Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational complexity of large-scale architectures and datasets. Node-based BNNs have recently been introduced as scalable alternatives, which induce epistemic uncertainty by multiplying each hidden node with latent random variables, while learning a point-estimate of the weights. In this paper, we interpret these latent noise variables as implicit representations of simple and domain-agnostic data perturbations during training, producing BNNs that perform well under covariate shift due to input corruptions. We observe that the diversity of the implicit corruptions depends on the entropy of the latent variables, and propose a straightforward approach to increase the entropy of these variables during training. We evaluate the method on out-of-distribution image classification benchmarks, and show improved uncertainty estimation of node-based BNNs under covariate shift due to input perturbations. As a side effect, the method also provides robustness against noisy training labels.
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We propose a general model that jointly characterizes degree heterogeneity and homophily in weighted, undirected networks. We present a moment estimation method using node degrees and homophily statistics. We establish consistency and asymptotic normality of our estimator using novel analysis. We apply our general framework to three applications, including both exponential family and non-exponential family models. Comprehensive numerical studies and a data example also demonstrate the usefulness of our method.
In this article we consider Bayesian inference associated to deep neural networks (DNNs) and in particular, trace-class neural network (TNN) priors which were proposed by Sell et al. [39]. Such priors were developed as more robust alternatives to classical architectures in the context of inference problems. For this work we develop multilevel Monte Carlo (MLMC) methods for such models. MLMC is a popular variance reduction technique, with particular applications in Bayesian statistics and uncertainty quantification. We show how a particular advanced MLMC method that was introduced in [4] can be applied to Bayesian inference from DNNs and establish mathematically, that the computational cost to achieve a particular mean square error, associated to posterior expectation computation, can be reduced by several orders, versus more conventional techniques. To verify such results we provide numerous numerical experiments on model problems arising in machine learning. These include Bayesian regression, as well as Bayesian classification and reinforcement learning.
Adversarial attacks provide a good way to study the robustness of deep learning models. One category of methods in transfer-based black-box attack utilizes several image transformation operations to improve the transferability of adversarial examples, which is effective, but fails to take the specific characteristic of the input image into consideration. In this work, we propose a novel architecture, called Adaptive Image Transformation Learner (AITL), which incorporates different image transformation operations into a unified framework to further improve the transferability of adversarial examples. Unlike the fixed combinational transformations used in existing works, our elaborately designed transformation learner adaptively selects the most effective combination of image transformations specific to the input image. Extensive experiments on ImageNet demonstrate that our method significantly improves the attack success rates on both normally trained models and defense models under various settings.
Techniques of hybridisation and ensemble learning are popular model fusion techniques for improving the predictive power of forecasting methods. With limited research that instigates combining these two promising approaches, this paper focuses on the utility of the Exponential-Smoothing-Recurrent Neural Network (ES-RNN) in the pool of base models for different ensembles. We compare against some state of the art ensembling techniques and arithmetic model averaging as a benchmark. We experiment with the M4 forecasting data set of 100,000 time-series, and the results show that the Feature-based Forecast Model Averaging (FFORMA), on average, is the best technique for late data fusion with the ES-RNN. However, considering the M4's Daily subset of data, stacking was the only successful ensemble at dealing with the case where all base model performances are similar. Our experimental results indicate that we attain state of the art forecasting results compared to N-BEATS as a benchmark. We conclude that model averaging is a more robust ensemble than model selection and stacking strategies. Further, the results show that gradient boosting is superior for implementing ensemble learning strategies.
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian estimators to the quantum setting. Unlike classically, where any univariate estimator can be turned into a multivariate estimator with at most a logarithmic overhead in the dimension, no similar result can be proved in the quantum setting. Indeed, Heinrich ruled out the existence of a quantum advantage for the mean estimation problem when the sample complexity is smaller than the dimension. Our main result is to show that, outside this low-precision regime, there is a quantum estimator that outperforms any classical estimator. Our approach is substantially more involved than in the univariate setting, where most quantum estimators rely only on phase estimation. We exploit a variety of additional algorithmic techniques such as amplitude amplification, the Bernstein-Vazirani algorithm, and quantum singular value transformation. Our analysis also uses concentration inequalities for multivariate truncated statistics. We develop our quantum estimators in two different input models that showed up in the literature before. The first one provides coherent access to the binary representation of the random variable and it encompasses the classical setting. In the second model, the random variable is directly encoded into the phases of quantum registers. This model arises naturally in many quantum algorithms but it is often incomparable to having classical samples. We adapt our techniques to these two settings and we show that the second model is strictly weaker for solving the mean estimation problem. Finally, we describe several applications of our algorithms, notably in measuring the expectation values of commuting observables and in the field of machine learning.
Neural networks are vulnerable to adversarial attacks: adding well-crafted, imperceptible perturbations to their input can modify their output. Adversarial training is one of the most effective approaches in training robust models against such attacks. However, it is much slower than vanilla training of neural networks since it needs to construct adversarial examples for the entire training data at every iteration, hampering its effectiveness. Recently, Fast Adversarial Training (FAT) was proposed that can obtain robust models efficiently. However, the reasons behind its success are not fully understood, and more importantly, it can only train robust models for $\ell_\infty$-bounded attacks as it uses FGSM during training. In this paper, by leveraging the theory of coreset selection, we show how selecting a small subset of training data provides a general, more principled approach toward reducing the time complexity of robust training. Unlike existing methods, our approach can be adapted to a wide variety of training objectives, including TRADES, $\ell_p$-PGD, and Perceptual Adversarial Training (PAT). Our experimental results indicate that our approach speeds up adversarial training by 2-3 times while experiencing a slight reduction in the clean and robust accuracy.
Artificial intelligence has made great progresses in medical data analysis, but the lack of robustness and interpretability has kept these methods from being widely deployed. In particular, data-driven models are vulnerable to adversarial attacks, which are small, targeted perturbations that dramatically degrade model performance. As a recent example, while deep learning has shown impressive performance in electrocardiogram (ECG) classification, Han et al. crafted realistic perturbations that fooled the network 74% of the time [2020]. Current adversarial defense paradigms are computationally intensive and impractical for many high dimensional problems. Previous research indicates that a network vulnerability is related to the features learned during training. We propose a novel approach based on ensemble decorrelation and Fourier partitioning for training parallel network arms into a decorrelated architecture to learn complementary features, significantly reducing the chance of a perturbation fooling all arms of the deep learning model. We test our approach in ECG classification, demonstrating a much-improved 77.2% chance of at least one correct network arm on the strongest adversarial attack tested, in contrast to a 21.7% chance from a comparable ensemble. Our approach does not require expensive optimization with adversarial samples, and thus can be scaled to large problems. These methods can easily be applied to other tasks for improved network robustness.
Deep graph neural networks (GNNs) have achieved excellent results on various tasks on increasingly large graph datasets with millions of nodes and edges. However, memory complexity has become a major obstacle when training deep GNNs for practical applications due to the immense number of nodes, edges, and intermediate activations. To improve the scalability of GNNs, prior works propose smart graph sampling or partitioning strategies to train GNNs with a smaller set of nodes or sub-graphs. In this work, we study reversible connections, group convolutions, weight tying, and equilibrium models to advance the memory and parameter efficiency of GNNs. We find that reversible connections in combination with deep network architectures enable the training of overparameterized GNNs that significantly outperform existing methods on multiple datasets. Our models RevGNN-Deep (1001 layers with 80 channels each) and RevGNN-Wide (448 layers with 224 channels each) were both trained on a single commodity GPU and achieve an ROC-AUC of $87.74 \pm 0.13$ and $88.14 \pm 0.15$ on the ogbn-proteins dataset. To the best of our knowledge, RevGNN-Deep is the deepest GNN in the literature by one order of magnitude. Please visit our project website //www.deepgcns.org/arch/gnn1000 for more information.
Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.
The prevalence of networked sensors and actuators in many real-world systems such as smart buildings, factories, power plants, and data centers generate substantial amounts of multivariate time series data for these systems. The rich sensor data can be continuously monitored for intrusion events through anomaly detection. However, conventional threshold-based anomaly detection methods are inadequate due to the dynamic complexities of these systems, while supervised machine learning methods are unable to exploit the large amounts of data due to the lack of labeled data. On the other hand, current unsupervised machine learning approaches have not fully exploited the spatial-temporal correlation and other dependencies amongst the multiple variables (sensors/actuators) in the system for detecting anomalies. In this work, we propose an unsupervised multivariate anomaly detection method based on Generative Adversarial Networks (GANs). Instead of treating each data stream independently, our proposed MAD-GAN framework considers the entire variable set concurrently to capture the latent interactions amongst the variables. We also fully exploit both the generator and discriminator produced by the GAN, using a novel anomaly score called DR-score to detect anomalies by discrimination and reconstruction. We have tested our proposed MAD-GAN using two recent datasets collected from real-world CPS: the Secure Water Treatment (SWaT) and the Water Distribution (WADI) datasets. Our experimental results showed that the proposed MAD-GAN is effective in reporting anomalies caused by various cyber-intrusions compared in these complex real-world systems.
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