Neural network (NN) compression has become essential to enable deploying over-parameterized NN models on resource-constrained devices. As a simple and easy-to-implement method, pruning is one of the most established NN compression techniques. Although it is a mature method with more than 30 years of history, there is still a lack of good understanding and systematic analysis of why pruning works well even with aggressive compression ratios. In this work, we answer this question by studying NN compression from an information-theoretic approach and show that rate distortion theory suggests pruning to achieve the theoretical limits of NN compression. Our derivation also provides an end-to-end compression pipeline involving a novel pruning strategy. That is, in addition to pruning the model, we also find a minimum-length binary representation of it via entropy coding. Our method consistently outperforms the existing pruning strategies and reduces the pruned model's size by 2.5 times. We evaluate the efficacy of our strategy on MNIST, CIFAR-10 and ImageNet datasets using 5 distinct architectures.

Teacher-student models provide a powerful framework in which the typical case performance of high-dimensional supervised learning tasks can be studied in closed form. In this setting, labels are assigned to data - often taken to be Gaussian i.i.d. - by a teacher model, and the goal is to characterise the typical performance of the student model in recovering the parameters that generated the labels. In this manuscript we discuss a generalisation of this setting where the teacher and student can act on different spaces, generated with fixed, but generic feature maps. This is achieved via the rigorous study of a high-dimensional Gaussian covariate model. Our contribution is two-fold: First, we prove a rigorous formula for the asymptotic training loss and generalisation error achieved by empirical risk minimization for this model. Second, we present a number of situations where the learning curve of the model captures the one of a \emph{realistic data set} learned with kernel regression and classification, with out-of-the-box feature maps such as random projections or scattering transforms, or with pre-learned ones - such as the features learned by training multi-layer neural networks. We discuss both the power and the limitations of the Gaussian teacher-student framework as a typical case analysis capturing learning curves as encountered in practice on real data sets.

We study online learning for optimal allocation when the resource to be allocated is time. Examples of possible applications include a driver filling a day with rides, a landlord renting an estate, etc. Following our initial motivation, a driver receives ride proposals sequentially according to a Poisson process and can either accept or reject a proposed ride. If she accepts the proposal, she is busy for the duration of the ride and obtains a reward that depends on the ride duration. If she rejects it, she remains on hold until a new ride proposal arrives. We study the regret incurred by the driver first when she knows her reward function but does not know the distribution of the ride duration, and then when she does not know her reward function, either. Faster rates are finally obtained by adding structural assumptions on the distribution of rides or on the reward function. This natural setting bears similarities with contextual (one-armed) bandits, but with the crucial difference that the normalized reward associated to a context depends on the whole distribution of contexts.

Multi-label classification (MLC) has recently received increasing interest from the machine learning community. Several studies provide reviews of methods and datasets for MLC and a few provide empirical comparisons of MLC methods. However, they are limited in the number of methods and datasets considered. This work provides a comprehensive empirical study of a wide range of MLC methods on a plethora of datasets from various domains. More specifically, our study evaluates 26 methods on 42 benchmark datasets using 20 evaluation measures. The adopted evaluation methodology adheres to the highest literature standards for designing and executing large scale, time-budgeted experimental studies. First, the methods are selected based on their usage by the community, assuring representation of methods across the MLC taxonomy of methods and different base learners. Second, the datasets cover a wide range of complexity and domains of application. The selected evaluation measures assess the predictive performance and the efficiency of the methods. The results of the analysis identify RFPCT, RFDTBR, ECCJ48, EBRJ48 and AdaBoostMH as best performing methods across the spectrum of performance measures. Whenever a new method is introduced, it should be compared to different subsets of MLC methods, determined on the basis of the different evaluation criteria.

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We consider some supervised binary classification tasks and a regression task, whereas SVM and Deep Learning, at present, exhibit the best generalization performances. We extend the work [3] on a generalized quadratic loss for learning problems that examines pattern correlations in order to concentrate the learning problem into input space regions where patterns are more densely distributed. From a shallow methods point of view (e.g.: SVM), since the following mathematical derivation of problem (9) in [3] is incorrect, we restart from problem (8) in [3] and we try to solve it with one procedure that iterates over the dual variables until the primal and dual objective functions converge. In addition we propose another algorithm that tries to solve the classification problem directly from the primal problem formulation. We make also use of Multiple Kernel Learning to improve generalization performances. Moreover, we introduce for the first time a custom loss that takes in consideration pattern correlation for a shallow and a Deep Learning task. We propose some pattern selection criteria and the results on 4 UCI data-sets for the SVM method. We also report the results on a larger binary classification data-set based on Twitter, again drawn from UCI, combined with shallow Learning Neural Networks, with and without the generalized quadratic loss. At last, we test our loss with a Deep Neural Network within a larger regression task taken from UCI. We compare the results of our optimizers with the well known solver SVMlight and with Keras Multi-Layers Neural Networks with standard losses and with a parameterized generalized quadratic loss, and we obtain comparable results.

We consider a decentralized online convex optimization (OCO) setting with multiple agents that share information across a network to improve the prediction quality of the network as a whole. Our motivation comes from cases where local computation is cheap, but communication is relatively expensive. This is the case, for instance, in sensor networks, where the energy cost of wireless communication is typically the main bottleneck, and long-distance communication requires much more energy than communication between nearby sensors (Rabbat, Nowak, 2004). It also applies to cases where communication is relatively slow compared to the volume of prediction requests that each agent must serve. For instance, in climate informatics communication may be slow because agents are geographically spread out (McQuade, Monteleoni, 2012, 2017), and in finance or online advertising the rate of prediction requests may be so high that communication is slow by comparison. To model such scenarios, we limit communication in two ways: first, agents can only directly communicate to their neighbors in a communication graph G and, second, the messages that the agents can send are limited to contain at most b bits. We further assume that learning is fully decentralized, so there is no central coordinating agent as in federated learning (Kairouz et al., 2019), and no single agent that dictates the predictions for all other agents as in distributed online optimization for consensus problems (Hosseini et al., 2013; Yan et al., 2013).

In this paper, we introduce the Layer-Peeled Model, a nonconvex yet analytically tractable optimization program, in a quest to better understand deep neural networks that are trained for a sufficiently long time. As the name suggests, this new model is derived by isolating the topmost layer from the remainder of the neural network, followed by imposing certain constraints separately on the two parts. We demonstrate that the Layer-Peeled Model, albeit simple, inherits many characteristics of well-trained neural networks, thereby offering an effective tool for explaining and predicting common empirical patterns of deep learning training. First, when working on class-balanced datasets, we prove that any solution to this model forms a simplex equiangular tight frame, which in part explains the recently discovered phenomenon of neural collapse in deep learning training [PHD20]. Moreover, when moving to the imbalanced case, our analysis of the Layer-Peeled Model reveals a hitherto unknown phenomenon that we term Minority Collapse, which fundamentally limits the performance of deep learning models on the minority classes. In addition, we use the Layer-Peeled Model to gain insights into how to mitigate Minority Collapse. Interestingly, this phenomenon is first predicted by the Layer-Peeled Model before its confirmation by our computational experiments.

In the past few years, we have observed a huge supply-demand gap for autonomous driving engineers. The core problem is that autonomous driving is not one single technology but rather a complex system integrating many technologies, and no one single academic department can provide comprehensive education in this field. We advocate to create a cross-disciplinary program to expose students with technical background in computer science, computer engineering, electrical engineering, as well as mechanical engineering. On top of the cross-disciplinary technical foundation, a capstone project that provides students with hands-on experiences of working with a real autonomous vehicle is required to consolidate the technical foundation.

Existing e-learning environments primarily focus on the aspect of providing intuitive learning contents and to recommend learning units in a personalized fashion. The major focus of the KnowledgeCheckR environment is to take into account forgetting processes which immediately start after a learning unit has been completed. In this context, techniques are needed that are able to predict which learning units are the most relevant ones to be repeated in future learning sessions. In this paper, we provide an overview of the recommendation approaches integrated in KnowledgeCheckR. Examples thereof are utility-based recommendation that helps to identify learning contents to be repeated in the future, collaborative filtering approaches that help to implement session-based recommendation, and content-based recommendation that supports intelligent question answering. In order to show the applicability of the presented techniques, we provide an overview of the results of empirical studies that have been conducted in real-world scenarios.