We propose a framework for distributed robust statistical learning on big contaminated data . The Distributed Robust Learning (DRL) framework can reduce the computational time of traditional robust learning methods by several orders of magnitude. We analyze the robustness property of DRL, showing that DRL not only preserves the robustness of the base robust learning method, but also tolerates contaminations on a constant fraction of results from computing nodes (node failures). More precisely, even in presence of the most adversarial outlier distribution over computing nodes, DRL still achieves a breakdown point of at least @math , where @math is the break down point of corresponding centralized algorithm. This is in stark contrast with naive division-and-averaging implementation, which may reduce the breakdown point by a factor of @math when @math computing nodes are used. We then specialize the DRL framework for two concrete cases: distributed robust principal component analysis and distributed robust regression. We demonstrate the efficiency and the robustness advantages of DRL through comprehensive simulations and predicting image tags on a large-scale image set.
Recently, several online robust learning algorithms were proposed to process the data in a sequential manner @cite_15 . Online learning methods partially mitigate the scalability issue of robust learning by reducing the memory cost for machines. However, the time complexity of those methods still depends linearly on the sample size, hardly affordable in practice when dealing with ultra-large datasets.
@cite_15
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The promise of unsupervised learning methods lies in their potential to use vast amounts of unlabeled data to learn complex, highly nonlinear models with millions of free parameters. We consider two well-known unsupervised learning models, deep belief networks (DBNs) and sparse coding, that have recently been applied to a flurry of machine learning applications (Hinton & Salakhutdinov, 2006; , 2007). Unfortunately, current learning algorithms for both models are too slow for large-scale applications, forcing researchers to focus on smaller-scale models, or to use fewer training examples. In this paper, we suggest massively parallel methods to help resolve these problems. We argue that modern graphics processors far surpass the computational capabilities of multicore CPUs, and have the potential to revolutionize the applicability of deep unsupervised learning methods. We develop general principles for massively parallelizing unsupervised learning tasks using graphics processors. We show that these principles can be applied to successfully scaling up learning algorithms for both DBNs and sparse coding. Our implementation of DBN learning is up to 70 times faster than a dual-core CPU implementation for large models. For example, we are able to reduce the time required to learn a four-layer DBN with 100 million free parameters from several weeks to around a single day. For sparse coding, we develop a simple, inherently parallel algorithm, that leads to a 5 to 15-fold speedup over previous methods. The growth of data, the need for scalability and the complexity of models used in modern machine learning calls for distributed implementations. Yet, as of today, distributed machine learning frameworks have largely ignored the possibility of arbitrary (i.e., Byzantine) failures. In this paper, we study the robustness to Byzantine failures at the fundamental level of stochastic gradient descent (SGD), the heart of most machine learning algorithms. Assuming a set of @math workers, up to @math of them being Byzantine, we ask how robust can SGD be, without limiting the dimension, nor the size of the parameter space. We first show that no gradient descent update rule based on a linear combination of the vectors proposed by the workers (i.e, current approaches) tolerates a single Byzantine failure. We then formulate a resilience property of the update rule capturing the basic requirements to guarantee convergence despite @math Byzantine workers. We finally propose Krum, an update rule that satisfies the resilience property aforementioned. For a @math -dimensional learning problem, the time complexity of Krum is @math . A common way to speed up training of large convolutional networks is to add computational units. Training is then performed using data-parallel synchronous Stochastic Gradient Descent (SGD) with mini-batch divided between computational units. With an increase in the number of nodes, the batch size grows. But training with large batch size often results in the lower model accuracy. We argue that the current recipe for large batch training (linear learning rate scaling with warm-up) is not general enough and training may diverge. To overcome this optimization difficulties we propose a new training algorithm based on Layer-wise Adaptive Rate Scaling (LARS). Using LARS, we scaled Alexnet up to a batch size of 8K, and Resnet-50 to a batch size of 32K without loss in accuracy. In this paper, we consider the problem of preserving privacy in the context of online learning. Online learning involves learning from data in real-time, due to which the learned model as well as its predictions are continuously changing. This makes preserving privacy of each data point significantly more challenging as its effect on the learned model can be easily tracked by observing changes in the subsequent predictions. Furthermore, with more and more online systems (e.g. search engines like Bing, Google etc.) trying to learn their customers’ behavior by leveraging their access to sensitive customer data (through cookies etc.), the problem of privacy preserving online learning has become critical. We study the problem in the framework of online convex programming (OCP)—a popular online learning setting with several theoretical and practical implications—while using differential privacy as the formal measure of privacy. For this problem, we provide a generic framework that can be used to convert any given OCP algorithm into a private OCP algorithm with provable privacy as well as regret guarantees (utility), provided that the given OCP algorithm satisfies the following two criteria: 1) linearly decreasing sensitivity, i.e., the effect of the new data points on the learned model decreases linearly, 2) sub-linear regret. We then illustrate our approach by converting two popular OCP algorithms into corresponding differentially private algorithms while guaranteeing O( p T ) regret for strongly convex functions. Next, we consider the practically important class of online linear regression problems, for which we generalize the approach by (2010a) to provide a differentially private algorithm with just poly-log regret. Finally, we show that our online learning framework can be used to provide differentially private algorithms for the offline learning problem as well. For the offline learning problem, our approach guarantees better error bounds and is more practical than the existing state-of-the-art methods (, 2011; , 2009).