We present an approach for efficiently training Gaussian Mixture Models (GMMs) with Stochastic Gradient Descent (SGD) on large amounts of high-dimensional data (e.g., images). In such a scenario, SGD is strongly superior in terms of execution time and memory usage, although it is conceptually more complex than the traditional Expectation-Maximization (EM) algorithm. For enabling SGD training, we propose three novel ideas: First, we show that minimizing an upper bound to the GMM log likelihood instead of the full one is feasible and numerically much more stable way in high-dimensional spaces. Secondly, we propose a new annealing procedure that prevents SGD from converging to pathological local minima. We also propose an SGD-compatible simplification to the full GMM model based on local principal directions, which avoids excessive memory use in high-dimensional spaces due to quadratic growth of covariance matrices. Experiments on several standard image datasets show the validity of our approach, and we provide a publicly available TensorFlow implementation.

Hierarchical neural networks are exponentially more efficient than their corresponding "shallow" counterpart with the same expressive power, but involve huge number of parameters and require tedious amounts of training. By approximating the tangent subspace, we suggest a sparse representation that enables switching to shallow networks, GradNet after a very early training stage. Our experiments show that the proposed approximation of the metric improves and sometimes even surpasses the achievable performance of the original network significantly even after a few epochs of training the original feedforward network.

An Intrusion Detection System (IDS) is a key cybersecurity tool for network administrators as it identifies malicious traffic and cyberattacks. With the recent successes of machine learning techniques such as deep learning, more and more IDS are now using machine learning algorithms to detect attacks faster. However, these systems lack robustness when facing previously unseen types of attacks. With the increasing number of new attacks, especially against Internet of Things devices, having a robust IDS able to spot unusual and new attacks becomes necessary. This work explores the possibility of leveraging generative adversarial models to improve the robustness of machine learning based IDS. More specifically, we propose a new method named SIGMA, that leverages adversarial examples to strengthen IDS against new types of attacks. Using Generative Adversarial Networks (GAN) and metaheuristics, SIGMA %Our method consists in generates adversarial examples, iteratively, and uses it to retrain a machine learning-based IDS, until a convergence of the detection rate (i.e. until the detection system is not improving anymore). A round of improvement consists of a generative phase, in which we use GANs and metaheuristics to generate instances ; an evaluation phase in which we calculate the detection rate of those newly generated attacks ; and a training phase, in which we train the IDS with those attacks. We have evaluated the SIGMA method for four standard machine learning classification algorithms acting as IDS, with a combination of GAN and a hybrid local-search and genetic algorithm, to generate new datasets of attacks. Our results show that SIGMA can successfully generate adversarial attacks against different machine learning based IDS. Also, using SIGMA, we can improve the performance of an IDS to up to 100\% after as little as two rounds of improvement.

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and exploitable structure that one can extract from them. In this paper, we introduce the problem of finding a tensor of adaptive aggregated granularity that can be decomposed to reveal meaningful latent concepts (structures) from datasets that, in their original form, are not amenable to tensor analysis. Such datasets fall under the broad category of sparse point processes that evolve over space and/or time. To the best of our knowledge, this is the first work that explores adaptive granularity aggregation in tensors. Furthermore, we formally define the problem and discuss what different definitions of "good structure" can be in practice, and show that optimal solution is of prohibitive combinatorial complexity. Subsequently, we propose an efficient and effective greedy algorithm which follows a number of intuitive decision criteria that locally maximize the "goodness of structure", resulting in high-quality tensors. We evaluate our method on both semi-synthetic data where ground truth is known and real datasets for which we do not have any ground truth. In both cases, our proposed method constructs tensors that have very high structure quality. Finally, our proposed method is able to discover different natural resolutions of a multi-aspect dataset, which can lead to multi-resolution analysis.

There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. Most of the work is limited to either independent and identically distributed setting, or time series with independent and/or (sub-)Gaussian innovations. We extend current literature to a broader set of innovation processes, by assuming that the error process is non-sub-Gaussian and conditionally heteroscedastic, and the generating process is not necessarily sparse. This setting covers fat tailed, conditionally dependent innovations which is of particular interest for financial risk modeling. It covers several multivariate-GARCH specifications, such as the BEKK model, and other factor stochastic volatility specifications.

Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous works on theoretical properties of spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and analyses, and thus can not be generalized directly. In this paper, we propose a class of generic spike-and-slab priors and develop a unified framework to rigorously assess their theoretical properties. Technically, we provide general conditions under which generic spike-and-slab priors can achieve a nearly-optimal posterior contraction rate and model selection consistency. Our results include those of Castillo et al. (2015) and Narisetty and He (2014) as special cases.

This paper explores the scenarios under which an attacker can claim that 'Noise and access to the softmax layer of the model is all you need' to steal the weights of a convolutional neural network whose architecture is already known. We were able to achieve 96% test accuracy using the stolen MNIST model and 82% accuracy using the stolen KMNIST model learned using only i.i.d. Bernoulli noise inputs. We posit that this theft-susceptibility of the weights is indicative of the complexity of the dataset and propose a new metric that captures the same. The goal of this dissemination is to not just showcase how far knowing the architecture can take you in terms of model stealing, but to also draw attention to this rather idiosyncratic weight learnability aspects of CNNs spurred by i.i.d. noise input. We also disseminate some initial results obtained with using the Ising probability distribution in lieu of the i.i.d. Bernoulli distribution.

The interplay between inter-neuronal network topology and cognition has been studied deeply by connectomics researchers and network scientists, which is crucial towards understanding the remarkable efficacy of biological neural networks. Curiously, the deep learning revolution that revived neural networks has not paid much attention to topological aspects. The architectures of deep neural networks (DNNs) do not resemble their biological counterparts in the topological sense. We bridge this gap by presenting initial results of Deep Connectomics Networks (DCNs) as DNNs with topologies inspired by real-world neuronal networks. We show high classification accuracy obtained by DCNs whose architecture was inspired by the biological neuronal networks of C. Elegans and the mouse visual cortex.

This paper investigates multilevel initialization strategies for training very deep neural networks with a layer-parallel multigrid solver. The scheme is based on the continuous interpretation of the training problem as a problem of optimal control, in which neural networks are represented as discretizations of time-dependent ordinary differential equations. A key goal is to develop a method able to intelligently initialize the network parameters for the very deep networks enabled by scalable layer-parallel training. To do this, we apply a refinement strategy across the time domain, that is equivalent to refining in the layer dimension. The resulting refinements create deep networks, with good initializations for the network parameters coming from the coarser trained networks. We investigate the effectiveness of such multilevel "nested iteration" strategies for network training, showing supporting numerical evidence of reduced run time for equivalent accuracy. In addition, we study whether the initialization strategies provide a regularizing effect on the overall training process and reduce sensitivity to hyperparameters and randomness in initial network parameters.

Machine Learning (ML) is widely used for several tasks with time-series and biosensor data such as for human activity recognition, electronic health records data-based predictions (Ismail Fawaz et al., 2019), and real-time bionsensor-based decisions. V arious classification goals are addressed related to electrocardiography (ECG) (Jambukia et al., 2015), elec-troencephalography (EEG) (Craik et al., 2019; Dose et al., 2018), and electromyograpy (EMG) (Ketyk et al., 2019; Hu et al., 2018; Patricia et al., 2014; Du et al., 2017). Sensing hand gestures can be done by means of wearables or by means of image or video analysis of hand or finger motion. A wearable-based detection can physically rely on measuring the acceleration and rotations of our body parts (arms, hands or fingers) with Inertial Measurement Unit (IMU) sensors or by measuring the myo-electric signals generated by the various muscles of our arms or fingers with EMG sensors. Surface EMG (sEMG) records muscle activity from the surface of the skin which is above the muscle being evaluated. The signal is collected via surface electrodes. We are interested in sEMG-sensor placement to the forearm and performing hand gesture recognition with ML.