Deep Learning (DL) models are revolutionizing the business and technology world with jaw-dropping performances in one application area after another -- image classification, object detection, object tracking, pose recognition, video analytics, synthetic picture generation -- just to name a few. However, they are like anything but classical Machine Learning (ML) algorithms/techniques. DL models use millions of parameters and create extremely complex and highly nonlinear internal representations of the images or datasets that are fed to these models. Whereas for the classical ML, domain experts and data scientists often have to write hand-crafted algorithms to extract and represent high-dimensional features from the raw data, deep learning models, on the other hand, automatically extracts and work on these complex features. A lot of theory and mathematical machines behind the classical ML (regression, support vector machines, etc.) were developed with linear models in mind. However, practical real-life problems are often nonlinear in nature and therefore cannot be effectively solved using those ML methods.

Epilepsy occurs when localized electrical activity of neurons suffer from an imbalance. One of the most adequate methods for diagnosing and monitoring is via the analysis of electroencephalographic (EEG) signals. Despite there is a wide range of alternatives to characterize and classify EEG signals for epilepsy analysis purposes, many key aspects related to accuracy and physiological interpretation are still considered as open issues. In this paper, this work performs an exploratory study in order to identify the most adequate frequently-used methods for characterizing and classifying epileptic seizures. In this regard, a comparative study is carried out on several subsets of features using four representative classifiers: Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), K-Nearest Neighbor (KNN), and Support Vector Machine (SVM).

Data privacy and security becomes a major concern in building machine learning models from different data providers. Federated learning shows promise by leaving data at providers locally and exchanging encrypted information. This paper studies the vertical federated learning structure for logistic regression where the data sets at two parties have the same sample IDs but own disjoint subsets of features. Existing frameworks adopt the first-order stochastic gradient descent algorithm, which requires large number of communication rounds. To address the communication challenge, we propose a quasi-Newton method based vertical federated learning framework for logistic regression under the additively homomorphic encryption scheme.

In BO, nonparametric Gaussian processes (GPs) provide flexible and fast-to-evaluate surrogates of the objective functions. Sequential design decisions, so-called acquisitions, judiciously balance exploration and exploitation in search for global optima, leveraging the uncertainty estimates provided by the GP posterior distributions (see Mockus et al. (1978); Jones et al. (1998) for early works or Shahriari et al. (2015) for a recent review). One of the weaknesses of vanilla BO lies in the underlying assumption that the objective function is a realisation of a GP: when this assumption is strongly violated, the GP model is weakly predictive and BO becomes inefficient. Two classical examples where BO fails are ill-conditioned problems, when the objective function has strong variations on the domain boundaries but is very flat in its central region (or conversely), and non-Lipschitz objectives, for instance with local discontinuities. High conditioning is typical in "exploratory" optimisation problems, when the parameter space is initially chosen very large. Discontinuities are frequent in computational fluid dynamics problems for instance, where a small change in the parameters results in a change of physics (e.g.

Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is the study of generalization in simple synthetic-data models. Here we discuss the connections between these approaches and focus on the link between the Rademacher complexity in statistical learning and the theories of generalization for typical-case synthetic models from statistical physics, involving quantities known as Gardner capacity and ground state energy. We show that in these models the Rademacher complexity is closely related to the ground state energy computed by replica theories. Using this connection, one may reinterpret many results of the literature as rigorous Rademacher bounds in a variety of models in the high-dimensional statistics limit. Somewhat surprisingly, we also show that statistical learning theory provides predictions for the behavior of the ground-state energies in some full replica symmetry breaking models.

This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our proposed VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framework for SGPR models where its posterior belief is learned together with that of the other variational variables (i.e., inducing variables and kernel hyperparameters). In particular, we transform the discrete kernel belief into a continuous parametric distribution via reparameterization in order to apply VI. Though it is computationally challenging to jointly optimize a large number of hyperparameters due to many kernels being evaluated simultaneously by our VBKS algorithm, we show that the variational lower bound of the log-marginal likelihood can be decomposed into an additive form such that each additive term depends only on a disjoint subset of the variational variables and can thus be optimized independently. Stochastic optimization is then used to maximize the variational lower bound by iteratively improving the variational approximation of the exact posterior belief via stochastic gradient ascent, which incurs constant time per iteration and hence scales to big data. We empirically evaluate the performance of our VBKS algorithm on synthetic and massive real-world datasets.

Department of Electrical, Electronic and Information Engineering Alma Mater Studiorum - Universit a di Bologna Bologna, Italy Abstract In this paper, we introduce the concept of collective learning (CL) which exploits the notion of collective intelligence in the field of distributed semi-supervised learning. The proposed framework draws inspiration from the learning behavior of human beings, who alternate phases involving collaboration, confrontation and exchange of views with other consisting of studying and learning on their own. On this regard, CL comprises two main phases: a self-training phase in which learning is performed on local private (labeled) data only and a collective training phase in which proxy-labels are assigned to shared (unlabeled) data by means of a consensus-based algorithm. In the considered framework, heterogeneous systems can be connected over the same network, each with different computational capabilities and resources and everyone in the network may take advantage of the cooperation and will eventually reach higher performance with respect to those it can reach on its own. An extensive experimental campaign on an image classification problem emphasizes the properties of CL by analyzing the performance achieved by the cooperating agents. 1 Introduction The notion of collective intelligence has been firstly introduced in [Engelbart, 1962] and widespread in the sociological field by Pierre L evy in [L evy and Bononno, 1997]. By borrowing the words of L evy, collective intelligence " is a form of universally distributed intelligence, constantly enhanced, coordinated in real time, and resulting in the effective mobilization of skills ". Moreover, " the basis and goal of collective intelligence is mutual recognition and enrichment of individuals rather than the cult of fetishized or hypostatized communities ". In this paper, we aim to exploit some concepts borrowed from the notion of collective intelligence in a distributed machine learning scenario. In fact, by cooperating with each other, machines may exhibit performance higher than those they can obtain by learning on their own. We call this framework collective learning (CL) . Distributed systems 1 have received a steadily growing attention in the last years and1 When talking about distributed systems, the word distributed can be used with different meanings.

We seek to align agent behavior with a user's objectives in a reinforcement learning setting with unknown dynamics, an unknown reward function, and unknown unsafe states. The user knows the rewards and unsafe states, but querying the user is expensive. To address this challenge, we propose an algorithm that safely and interactively learns a model of the user's reward function. We start with a generative model of initial states and a forward dynamics model trained on off-policy data. Our method uses these models to synthesize hypothetical behaviors, asks the user to label the behaviors with rewards, and trains a neural network to predict the rewards. The key idea is to actively synthesize the hypothetical behaviors from scratch by maximizing tractable proxies for the value of information, without interacting with the environment. We call this method reward query synthesis via trajectory optimization (ReQueST). We evaluate ReQueST with simulated users on a state-based 2D navigation task and the image-based Car Racing video game. The results show that ReQueST significantly outperforms prior methods in learning reward models that transfer to new environments with different initial state distributions. Moreover, ReQueST safely trains the reward model to detect unsafe states, and corrects reward hacking before deploying the agent.

Differential Privacy (DP) provides strong guarantees on the risk of compromising a user's data in statistical learning applications, though these strong protections make learning challenging and may be too stringent for some use cases. To address this, we propose element level differential privacy, which extends differential privacy to provide protection against leaking information about any particular "element" a user has, allowing better utility and more robust results than classical DP. By carefully choosing these "elements," it is possible to provide privacy protections at a desired granularity. We provide definitions, associated privacy guarantees, and analysis to identify the tradeoffs with the new definition; we also develop several private estimation and learning methodologies, providing careful examples for item frequency and M-estimation (empirical risk minimization) with concomitant privacy and utility analysis. We complement our theoretical and methodological advances with several real-world applications, estimating histograms and fitting several large-scale prediction models, including deep networks.