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.

Unlike human speakers, typical text-to-speech (TTS) systems are unable to produce multiple distinct renditions of a given sentence. This has previously been addressed by adding explicit external control. In contrast, generative models are able to capture a distribution over multiple renditions and thus produce varied renditions using sampling. Typical neural TTS models learn the average of the data because they minimise mean squared error. In the context of prosody, taking the average produces flatter, more boring speech: an "average prosody". A generative model that can synthesise multiple prosodies will, by design, not model average prosody. We use variational autoencoders (VAE) which explicitly place the most "average" data close to the mean of the Gaussian prior. We propose that by moving towards the tails of the prior distribution, the model will transition towards generating more idiosyncratic, varied renditions. Focusing here on intonation, we investigate the trade-off between naturalness and intonation variation and find that typical acoustic models can either be natural, or varied, but not both. However, sampling from the tails of the VAE prior produces much more varied intonation than the traditional approaches, whilst maintaining the same level of naturalness.

In experimental design, we are given $n$ vectors in $d$ dimensions, and our goal is to select $k\ll n$ of them to perform expensive measurements, e.g., to obtain labels/responses, for a linear regression task. Many statistical criteria have been proposed for choosing the optimal design, with popular choices including A- and D-optimality. If prior knowledge is given, typically in the form of a $d\times d$ precision matrix $\mathbf A$, then all of the criteria can be extended to incorporate that information via a Bayesian framework. In this paper, we demonstrate a new fundamental connection between Bayesian experimental design and determinantal point processes, the latter being widely used for sampling diverse subsets of data. We use this connection to develop new efficient algorithms for finding $(1+\epsilon)$-approximations of optimal designs under four optimality criteria: A, C, D and V. Our algorithms can achieve this when the desired subset size $k$ is $\Omega(\frac{d_{\mathbf A}}{\epsilon} + \frac{\log 1/\epsilon}{\epsilon^2})$, where $d_{\mathbf A}\leq d$ is the $\mathbf A$-effective dimension, which can often be much smaller than $d$. Our results offer direct improvements over a number of prior works, for both Bayesian and classical experimental design, in terms of algorithm efficiency, approximation quality, and range of applicable criteria.

The desire to run neural networks on low-capacity edge devices has led to the development of a wealth of compression techniques. Moonshine (Crowley et al., 2018a) is a simple and powerful example of this: one takes a large pre-trained network and substitutes each of its convolutional blocks with a selected cheap alternative block, then distills the resultant network with the original. However, not all blocks are created equally; for a required parameter budget there may exist a potent combination of many different cheap blocks. In this work, we find these by developing BlockSwap: an algorithm for choosing networks with interleaved block types by passing a single minibatch of training data through randomly initialised networks and gauging their Fisher potential. We show that block-wise cheapening yields more accurate networks than single block-type networks across a spectrum of parameter budgets. Code is available at https://github.com/BayesWatch/

Unsupervised domain adaptation aims to transfer the classifier learned from the source domain to the target domain in an unsupervised manner. With the help of target pseudo-labels, aligning class-level distributions and learning the classifier in the target domain are two widely used objectives. Existing methods often separately optimize these two individual objectives, which makes them suffer from the neglect of the other. However, optimizing these two aspects together is not trivial. To alleviate the above issues, we propose a novel method that jointly optimizes semantic domain alignment and target classifier learning in a holistic way. The joint optimization mechanism can not only eliminate their weaknesses but also complement their strengths. The theoretical analysis also verifies the favor of the joint optimization mechanism. Extensive experiments on benchmark datasets show that the proposed method yields the best performance in comparison with the state-of-the-art unsupervised domain adaptation methods.

Convolutional neural networks (CNN) are generally designed with a heuristic initialization of network architecture and trained for a certain task. This often leads to overparametrization after learning and induces redundancy in the information flow paths within the network. This robustness and reliability is at the increased cost of redundant computations. Several methods have been proposed which leverage metrics that quantify the redundancy in each layer. However, layer-wise evaluation in these methods disregards the long-range redundancy which exists across depth on account of the distributed nature of the features learned by the model. In this paper, we propose (i) a mechanism to empirically demonstrate the robustness in performance of a CNN on account of redundancy across its depth, (ii) a method to identify the systemic redundancy in response of a CNN across depth using the understanding of unit impulse response, we subsequently demonstrate use of these methods to interpret redundancy in few networks as example. These techniques provide better insights into the internal dynamics of a CNN