We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of a translation operator on a graph structure. In regular settings such as images, convolutional layers are designed by translating a convolutional kernel over all pixels, thus enforcing translation equivariance. In the case of general graphs however, translation is not a well-defined operation, which makes shifting a convolutional kernel not straightforward. In this article, we introduce a methodology to allow the design of convolutional layers that are adapted to signals evolving on irregular topologies, even in the absence of a natural translation. Using the designed layers, we build a CNN that we train using the initial set of signals. Contrary to other approaches that aim at extending CNNs to irregular domains, we incorporate the classical settings of CNNs for 2D signals as a particular case of our approach. Designing convolutional layers in the vertex domain directly implies weight sharing, which in other approaches is generally estimated a posteriori using heuristics.

We propose and study kernel conjugate gradient methods (KCGM) with random projections for least-squares regression over a separable Hilbert space. Considering two types of random projections generated by randomized sketches and Nystr\"{o}m subsampling, we prove optimal statistical results with respect to variants of norms for the algorithms under a suitable stopping rule. Particularly, our results show that if the projection dimension is proportional to the effective dimension of the problem, KCGM with randomized sketches can generalize optimally, while achieving a computational advantage. As a corollary, we derive optimal rates for classic KCGM in the case that the target function may not be in the hypothesis space, filling a theoretical gap.

The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for scalable semi-supervised learning from multi-relational data. Key aspects of the novel GRNN architecture are the use of multi-relational graphs, the dynamic adaptation to the different relations via learnable weights, and the consideration of graph-based regularizers to promote smoothness and alleviate over-parametrization. Our ultimate goal is to design a powerful learning architecture able to: discover complex and highly non-linear data associations, combine (and select) multiple types of relations, and scale gracefully with respect to the size of the graph. Numerical tests with real data sets corroborate the design goals and illustrate the performance gains relative to competing alternatives.

We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error have recently been proposed in high-dimensional statistics literature. However, the variance of the error term in the linear model is intricately connected to the optimal parameter used to define the shape of the Huber loss. Our main idea is to use an adaptive technique, based on Lepski's method, to overcome the difficulties in solving a joint nonconvex optimization problem with respect to the location and scale parameters.

Machine learning has been applied to a broad range of applications and some of them are available online as application programming interfaces (APIs) with either free (trial) or paid subscriptions. In this paper, we study adversarial machine learning in the form of back-box attacks on online classifier APIs. We start with a deep learning based exploratory (inference) attack, which aims to build a classifier that can provide similar classification results (labels) as the target classifier. To minimize the difference between the labels returned by the inferred classifier and the target classifier, we show that the deep learning based exploratory attack requires a large number of labeled training data samples. These labels can be collected by calling the online API, but usually there is some strict rate limitation on the number of allowed API calls. To mitigate the impact of limited training data, we develop an active learning approach that first builds a classifier based on a small number of API calls and uses this classifier to select samples to further collect their labels. Then, a new classifier is built using more training data samples. This updating process can be repeated multiple times. We show that this active learning approach can build an adversarial classifier with a small statistical difference from the target classifier using only a limited number of training data samples. We further consider evasion and causative (poisoning) attacks based on the inferred classifier that is built by the exploratory attack. Evasion attack determines samples that the target classifier is likely to misclassify, whereas causative attack provides erroneous training data samples to reduce the reliability of the re-trained classifier. The success of these attacks show that adversarial machine learning emerges as a feasible threat in the realistic case with limited training data.

Deep neural networks use stacked layers of feature detectors to repeatedly transform the input data, so that structurally different classes of input become well separated in the final layer. While the method has turned out extremely powerful in many applications, its success depends critically on the correct choice of hyperparameters, in particular the number of network layers. Here, we introduce a new measure, called the generalized discrimination value (GDV), which quantifies how well different object classes separate in each layer. Due to its definition, the GDV is invariant to translation and scaling of the input data, independent of the number of features, as well as independent of the number and permutation of the neurons within a layer. We compute the GDV in each layer of a Deep Belief Network that was trained unsupervised on the MNIST data set. Strikingly, we find that the GDV first improves with each successive network layer, but then gets worse again beyond layer 30, thus indicating the optimal network depth for this data classification task. Our further investigations suggest that the GDV can serve as a universal tool to determine the optimal number of layers in deep neural networks for any type of input data.

In this paper, we extend the $\beta$-CNMF to two dimensions and derive exact multiplicative updates for its factors. The new updates generalize and correct the nonnegative matrix factor deconvolution previously proposed by Schmidt and M{\o}rup. We show by simulation that the updates lead to a monotonically decreasing $\beta$-divergence in terms of the mean and the standard deviation and that the corresponding convergence curves are consistent across the most common values for $\beta$.

We present a novel approach to leverage large unlabeled datasets by pre-training state-of-the-art deep neural networks on randomly-labeled datasets. Specifically, we train the neural networks to memorize arbitrary labels for all the samples in a dataset and use these pre-trained networks as a starting point for regular supervised learning. Our assumption is that the "memorization infrastructure" learned by the network during the random-label training proves to be beneficial for the conventional supervised learning as well. We test the effectiveness of our pre-training on several video action recognition datasets (HMDB51, UCF101, Kinetics) by comparing the results of the same network with and without the random label pre-training. Our approach yields an improvement - ranging from 1.5% on UCF-101 to 5% on Kinetics - in classification accuracy, which calls for further research in this direction.

In this paper we analyze, evaluate, and improve the performance of training generalized linear models on modern CPUs. We start with a state-of-the-art asynchronous parallel training algorithm, identify system-level performance bottlenecks, and apply optimizations that improve data parallelism, cache line locality, and cache line prefetching of the algorithm. These modifications reduce the per-epoch run-time significantly, but take a toll on algorithm convergence in terms of the required number of epochs. To alleviate these shortcomings of our systems-optimized version, we propose a novel, dynamic data partitioning scheme across threads which allows us to approach the convergence of the sequential version. The combined set of optimizations result in a consistent bottom line speedup in convergence of up to $\times12$ compared to the initial asynchronous parallel training algorithm and up to $\times42$, compared to state of the art implementations (scikit-learn and h2o) on a range of multi-core CPU architectures.

Epilepsy is the most common neurological disorder and an accurate forecast of seizures would help to overcome the patient's uncertainty and helplessness. In this contribution, we present and discuss a novel methodology for the classification of intracranial electroencephalography (iEEG) for seizure prediction. Contrary to previous approaches, we categorically refrain from an extraction of hand-crafted features and use a convolutional neural network (CNN) topology instead for both the determination of suitable signal characteristics and the binary classification of preictal and interictal segments. Three different models have been evaluated on public datasets with long-term recordings from four dogs and three patients. Overall, our findings demonstrate the general applicability. In this work we discuss the strengths and limitations of our methodology.