We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally connected regions on the input graph. Our proposal generalises well-established neural models such as Convolutional Neural Networks (CNNs) on irregular and complex domains, by means of the exploitation of the weight sharing property in a graph-oriented architecture. In this work, such property is based on the centrality of each vertex within its soft-assigned cluster. Extensive experiments on NTU RGB+D, CIFAR-10 and 20NEWS demonstrate the effectiveness of the proposed technique in capturing both local and global patterns in graph-structured data out of different domains.

We investigate conditions under which test statistics exist that can reliably detect examples, which have been adversarially manipulated in a white-box attack. These statistics can be easily computed and calibrated by randomly corrupting inputs. They exploit certain anomalies that adversarial attacks introduce, in particular if they follow the paradigm of choosing perturbations optimally under p-norm constraints. Access to the log-odds is the only requirement to defend models. We justify our approach empirically, but also provide conditions under which detectability via the suggested test statistics is guaranteed to be effective. In our experiments, we show that it is even possible to correct test time predictions for adversarial attacks with high accuracy.

This paper considers the perturbed stochastic gradient descent algorithm and shows that it finds $\epsilon$-second order stationary points ($\left\|\nabla f(x)\right\|\leq \epsilon$ and $\nabla^2 f(x) \succeq -\sqrt{\epsilon} \mathbf{I}$) in $\tilde{O}(d/\epsilon^4)$ iterations, giving the first result that has linear dependence on dimension for this setting. For the special case, where stochastic gradients are Lipschitz, the dependence on dimension reduces to polylogarithmic. In addition to giving new results, this paper also presents a simplified proof strategy that gives a shorter and more elegant proof of previously known results (Jin et al. 2017) on perturbed gradient descent algorithm.

We study the expressive power of kernel methods and the algorithmic feasibility of multiple kernel learning for a special rich class of kernels. Specifically, we define \emph{Euclidean kernels}, a diverse class that includes most, if not all, families of kernels studied in literature such as polynomial kernels and radial basis functions. We then describe the geometric and spectral structure of this family of kernels over the hypercube (and to some extent for any compact domain). Our structural results allow us to prove meaningful limitations on the expressive power of the class as well as derive several efficient algorithms for learning kernels over different domains.

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then updates its predictor for the next round according to the received local feedback and information received from neighboring nodes. The predictions made at a given node are assessed through the notion of regret, defined as the difference between their cumulative network-wide square errors and those of the best off-line network-wide linear predictor. Various scenarios are investigated, depending on the nature of the local feedback (full information or bandit feedback), on the set of available predictors (the decision set), and the way data is generated (by an oblivious or adaptive adversary). We propose simple and natural distributed regression algorithms, involving, at each node and in each round, a local gradient descent step and a communication and averaging step where nodes aim at aligning their predictors to those of their neighbors. We establish regret upper bounds typically in ${\cal O}(T^{3/4})$ when the decision set is unbounded and in ${\cal O}(\sqrt{T})$ in case of bounded decision set.

Manifold regularization, such as laplacian regularized least squares (LapRLS) and laplacian support vector machine (LapSVM), has been widely used in semi-supervised learning, and its performance greatly depends on the choice of some hyper-parameters. Cross-validation (CV) is the most popular approach for selecting the optimal hyper-parameters, but it has high complexity due to multiple times of learner training. In this paper, we provide a method to approximate the CV for manifold regularization based on a notion of robust statistics, called Bouligand influence function (BIF). We first provide a strategy for approximating the CV via the Taylor expansion of BIF. Then, we show how to calculate the BIF for general loss function,and further give the approximate CV criteria for model selection in manifold regularization. The proposed approximate CV for manifold regularization requires training only once, hence can significantly improve the efficiency of traditional CV. Experimental results show that our approximate CV has no statistical discrepancy with the original one, but much smaller time cost.

We cast doubt on the power of uniform convergence-based generalization bounds to provide a complete picture of why overparameterized deep networks generalize well. While it is well-known that many existing bounds are numerically large, through a variety of experiments, we first bring to light another crucial and more concerning aspect of these bounds: in practice, these bounds can {\em increase} with the dataset size. Guided by our observations, we then show how uniform convergence could provably break down even in a simple setup that preserves the key elements of deep learning: we present a {\em noisy} algorithm that learns a mildly {\em overparameterized} linear classifier such that uniform convergence cannot "explain generalization," even if we take into account implicit regularization {\em to the fullest extent possible}. More precisely, even if we consider only the set of classifiers output by the algorithm that have test errors less than some small $\epsilon$, applying (two-sided) uniform convergence on this set of classifiers yields a generalization guarantee that is larger than $1-\epsilon$ and is therefore nearly vacuous.

Learning sentence vectors from an unlabeled corpus has attracted attention because such vectors can represent sentences in a lower dimensional and continuous space. Simple heuristics using pre-trained word vectors are widely applied to machine learning tasks. However, they are not well understood from a theoretical perspective. We analyze learning sentence vectors from a transfer learning perspective by using a PAC-Bayes bound that enables us to understand existing heuristics. We show that simple heuristics such as averaging and inverse document frequency weighted averaging are derived by our formulation. Moreover, we propose novel sentence vector learning algorithms on the basis of our PAC-Bayes analysis.

In this work we provide a theoretical framework for structured prediction that generalizes the existing theory of surrogate methods for binary and multiclass classification based on estimating conditional probabilities with smooth convex surrogates (e.g. logistic regression). The theory relies on a natural characterization of structural properties of the task loss and allows to derive statistical guarantees for many widely used methods in the context of multilabeling, ranking, ordinal regression and graph matching. In particular, we characterize the smooth convex surrogates compatible with a given task loss in terms of a suitable Bregman divergence composed with a link function. This allows to derive tight bounds for the calibration function and to obtain novel results on existing surrogate frameworks for structured prediction such as conditional random fields and quadratic surrogates.

The cloud radio access network (CRAN) is a promising paradigm to meet the stringent requirements of the fifth generation (5G) wireless systems. Meanwhile, wireless traffic prediction is a key enabler for C-RANs to improve both the spectrum efficiency and energy efficiency through load-aware network managements. This paper proposes a scalable Gaussian process (GP) framework as a promising solution to achieve large-scale wireless traffic prediction in a cost-efficient manner. First, to the best of our knowledge, this paper is the first to empower GP regression with the alternating direction method of multipliers (ADMM) for parallel hyper-parameter optimization in the training phase, where such a scalable training framework well balances the local estimation in baseband units (BBUs) and information consensus among BBUs in a principled way for large-scale executions. Second, in the prediction phase, we fuse local predictions obtained from the BBUs via a cross-validation based optimal strategy, which demonstrates itself to be reliable and robust for general regression tasks. Moreover, such a cross-validation based optimal fusion strategy is built upon a well acknowledged probabilistic model to retain the valuable closed-form GP inference properties. Third, we propose a CRAN based scalable wireless prediction architecture, where the prediction accuracy and the time consumption can be balanced by tuning the number of the BBUs according to the real-time system demands. Experimental results show that our proposed scalable GP model can outperform the state-of-the-art approaches considerably, in terms of wireless traffic prediction performance. I. INTRODUCTION The fifth generation (5G) system is expected to provide approximately 1000 times higher wireless capacity and reduce up to 90 percent of energy consumption compared with the current 4G system [1]. A CRAN is composed of two parts: the distributed remote radio heads (RRHs) with basic radio functionalities to provide coverage over a large area, and the centralized baseband units (BBUs) pool with parallel BBUs to support joint processing and cooperative network management. The BBUs can perform dynamic resource allocation in accordance with realtime networkdemands based on the virtualized resources in cloud computing. One major feature for the C-RANs to enable high energy-efficient services is the fast adaptability to nonuniform traffic variations [1]-[4], e.g., the tidal effects. Consequently, wireless traffic prediction techniques stand out as the key enabler to realize such loadaware managementand proactive control in C-RANs, e.g., the load-aware RRH on/off operation [4].