating its effectiveness and the advantages of the proposed interpolation method.
Channel pruning is widely accepted to accelerate modern convolutional neural networks (CNNs). The resulting pruned model benefits from its immediate deployment on general-purpose software and hardware resources. However, its large pruning granularity, specifically at the unit of a convolution filter, often leads to undesirable accuracy drops due to the inflexibility of deciding how and where to introduce sparsity to the CNNs. In this paper, we propose REPrune, a novel channel pruning technique that emulates kernel pruning, fully exploiting the finer but structured granularity. REPrune identifies similar kernels within each channel using agglomerative clustering. Then, it selects filters that maximize the incorporation of kernel representatives while optimizing the maximum cluster coverage problem. By integrating with a simultaneous training-pruning paradigm, REPrune promotes efficient, progressive pruning throughout training CNNs, avoiding the conventional train-prune-finetune sequence. Experimental results highlight that REPrune performs better in computer vision tasks than existing methods, effectively achieving a balance between acceleration ratio and performance retention.
We address the Individualized continuous treatment effect (ICTE) estimation problem where we predict the effect of any continuous valued treatment on an individual using ob- servational data. The main challenge in this estimation task is the potential confounding of treatment assignment with in- dividual’s covariates in the training data, whereas during in- ference ICTE requires prediction on independently sampled treatments. In contrast to prior work that relied on regularizers or unstable GAN training, we advocate the direct approach of augmenting training individuals with independently sam- pled treatments and inferred counterfactual outcomes. We in- fer counterfactual outcomes using a two-pronged strategy: a Gradient Interpolation for close-to-observed treatments, and a Gaussian Process based Kernel Smoothing which allows us to down weigh high variance inferences. We evaluate our method on five benchmarks and show that our method out- performs six state-of-the-art methods on the counterfactual estimation error. We analyze the superior performance of our method by showing that (1) our inferred counterfactual re- sponses are more accurate, and (2) adding them to the train- ing data reduces the distributional distance between the con- founded training distribution and test distribution where treat- ment is independent of covariates. Our proposed method is model-agnostic and we show that it improves ICTE accuracy of several existing models.
Attention-Induced Embedding Imputation for Incomplete Multi-View Partial Multi-Label Classification
PDF ↗As a combination of emerging multi-view learning methods and traditional multi-label classification tasks, multi-view multi-label classification has shown broad application prospects. The diverse semantic information contained in heterogeneous data effectively enables the further development of multi-label classification. However, the widespread incompleteness problem on multi-view features and labels greatly hinders the practical application of multi-view multi-label classification. Therefore, in this paper, we propose an attention-induced missing instances imputation technique to enhance the generalization ability of the model. Different from existing incomplete multi-view completion methods, we attempt to approximate the latent features of missing instances in embedding space according to cross-view joint attention, instead of recovering missing views in kernel space or original feature space. Accordingly, multi-view completed features are dynamically weighted by the confidence derived from joint attention in the late fusion phase. In addition, we propose a multi-view multi-label classification framework based on label-semantic feature learning, utilizing the statistical weak label correlation matrix and graph attention network to guide the learning process of label-specific features. Finally, our model is compatible with missing multi-view and partial multi-label data simultaneously and extensive experiments on five datasets confirm the advancement and effectiveness of our embedding imputation method and multi-view multi-label classification model.
We consider the problem of predictive modeling from irregularly and sparsely sampled longitudinal data with unknown, complex correlation structures and abrupt discontinuities. To address these challenges, we introduce a novel inducing clusters longitudinal deep kernel Gaussian Process (ICDKGP). ICDKGP approximates the data generating process by a zero-mean GP with a longitudinal deep kernel that models the unknown complex correlation structure in the data and a deterministic non-zero mean function to model the abrupt discontinuities. To improve the scalability and interpretability of ICDKGP, we introduce inducing clusters corresponding to centers of clusters in the training data. We formulate the training of ICDKGP as a constrained optimization problem and derive its evidence lower bound. We introduce a novel relaxation of the resulting problem which under rather mild assumptions yields a solution with error bounded relative to the original problem. We describe the results of extensive experiments demonstrating that ICDKGP substantially outperforms the state-of-the-art longitudinal methods on data with both smoothly and non-smoothly varying outcomes.
Machine learning techniques, such as deep learning and ensemble methods, are widely used in various domains due to their ability to handle complex real-world tasks. However, their black-box nature has raised multiple concerns about the fairness, trustworthiness, and transparency of computer-assisted decision-making. This has led to the emergence of local post-hoc explainability methods, which offer explanations for individual decisions made by black-box algorithms. Among these methods, Kernel SHAP is widely used due to its model-agnostic nature and its well-founded theoretical framework. Despite these strengths, Kernel SHAP suffers from high instability: different executions of the method with the same inputs can lead to significantly different explanations, which diminishes the relevance of the explanations. The contribution of this paper is two-fold. On the one hand, we show that Kernel SHAP's instability is caused by its stochastic neighbor selection procedure, which we adapt to achieve full stability without compromising explanation fidelity. On the other hand, we show that by restricting the neighbors generation to perturbations of size 1 -- which we call the coalitions of Layer 1 -- we obtain a novel feature-attribution method that is fully stable, computationally efficient, and still meaningful.
Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation
PDF ↗Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.
Compressing Image-to-Image Translation GANs Using Local Density Structures on Their Learned Manifold
PDF ↗Generative Adversarial Networks (GANs) have shown remarkable success in modeling complex data distributions for image-to-image translation. Still, their high computational demands prohibit their deployment in practical scenarios like edge devices. Existing GAN compression methods mainly rely on knowledge distillation or convolutional classifiers' pruning techniques. Thus, they neglect the critical characteristic of GANs: their local density structure over their learned manifold. Accordingly, we approach GAN compression from a new perspective by explicitly encouraging the pruned model to preserve the density structure of the original parameter-heavy model on its learned manifold. We facilitate this objective for the pruned model by partitioning the learned manifold of the original generator into local neighborhoods around its generated samples. Then, we propose a novel pruning objective to regularize the pruned model to preserve the local density structure over each neighborhood, resembling the kernel density estimation method. Also, we develop a collaborative pruning scheme in which the discriminator and generator are pruned by two pruning agents. We design the agents to capture interactions between the generator and discriminator by exchanging their peer's feedback when determining corresponding models' architectures. Thanks to such a design, our pruning method can efficiently find performant sub-networks and can maintain the balance between the generator and discriminator more effectively compared to baselines during pruning, thereby showing more stable pruning dynamics. Our experiments on image translation GAN models, Pix2Pix and CycleGAN, with various benchmark datasets and architectures demonstrate our method's effectiveness.
Unsupervised and self-supervised representation learning has become popular in recent years for learning useful features from unlabelled data. Representation learning has been mostly developed in the neural network literature, and other models for representation learning are surprisingly unexplored. In this work, we introduce and analyze several kernel-based representation learning approaches: Firstly, we define two kernel Self-Supervised Learning (SSL) models using contrastive loss functions and secondly, a Kernel Autoencoder (AE) model based on the idea of embedding and reconstructing data. We argue that the classical representer theorems for supervised kernel machines are not always applicable for (self-supervised) representation learning, and present new representer theorems, which show that the representations learned by our kernel models can be expressed in terms of kernel matrices. We further derive generalisation error bounds for representation learning with kernel SSL and AE, and empirically evaluate the performance of these methods in both small data regimes as well as in comparison with neural network based models.
Multi kernel learning (MKL) is a representative supervised multi-view learning method widely applied in multi-modal and multi-view applications. MKL aims to classify data by integrating complementary information from predefined kernels. Although existing MKL methods achieve promising performance, they fail to consider the tradeoff between diversity and classification accuracy of kernels, preventing further improvement of classification performance. In this paper, we tackle this problem by generating a number of high-quality base learning kernels and selecting a kernel subset with maximum pairwise diversity and minimum generalization errors. We first formulate this idea as a nonconvex quadratic integer programming problem. Then we transform this nonconvex problem into a convex optimization problem and prove it is equivalent to a semidefinite relaxation problem, which a semidefinite-based branch-and-bound algorithm can quickly solve. Experimental results on the real-world datasets demonstrate the superiority of the proposed method. The results also show that our method works for the support vector machine (SVM) classifier and other state-of-the-art kernel classifiers.
Neural population coding can represent continuous information by neurons with a series of discrete preferred stimuli, and we find that the bell-shaped tuning curve plays an important role in this mechanism. Inspired by this, we incorporate a bell-shaped tuning curve into the discrete group convolution to achieve continuous group equivariance. Simply, we modulate group convolution kernels by Gauss functions to obtain bell-shaped tuning curves. Benefiting from the modulation, kernels also gain smooth gradients on geometric dimensions (e.g., location dimension and orientation dimension). It allows us to generate group convolution kernels from sparse weights with learnable geometric parameters, which can achieve both competitive performances and parameter efficiencies. Furthermore, we quantitatively prove that discrete group convolutions with proper tuning curves (bigger than 1x sampling step) can achieve continuous equivariance. Experimental results show that 1) our approach achieves very competitive performances on MNIST-rot with at least 75% fewer parameters compared with previous SOTA methods, which is efficient in parameter; 2) Especially with small sample sizes, our approach exhibits more pronounced performance improvements (up to 24%); 3) It also has excellent rotation generalization ability on various datasets such as MNIST, CIFAR, and ImageNet with both plain and ResNet architectures.
PG-LBO: Enhancing High-Dimensional Bayesian Optimization with Pseudo-Label and Gaussian Process Guidance
PDF ↗Variational Autoencoder based Bayesian Optimization (VAE-BO) has demonstrated its excellent performance in addressing high-dimensional structured optimization problems. However, current mainstream methods overlook the potential of utilizing a pool of unlabeled data to construct the latent space, while only concentrating on designing sophisticated models to leverage the labeled data. Despite their effective usage of labeled data, these methods often require extra network structures, additional procedure, resulting in computational inefficiency. To address this issue, we propose a novel method to effectively utilize unlabeled data with the guidance of labeled data. Specifically, we tailor the pseudo-labeling technique from semi-supervised learning to explicitly reveal the relative magnitudes of optimization objective values hidden within the unlabeled data. Based on this technique, we assign appropriate training weights to unlabeled data to enhance the construction of a discriminative latent space. Furthermore, we treat the VAE encoder and the Gaussian Process (GP) in Bayesian optimization as a unified deep kernel learning process, allowing the direct utilization of labeled data, which we term as Gaussian Process guidance. This directly and effectively integrates the goal of improving GP accuracy into the VAE training, thereby guiding the construction of the latent space. The extensive experiments demonstrate that our proposed method outperforms existing VAE-BO algorithms in various optimization scenarios. Our code will be published at https://github.com/TaicaiChen/PG-LBO.
With the rapid growth of audio data, there's a pressing need for automatic audio classification. As a type of time-series data, audio exhibits waveform fluctuations in both the time and frequency domains that evolve over time, with similar instances sharing consistent patterns. This study introduces the Audio Scanning Network (ASNet), designed to leverage abundant information for achieving stable and effective audio classification. ASNet captures real-time changes in audio waveforms across both time and frequency domains through reservoir computing, supported by Reservoir Kernel Canonical Correlation Analysis (RKCCA) to explore correlations between time-domain and frequency-domain waveform fluctuations. This innovative approach empowers ASNet to comprehensively capture the changes and inherent correlations within the audio waveform, and without the need for time-consuming iterative training. Instead of converting audio into spectrograms, ASNet directly utilizes audio feature sequences to uncover associations between time and frequency fluctuations. Experiments on environmental sound and music genre classification tasks demonstrate ASNet's comparable performance to state-of-the-art methods.
Limited Memory Online Gradient Descent for Kernelized Pairwise Learning with Dynamic Averaging
PDF ↗Pairwise learning, an important domain within machine learning, addresses loss functions defined on pairs of training examples, including those in metric learning and AUC maximization. Acknowledging the quadratic growth in computation complexity accompanying pairwise loss as the sample size grows, researchers have turned to online gradient descent (OGD) methods for enhanced scalability. Recently, an OGD algorithm emerged, employing gradient computation involving prior and most recent examples, a step that effectively reduces algorithmic complexity to O(T), with T being the number of received examples. This approach, however, confines itself to linear models while assuming the independence of example arrivals. We introduce a lightweight OGD algorithm that does not require the independence of examples and generalizes to kernel pairwise learning. Our algorithm builds the gradient based on a random example and a moving average representing the past data, which results in a sub-linear regret bound with a complexity of O(T). Furthermore, through the integration of O(√T logT) random Fourier features, the complexity of kernel calculations is effectively minimized. Several experiments with real-world datasets show that the proposed technique outperforms kernel and linear algorithms in offline and online scenarios.
We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. The method is built of two main types of blocks: (i) We introduce unsupervised kernel machine layers propagating the node features in a one-hop neighborhood, using implicit node feature mappings. (ii) We specify a semi-supervised classification kernel machine through the lens of the Fenchel-Young inequality. We derive an effective initialization scheme and efficient end-to-end training algorithm in the dual variables for the full architecture. The main idea underlying GCKM is that, because of the unsupervised core, the final model can achieve higher performance in semi-supervised node classification when few labels are available for training. Experimental results demonstrate the effectiveness of the proposed framework.
Training state-of-the-art (SOTA) deep models often requires extensive data, resulting in substantial training and storage costs. To address these challenges, dataset condensation has been developed to learn a small synthetic set that preserves essential information from the original large-scale dataset. Nowadays, optimization-oriented methods have been the primary method in the field of dataset condensation for achieving SOTA results. However, the bi-level optimization process hinders the practical application of such methods to realistic and larger datasets. To enhance condensation efficiency, previous works proposed Distribution-Matching (DM) as an alternative, which significantly reduces the condensation cost. Nonetheless, current DM-based methods still yield less comparable results to SOTA optimization-oriented methods. In this paper, we argue that existing DM-based methods overlook the higher-order alignment of the distributions, which may lead to sub-optimal matching results. Inspired by this, we present a novel DM-based method named M3D for dataset condensation by Minimizing the Maximum Mean Discrepancy between feature representations of the synthetic and real images. By embedding their distributions in a reproducing kernel Hilbert space, we align all orders of moments of the distributions of real and synthetic images, resulting in a more generalized condensed set. Notably, our method even surpasses the SOTA optimization-oriented method IDC on the high-resolution ImageNet dataset. Extensive analysis is conducted to verify the effectiveness of the proposed method. Source codes are available at https://github.com/Hansong-Zhang/M3D.
While self-supervised graph pretraining techniques have shown promising results in various domains, their application still experiences challenges of limited topology learning, human knowledge dependency, and incompetent multi-level interactions. To address these issues, we propose a novel solution, Dual-level Graph self-supervised Pretraining with Motif discovery (DGPM), which introduces a unique dual-level pretraining structure that orchestrates node-level and subgraph-level pretext tasks. Unlike prior approaches, DGPM autonomously uncovers significant graph motifs through an edge pooling module, aligning learned motif similarities with graph kernel-based similarities. A cross-matching task enables sophisticated node-motif interactions and novel representation learning. Extensive experiments on 15 datasets validate DGPM's effectiveness and generalizability, outperforming state-of-the-art methods in unsupervised representation learning and transfer learning settings. The autonomously discovered motifs demonstrate the potential of DGPM to enhance robustness and interpretability.
Graphs are typical non-Euclidean data of complex structures. In recent years, Riemannian graph representation learning has emerged as an exciting alternative to Euclidean ones. However, Riemannian methods are still in an early stage: most of them present a single curvature (radius) regardless of structural complexity, suffer from numerical instability due to the exponential/logarithmic map, and lack the ability to capture motif regularity. In light of the issues above, we propose the problem of Motif-aware Riemannian Graph Representation Learning, seeking a numerically stable encoder to capture motif regularity in a diverse-curvature manifold without labels. To this end, we present a novel Motif-aware Riemannian model with Generative-Contrastive learning (MotifRGC), which conducts a minmax game in Riemannian manifold in a self-supervised manner. First, we propose a new type of Riemannian GCN (D-GCN), in which we construct a diverse-curvature manifold by a product layer with the diversified factor, and replace the exponential/logarithmic map by a stable kernel layer. Second, we introduce a motif-aware Riemannian generative-contrastive learning to capture motif regularity in the constructed manifold and learn motif-aware node representation without external labels. Empirical results show the superiority of MofitRGC.