We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and experimentally demonstrate that our methods can be applied in various fields of machine learning including deep, convolutional and recurrent neural networks, reinforcement learning, normalizing flows and metric learning. We show an intriguing connection between efficient stochastic optimization on the orthogonal group and graph theory (e.g. matching problem, partition functions over graphs, graph-coloring). We leverage the theory of Lie groups and provide theoretical results for the designed class of algorithms. We demonstrate broad applicability of our methods by showing strong performance on the seemingly unrelated tasks of learning world models to obtain stable policies for the most difficult $\mathrm{Humanoid}$ agent from $\mathrm{OpenAI}$ $\mathrm{Gym}$ and improving convolutional neural networks.

Deep-learning-as-a-service is a novel and promising computing paradigm aiming at providing machine/deep learning solutions and mechanisms through Cloud-based computing infrastructures. Thanks to its ability to remotely execute and train deep learning models (that typically require high computational loads and memory occupation), such an approach guarantees high performance, scalability, and availability. Unfortunately, such an approach requires to send information to be processed (e.g., signals, images, positions, sounds, videos) to the Cloud, hence having potentially catastrophic-impacts on the privacy of users. This paper introduces a novel distributed architecture for deep-learning-as-a-service that is able to preserve the user sensitive data while providing Cloud-based machine and deep learning services. The proposed architecture, which relies on Homomorphic Encryption that is able to perform operations on encrypted data, has been tailored for Convolutional Neural Networks (CNNs) in the domain of image analysis and implemented through a client-server REST-based approach. Experimental results show the effectiveness of the proposed architecture.

We present a novel model called One Class Minimum Spanning Tree (OCmst) for novelty detection problem that uses a Convolutional Neural Network (CNN) as deep feature extractor and graph-based model based on Minimum Spanning Tree (MST). In a novelty detection scenario, the training data is no polluted by outliers (abnormal class) and the goal is to recognize if a test instance belongs to the normal class or to the abnormal class. Our approach uses the deep features from CNN to feed a pair of MSTs built starting from each test instance. To cut down the computational time we use a parameter $\gamma$ to specify the size of the MST's starting to the neighbours from the test instance. To prove the effectiveness of the proposed approach we conducted experiments on two publicly available datasets, well-known in literature and we achieved the state-of-the-art results on CIFAR10 dataset.

Recent years have seen a substantial development of quantitative methods, mostly led by the computer science community with the goal to develop better machine learning application, mainly focused on predictive modeling. However, economic, management, and technology forecasting research has up to now been hesitant to apply predictive modeling techniques and workflows. In this paper, we introduce to a machine learning (ML) approach to quantitative analysis geared towards optimizing the predictive performance, contrasting it with standard practices inferential statistics which focus on producing good parameter estimates. We discuss the potential synergies between the two fields against the backdrop of this at first glance, \enquote{target-incompatibility}. We discuss fundamental concepts in predictive modeling, such as out-of-sample model validation, variable and model selection, generalization and hyperparameter tuning procedures. Providing a hands-on predictive modelling for an quantitative social science audience, while aiming at demystifying computer science jargon. We use the example of \enquote{high-quality} patent identification guiding the reader through various model classes and procedures for data pre-processing, modelling and validation. We start of with more familiar easy to interpret model classes (Logit and Elastic Nets), continues with less familiar non-parametric approaches (Classification Trees and Random Forest) and finally presents artificial neural network architectures, first a simple feed-forward and then a deep autoencoder geared towards anomaly detection. Instead of limiting ourselves to the introduction of standard ML techniques, we also present state-of-the-art yet approachable techniques from artificial neural networks and deep learning to predict rare phenomena of interest.

Adversarial robustness has proven to be a required property of machine learning algorithms. A key and often overlooked aspect of this problem is to try to make the adversarial noise magnitude as large as possible to enhance the benefits of the model robustness. We show that the well-established algorithm called "adversarial training" fails to train a deep neural network given a large, but reasonable, perturbation magnitude. In this paper, we propose a simple yet effective initialization of the network weights that makes learning on higher levels of noise possible. We next evaluate this idea rigorously on MNIST ($\epsilon$ up to $\approx 0.40$) and CIFAR10 ($\epsilon$ up to $\approx 32/255$) datasets assuming the $\ell_{\infty}$ attack model. Additionally, in order to establish the limits of $\epsilon$ in which the learning is feasible, we study the optimal robust classifier assuming full access to the joint data and label distribution. Then, we provide some theoretical results on the adversarial accuracy for a simple multi-dimensional Bernoulli distribution, which yields some insights on the range of feasible perturbations for the MNIST dataset.

Atari games have been a long-standing benchmark in the reinforcement learning (RL) community for the past decade. This benchmark was proposed to test general competency of RL algorithms. Previous work has achieved good average performance by doing outstandingly well on many games of the set, but very poorly in several of the most challenging games. We propose Agent57, the first deep RL agent that outperforms the standard human benchmark on all 57 Atari games. To achieve this result, we train a neural network which parameterizes a family of policies ranging from very exploratory to purely exploitative. We propose an adaptive mechanism to choose which policy to prioritize throughout the training process. Additionally, we utilize a novel parameterization of the architecture that allows for more consistent and stable learning.

Point clouds are a popular representation for 3D shapes. However, they encode a particular sampling without accounting for shape priors or non-local information. We advocate for the use of a hierarchical Gaussian mixture model (hGMM), which is a compact, adaptive and lightweight representation that probabilistically defines the underlying 3D surface. We present PointGMM, a neural network that learns to generate hGMMs which are characteristic of the shape class, and also coincide with the input point cloud. PointGMM is trained over a collection of shapes to learn a class-specific prior. The hierarchical representation has two main advantages: (i) coarse-to-fine learning, which avoids converging to poor local-minima; and (ii) (an unsupervised) consistent partitioning of the input shape. We show that as a generative model, PointGMM learns a meaningful latent space which enables generating consistent interpolations between existing shapes, as well as synthesizing novel shapes. We also present a novel framework for rigid registration using PointGMM, that learns to disentangle orientation from structure of an input shape.

Nearly all model algorithms used in machine learning use two different sets of parameters: the training parameters and the meta-parameters (hyperparameters). While the training parameters are learned during the training phase, the values of the hyperparameters have to be specified before learning starts. For a given dataset, we would like to find the optimal combination of hyperparameter values, in a reasonable amount of time. This is a challenging task because of its computational complexity. In previous work [11], we introduced the Weighted Random Search (WRS) method, a combination of Random Search (RS) and probabilistic greedy heuristic. In the current paper, we compare the WRS method with several state-of-the art hyperparameter optimization methods with respect to Convolutional Neural Network (CNN) hyperparameter optimization. The criterion is the classification accuracy achieved within the same number of tested combinations of hyperparameter values. According to our experiments, the WRS algorithm outperforms the other methods.

Domain adaptation tackles the problem of transferring knowledge from a label-rich source domain to a label-scarce or even unlabeled target domain. Recently domain-adversarial training (DAT) has shown promising capacity to learn a domain-invariant feature space by reversing the gradient propagation of a domain classifier. However, DAT is still vulnerable in several aspects including (1) training instability due to the overwhelming discriminative ability of the domain classifier in adversarial training, (2) restrictive feature-level alignment, and (3) lack of interpretability or systematic explanation of the learned feature space. In this paper, we propose a novel Max-margin Domain-Adversarial Training (MDAT) by designing an Adversarial Reconstruction Network (ARN). The proposed MDAT stabilizes the gradient reversing in ARN by replacing the domain classifier with a reconstruction network, and in this manner ARN conducts both feature-level and pixel-level domain alignment without involving extra network structures. Furthermore, ARN demonstrates strong robustness to a wide range of hyper-parameters settings, greatly alleviating the task of model selection. Extensive empirical results validate that our approach outperforms other state-of-the-art domain alignment methods. Moreover, reconstructing adapted features reveals the domain-invariant feature space which conforms with our intuition.

Weather forecasting is a long standing scientific challenge with direct social and economic impact. The task is suitable for deep neural networks due to vast amounts of continuously collected data and a rich spatial and temporal structure that presents long range dependencies. We introduce MetNet, a neural network that forecasts precipitation up to 8 hours into the future at the high spatial resolution of 1 km$^2$ and at the temporal resolution of 2 minutes with a latency in the order of seconds. MetNet takes as input radar and satellite data and forecast lead time and produces a probabilistic precipitation map. The architecture uses axial self-attention to aggregate the global context from a large input patch corresponding to a million square kilometers. We evaluate the performance of MetNet at various precipitation thresholds and find that MetNet outperforms Numerical Weather Prediction at forecasts of up to 7 to 8 hours on the scale of the continental United States.