Online hate speech is a newborn problem in our modern society which is growing at a steady rate exploiting weaknesses of the corresponding regimes that characterise several social media platforms. Therefore, this phenomenon is mainly cultivated through such comments, either during users' interaction or on posted multimedia context. Nowadays, giant companies own platforms where many millions of users log in daily. Thus, protection of their users from exposure to similar phenomena for keeping up with the corresponding law, as well as for retaining a high quality of offered services, seems mandatory. Having a robust and reliable mechanism for identifying and preventing the uploading of related material would have a huge effect on our society regarding several aspects of our daily life. On the other hand, its absence would deteriorate heavily the total user experience, while its erroneous operation might raise several ethical issues. In this work, we present a protocol for creating a more suitable dataset, regarding its both informativeness and representativeness aspects, favouring the safer capture of hate speech occurrence, without at the same time restricting its applicability to other classification problems. Moreover, we produce and publish a textual dataset with two variants: binary and multi-label, called `ETHOS', based on YouTube and Reddit comments validated through figure-eight crowdsourcing platform. Our assumption about the production of more compatible datasets is further investigated by applying various classification models and recording their behaviour over several appropriate metrics.

Learning energy-based model (EBM) requires MCMC sampling of the learned model as the inner loop of the learning algorithm. However, MCMC sampling of EBM in data space is generally not mixing, because the energy function, which is usually parametrized by deep network, is highly multi-modal in the data space. This is a serious handicap for both the theory and practice of EBM. In this paper, we propose to learn EBM with a flow-based model serving as a backbone, so that the EBM is a correction or an exponential tilting of the flow-based model. We show that the model has a particularly simple form in the space of the latent variables of the flow-based model, and MCMC sampling of the EBM in the latent space, which is a simple special case of neural transport MCMC, mixes well and traverses modes in the data space. This enables proper sampling and learning of EBM.

We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to solutions that minimize a known norm, we flip the problem and investigate what is the corresponding norm minimized by an interpolating solution. Using this reasoning, we prove that for over-parameterized linear regression, projections onto linear spans can be used to move between different interpolating solutions. For under-parameterized linear classification, we prove that for any linear classifier separating the data, there exists a family of quadratic norms ||.||_P such that the classifier's direction is the same as that of the maximum P-margin solution. For linear classification, we argue that analyzing convergence to the standard maximum l2-margin is arbitrary and show that minimizing the norm induced by the data results in better generalization. Furthermore, for over-parameterized linear classification, projections onto the data-span enable us to use techniques from the under-parameterized setting. On the empirical side, we propose techniques to bias optimizers towards better generalizing solutions, improving their test performance. We validate our theoretical results via synthetic experiments, and use the neural tangent kernel to handle non-linear models.

The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both theoretically and computationally. Genetic programming based methods, that heuristically search over a very large space of functions, are the most commonly used methods to tackle SR problems. An alternative mathematical programming approach, proposed in the last decade, is to express the optimal symbolic expression as the solution of a system of nonlinear equations over continuous and discrete variables that minimizes a certain objective, and to solve this system via a global solver for mixed-integer nonlinear programming problems. Algorithms based on the latter approach are often very slow. We propose a hybrid algorithm that combines mixed-integer nonlinear optimization with explicit enumeration and incorporates constraints from dimensional analysis. We show that our algorithm is competitive, for some synthetic data sets, with a state-of-the-art SR software and a recent physics-inspired method called AI Feynman.

The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data demonstrate promising generalisation ability on unseen data from relevant domains, the computational cost of finetuning gradually becomes a bottleneck in transfering the learning to new domains. We address this issue by leveraging the low-rank property of learnt feature vectors produced from deep neural networks (DNNs) with the closed-form solution provided in kernel ridge regression (KRR). This frees transfer learning from finetuning and replaces it with an ensemble of linear systems with many fewer hyperparameters. Our method is successful on supervised and semi-supervised transfer learning tasks.

Learning in the presence of noisy data is a central challenge in machine learning. In this work, we study the efficient learnability of halfspaces when a fraction of the training labels is adversarially corrupted. As our main contribution, we show that non-convex SGD efficiently learns homogeneous halfspaces in the presence of adversarial label noise with respect to a broad family of well-behaved distributions, including log-concave distributions. Before we state our contributions, we provide some background and motivation for this work.

Automated machine learning (AutoML) and deep learning (DL) are two cutting-edge paradigms used to solve a myriad of inductive learning tasks. In spite of their successes, little guidance exists for when to choose one approach over the other in the context of specific real-world problems. Furthermore, relatively few tools exist that allow the integration of both AutoML and DL in the same analysis to yield results combining both of their strengths. Here, we seek to address both of these issues, by (1.) providing a head-to-head comparison of AutoML and DL in the context of binary classification on 6 well-characterized public datasets, and (2.) evaluating a new tool for genetic programming-based AutoML that incorporates deep estimators. Our observations suggest that AutoML outperforms simple DL classifiers when trained on similar datasets for binary classification but integrating DL into AutoML improves classification performance even further. However, the substantial time needed to train AutoML DL pipelines will likely outweigh performance advantages in many applications.

Generalization is a central problem in Machine Learning. Most prediction methods require careful calibration of hyperparameters carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of this paper is to present a novel approach based on a new measure of risk that allows us to develop novel fully automatic procedures for generalization. We illustrate the pertinence of this new framework in the regression problem. The main advantages of this new approach are: (i) it can simultaneously train the model and perform regularization in a single run of a gradient-based optimizer on all available data without any previous hyperparameter tuning; (ii) this framework can tackle several additional objectives simultaneously (correlation, sparsity,...) $via$ the introduction of regularization parameters. Noticeably, our approach transforms hyperparameter tuning as well as feature selection (a combinatorial discrete optimization problem) into a continuous optimization problem that is solvable via classical gradient-based methods ; (iii) the computational complexity of our methods is $O(npK)$ where $n,p,K$ denote respectively the number of observations, features and iterations of the gradient descent algorithm. We observe in our experiments a significantly smaller runtime for our methods as compared to benchmark methods for equivalent prediction score. Our procedures are implemented in PyTorch (code is available for replication).

We consider an existing conjecture addressing the asymptotic behavior of neural networks in the large width limit. The results that follow from this conjecture include tight bounds on the behavior of wide networks during stochastic gradient descent, and a derivation of their finite-width dynamics. We prove the conjecture for deep networks with polynomial activation functions, greatly extending the validity of these results. Finally, we point out a difference in the asymptotic behavior of networks with analytic (and non-linear) activation functions and those with piecewise-linear activations such as ReLU.

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the $\mathcal{\tilde O}(t^{-1/4})$ rate of convergence for the norm of the gradient of Moreau envelope, which is the standard stationarity measure for this class of problems. It matches the known rates that adaptive algorithms enjoy for the specific case of unconstrained smooth stochastic optimization. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly unbounded optimization domains. Finally, we illustrate the applications and extensions of our results to specific problems and algorithms.