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arXiv.org Machine Learning


Orthogonal Over-Parameterized Training

arXiv.org Machine Learning

The inductive bias of a neural network is largely determined by the architecture and the training algorithm. To achieve good generalization, how to effectively train a neural network is even more important than designing the architecture. We propose a novel orthogonal over-parameterized training (OPT) framework that can provably minimize the hyperspherical energy which characterizes the diversity of neurons on a hypersphere. By constantly maintaining the minimum hyperspherical energy during training, OPT can greatly improve the network generalization. Specifically, OPT fixes the randomly initialized weights of the neurons and learns an orthogonal transformation that applies to these neurons. We propose multiple ways to learn such an orthogonal transformation, including unrolling orthogonalization algorithms, applying orthogonal parameterization, and designing orthogonality-preserving gradient update. Interestingly, OPT reveals that learning a proper coordinate system for neurons is crucial to generalization and may be more important than learning a specific relative position of neurons. We further provide theoretical insights of why OPT yields better generalization. Extensive experiments validate the superiority of OPT.


Learning Bayesian Networks that enable full propagation of evidence

arXiv.org Machine Learning

This paper builds on recent developments in Bayesian network (BN) structure learning under the controversial assumption that the input variables are dependent. This assumption is geared towards real-world datasets that incorporate variables which are assumed to be dependent. It aims to address the problem of learning multiple disjoint subgraphs which do not enable full propagation of evidence. A novel hybrid structure learning algorithm is presented in this paper for this purpose, called SaiyanH. The results show that the algorithm discovers satisfactorily accurate connected DAGs in cases where all other algorithms produce multiple disjoint subgraphs for dependent variables. This problem is highly prevalent in cases where the sample size of the input data is low with respect to the dimensionality of the model, which is often the case when working with real data. Based on six case studies, five different sample sizes, three different evaluation metrics, and other state-of-the-art or well-established constraint-based, score-based and hybrid learning algorithms, the results rank SaiyanH 4th out of 13 algorithms for overall performance.


On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration

arXiv.org Machine Learning

We undertake a precise study of the asymptotic and non-asymptotic properties of stochastic approximation procedures with Polyak-Ruppert averaging for solving a linear system $\bar{A} \theta = \bar{b}$. When the matrix $\bar{A}$ is Hurwitz, we prove a central limit theorem (CLT) for the averaged iterates with fixed step size and number of iterations going to infinity. The CLT characterizes the exact asymptotic covariance matrix, which is the sum of the classical Polyak-Ruppert covariance and a correction term that scales with the step size. Under assumptions on the tail of the noise distribution, we prove a non-asymptotic concentration inequality whose main term matches the covariance in CLT in any direction, up to universal constants. When the matrix $\bar{A}$ is not Hurwitz but only has non-negative real parts in its eigenvalues, we prove that the averaged LSA procedure actually achieves an $O(1/T)$ rate in mean-squared error. Our results provide a more refined understanding of linear stochastic approximation in both the asymptotic and non-asymptotic settings. We also show various applications of the main results, including the study of momentum-based stochastic gradient methods as well as temporal difference algorithms in reinforcement learning.


Graph Highway Networks

arXiv.org Machine Learning

Graph Convolution Networks (GCN) are widely used in learning graph representations due to their effectiveness and efficiency. However, they suffer from the notorious over-smoothing problem, in which the learned representations of densely connected nodes converge to alike vectors when many (>3) graph convolutional layers are stacked. In this paper, we argue that there-normalization trick used in GCN leads to overly homogeneous information propagation, which is the source of over-smoothing. To address this problem, we propose Graph Highway Networks(GHNet) which utilize gating units to automatically balance the trade-off between homogeneity and heterogeneity in the GCN learning process. The gating units serve as direct highways to maintain heterogeneous information from the node itself after feature propagation. This design enables GHNet to achieve much larger receptive fields per node without over-smoothing and thus access to more of the graph connectivity information. Experimental results on benchmark datasets demonstrate the superior performance of GHNet over GCN and related models.


Learnable Subspace Clustering

arXiv.org Machine Learning

This paper studies the large-scale subspace clustering (LSSC) problem with million data points. Many popular subspace clustering methods cannot directly handle the LSSC problem although they have been considered as state-of-the-art methods for small-scale data points. A basic reason is that these methods often choose all data points as a big dictionary to build huge coding models, which results in a high time and space complexity. In this paper, we develop a learnable subspace clustering paradigm to efficiently solve the LSSC problem. The key idea is to learn a parametric function to partition the high-dimensional subspaces into their underlying low-dimensional subspaces instead of the expensive costs of the classical coding models. Moreover, we propose a unified robust predictive coding machine (RPCM) to learn the parametric function, which can be solved by an alternating minimization algorithm. In addition, we provide a bounded contraction analysis of the parametric function. To the best of our knowledge, this paper is the first work to efficiently cluster millions of data points among the subspace clustering methods. Experiments on million-scale datasets verify that our paradigm outperforms the related state-of-the-art methods in both efficiency and effectiveness.


Prune2Edge: A Multi-Phase Pruning Pipelines to Deep Ensemble Learning in IIoT

arXiv.org Machine Learning

Most recently, with the proliferation of IoT devices, computational nodes in manufacturing systems IIoT(Industrial-Internet-of-things) and the lunch of 5G networks, there will be millions of connected devices generating a massive amount of data. In such an environment, the controlling systems need to be intelligent enough to deal with a vast amount of data to detect defects in a real-time process. Driven by such a need, artificial intelligence models such as deep learning have to be deployed into IIoT systems. However, learning and using deep learning models are computationally expensive, so an IoT device with limited computational power could not run such models. To tackle this issue, edge intelligence had emerged as a new paradigm towards running Artificial Intelligence models on edge devices. Although a considerable amount of studies have been proposed in this area, the research is still in the early stages. In this paper, we propose a novel edge-based multi-phase pruning pipelines to ensemble learning on IIoT devices. In the first phase, we generate a diverse ensemble of pruned models, then we apply integer quantisation, next we prune the generated ensemble using a clustering-based technique. Finally, we choose the best representative from each generated cluster to be deployed to a distributed IoT environment. On CIFAR-100 and CIFAR-10, our proposed approach was able to outperform the predictability levels of a baseline model (up to 7%), more importantly, the generated learners have small sizes (up to 90% reduction in the model size) that minimise the required computational capabilities to make an inference on the resource-constraint devices.


Test-Time Adaptable Neural Networks for Robust Medical Image Segmentation

arXiv.org Machine Learning

Convolutional Neural Networks (CNNs) work very well for supervised learning problems when the training dataset is representative of the variations expected to be encountered at test time. In medical image segmentation, this premise is violated when there is a mismatch between training and test images in terms of their acquisition details, such as the scanner model or the protocol. Remarkable performance degradation of CNNs in this scenario is well documented in the literature. To address this problem, we design the segmentation CNN as a concatenation of two sub-networks: a relatively shallow image normalization CNN, followed by a deep CNN that segments the normalized image. We train both these sub-networks using a training dataset, consisting of annotated images from a particular scanner and protocol setting. Now, at test time, we adapt the image normalization sub-network for each test image, guided by an implicit prior on the predicted segmentation labels. We employ an independently trained denoising autoencoder (DAE) in order to model such an implicit prior on plausible anatomical segmentation labels. We validate the proposed idea on multi-center Magnetic Resonance imaging datasets of three anatomies: brain, heart and prostate. The proposed test-time adaptation consistently provides performance improvement, demonstrating the promise and generality of the approach. Being agnostic to the architecture of the deep CNN, the second sub-network, the proposed design can be utilized with any segmentation network to increase robustness to variations in imaging scanners and protocols.


k-Nearest Neighbour Classifiers -- 2nd Edition

arXiv.org Machine Learning

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours to determine the class of the query. This approach to classification is of particular importance because issues of poor run-time performance is not such a problem these days with the computational power that is available. This paper presents an overview of techniques for Nearest Neighbour classification focusing on; mechanisms for assessing similarity (distance), computational issues in identifying nearest neighbours and mechanisms for reducing the dimension of the data. This paper is the second edition of a paper previously published as a technical report. Sections on similarity measures for time-series, retrieval speed-up and intrinsic dimensionality have been added. An Appendix is included providing access to Python code for the key methods.


Probabilistic embeddings for speaker diarization

arXiv.org Machine Learning

Speaker embeddings (x-vectors) extracted from very short segments of speech have recently been shown to give competitive performance in speaker diarization. We generalize this recipe by extracting from each speech segment, in parallel with the x-vector, also a diagonal precision matrix, thus providing a path for the propagation of information about the quality of the speech segment into a PLDA scoring backend. These precisions quantify the uncertainty about what the values of the embeddings might have been if they had been extracted from high quality speech segments. The proposed probabilistic embeddings (x-vectors with precisions) are interfaced with the PLDA model by treating the x-vectors as hidden variables and marginalizing them out. We apply the proposed probabilistic embeddings as input to an agglomerative hierarchical clustering (AHC) algorithm to do diarization in the DIHARD'19 evaluation set. We compute the full PLDA likelihood 'by the book' for each clustering hypothesis that is considered by AHC. We do joint discriminative training of the PLDA parameters and of the probabilistic x-vector extractor. We demonstrate accuracy gains relative to a baseline AHC algorithm, applied to traditional xvectors (without uncertainty), and which uses averaging of binary log-likelihood-ratios, rather than by-the-book scoring.


Industrial Forecasting with Exponentially Smoothed Recurrent Neural Networks

arXiv.org Machine Learning

Industrial forecasting has entered an era of unprecedented growth in the size and complexity of data which require new modeling methodologies. While many new general purpose machine learning approaches have emerged, they remain poorly understand and irreconcilable with more traditional statistical modeling approaches. We present a general class of exponential smoothed recurrent neural networks (RNNs) which are well suited to modeling non-stationary dynamical systems arising in industrial applications such as electricity load management and financial risk and trading. In particular, we analyze their capacity to characterize the non-linear partial autocorrelation structure of time series and directly capture dynamic effects such as seasonality and regime changes. Application of exponentially smoothed RNNs to electricity load forecasting, weather data and financial time series, such as minute level Bitcoin prices and CME futures tick data, highlight the efficacy of exponential smoothing for multi-step time series forecasting. The results also suggest that popular, but more complicated neural network architectures originally designed for speech processing, such as LSTMs and GRUs, are likely over-engineered for industrial forecasting and light-weight exponentially smoothed architectures capture the salient features while being superior and more robust than simple RNNs.