The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models, however, is still an open problem. Bits-Back with Asymmetric Numeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makes bits-back coding practically feasible for latent variable models with one latent layer, but it is inefficient for hierarchical latent variable models. In this paper we propose Bit-Swap, a new compression scheme that generalizes BB-ANS and achieves strictly better compression rates for hierarchical latent variable models with Markov chain structure. Through experiments we verify that Bit-Swap results in lossless compression rates that are empirically superior to existing techniques. Our implementation is available at https://github.com/fhkingma/bitswap.

Boosting and other ensemble methods combine a large number of weak classifiers through weighted voting to produce stronger predictive models. To explain the successful performance of boosting algorithms, Schapire et al. (1998) showed that AdaBoost is especially effective at increasing the margins of the training data. Schapire et al. (1998) also developed an upper bound on the generalization error of any ensemble based on the margins of the training data, from which it was concluded that larger margins should lead to lower generalization error, everything else being equal (sometimes referred to as the ``large margins theory''). Tighter bounds have been derived and have reinforced the large margins theory hypothesis. For instance, Wang et al. (2011) suggest that specific margin instances, such as the equilibrium margin, can better summarize the margins distribution. These results have led many researchers to consider direct optimization of the margins to improve ensemble generalization error with mixed results. We show that the large margins theory is not sufficient for explaining the performance of voting classifiers. We do this by illustrating how it is possible to improve upon the margin distribution of an ensemble solution, while keeping the complexity fixed, yet not improve the test set performance.

We demonstrate, theoretically and empirically, that adversarial robustness can significantly benefit from semisupervised learning. Theoretically, we revisit the simple Gaussian model of Schmidt et al. that shows a sample complexity gap between standard and robust classification. We prove that this gap does not pertain to labels: a simple semisupervised learning procedure (self-training) achieves robust accuracy using the same number of labels required for standard accuracy. Empirically, we augment CIFAR-10 with 500K unlabeled images sourced from 80 Million Tiny Images and use robust self-training to outperform state-of-the-art robust accuracies by over 5 points in (i) $\ell_\infty$ robustness against several strong attacks via adversarial training and (ii) certified $\ell_2$ and $\ell_\infty$ robustness via randomized smoothing. On SVHN, adding the dataset's own extra training set with the labels removed provides gains of 4 to 10 points, within 1 point of the gain from using the extra labels as well.

In this paper, the authors aim to combine the latest state of the art models in image recognition with the best publicly available satellite images to create a system for landslide risk mitigation. We focus first on landslide detection and further propose a similar system to be used for prediction. Such models are valuable as they could easily be scaled up to provide data for hazard evaluation, as satellite imagery becomes increasingly available. The goal is to use satellite images and correlated data to enrich the public repository of data and guide disaster relief efforts for locating precise areas where landslides have occurred. Different image augmentation methods are used to increase diversity in the chosen dataset and create more robust classification. The resulting outputs are then fed into variants of 3-D convolutional neural networks. A review of the current literature indicates there is no research using CNNs (Convolutional Neural Networks) and freely available satellite imagery for classifying landslide risk. The model has shown to be ultimately able to achieve a significantly better than baseline accuracy.

Network slicing promises to provision diversified services with distinct requirements in one infrastructure. Deep reinforcement learning (e.g., deep $\mathcal{Q}$-learning, DQL) is assumed to be an appropriate algorithm to solve the demand-aware inter-slice resource management issue in network slicing by regarding the varying demands and the allocated bandwidth as the environment state and the action, respectively. However, allocating bandwidth in a finer resolution usually implies larger action space, and unfortunately DQL fails to quickly converge in this case. In this paper, we introduce discrete normalized advantage functions (DNAF) into DQL, by separating the $\mathcal{Q}$-value function as a state-value function term and an advantage term and exploiting a deterministic policy gradient descent (DPGD) algorithm to avoid the unnecessary calculation of $\mathcal{Q}$-value for every state-action pair. Furthermore, as DPGD only works in continuous action space, we embed a k-nearest neighbor algorithm into DQL to quickly find a valid action in the discrete space nearest to the DPGD output. Finally, we verify the faster convergence of the DNAF-based DQL through extensive simulations.

Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share an edge with high probability, they must be relatively close in all dimensions. This constraint may be overly restrictive for describing modern networks, in which having similarities in at least one area may be sufficient for having a high edge probability. We introduce a new model, which we call Latent Channel Networks, which allows for such features of a network. We present an EM algorithm for fitting the model, for which the computational complexity is linear in the number of edges and number of channels and apply the algorithm to both synthetic and classic network datasets.

We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and study its convergence properties. The MMD is an integral probability metric defined for a reproducing kernel Hilbert space (RKHS), and serves as a metric on probability measures for a sufficiently rich RKHS. We obtain conditions for convergence of the gradient flow towards a global optimum, that can be related to particle transport when optimizing neural networks. We also propose a way to regularize this MMD flow, based on an injection of noise in the gradient. This algorithmic fix comes with theoretical and empirical evidence. The practical implementation of the flow is straightforward, since both the MMD and its gradient have simple closed-form expressions, which can be easily estimated with samples.

Gradient descent-based optimization methods underpin the parameter training which results in the impressive results now found when testing neural networks. Introducing stochasticity is key to their success in practical problems, and there is some understanding of the role of stochastic gradient descent in this context. Momentum modifications of gradient descent such as Polyak's Heavy Ball method (HB) and Nesterov's method of accelerated gradients (NAG), are also widely adopted. In this work our focus is on understanding the role of momentum in the training of neural networks, concentrating on the common situation in which the momentum contribution is fixed at each step of the algorithm; to expose the ideas simply we work in the deterministic setting. We show that, contrary to popular belief, standard implementations of fixed momentum methods do no more than act to rescale the learning rate. We achieve this by showing that the momentum method converges to a gradient flow, with a momentum-dependent time-rescaling, using the method of modified equations from numerical analysis. Furthermore we show that the momentum method admits an exponentially attractive invariant manifold on which the dynamics reduces to a gradient flow with respect to a modified loss function, equal to the original one plus a small perturbation.

Arguably the most fundamental problem of statistics is that of estimating the expected value µ of a random variable X based on a sample of n independent, identically distributed draws from the distribution of X. The obvious choice of an estimator is, of course, the empirical mean. Its properties are well understood by classical results of probability theory. However, from the early days on, statisticians have been concerned about the quality of the empirical mean, especially when the distribution may be heavy-tailed or outliers may be present in the data. This concern gave rise to the area of robust statistics that addresses the problem of mean estimation (and other statistical problems) for such data.

Goal-oriented reinforcement learning has recently been a practical framework for robotic manipulation tasks, in which an agent is required to reach a certain goal defined by a function on the state space. However, the sparsity of such reward definition makes traditional reinforcement learning algorithms very inefficient. Hindsight Experience Replay (HER), a recent advance, has greatly improved sample efficiency and practical applicability for such problems. It exploits previous replays by constructing imaginary goals in a simple heuristic way, acting like an implicit curriculum to alleviate the challenge of sparse reward signal. In this paper, we introduce Hindsight Goal Generation (HGG), a novel algorithmic framework that generates valuable hindsight goals which are easy for an agent to achieve in the short term and are also potential for guiding the agent to reach the actual goal in the long term. We have extensively evaluated our goal generation algorithm on a number of robotic manipulation tasks and demonstrated substantially improvement over the original HER in terms of sample efficiency.