The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. In this article, we extend our recent mathematical formalization of this framework by providing quantitative mathematical definitions for measuring relations between concepts: We develop formal ways for computing concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational capabilities of our formalization and makes it the most thorough and comprehensive formalization of conceptual spaces developed so far.

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likelihoods by the model. Our approach provides an arbitrarily accurate approximation of the true posterior at the expense of extra computation. Using a new gradient estimator for the resulting unnormalized proposal distribution, we achieve average improvements of 3.71 nats and 0.21 nats over state-of-the-art single-sample and multi-sample alternatives respectively for estimating marginal log-likelihoods using sigmoid belief networks on the MNIST dataset.

We present an end-to-end trained memory system that quickly adapts to new data and generates samples like them. Inspired by Kanerva's sparse distributed memory, it has a robust distributed reading and writing mechanism. The memory is analytically tractable, which enables optimal on-line compression via a Bayesian update-rule. We formulate it as a hierarchical conditional generative model, where memory provides a rich data-dependent prior distribution. Consequently, the top-down memory and bottom-up perception are combined to produce the code representing an observation. Empirically, we demonstrate that the adaptive memory significantly improves generative models trained on both the Omniglot and CIFAR datasets. Compared with the Differentiable Neural Computer (DNC) and its variants, our memory model has greater capacity and is significantly easier to train.

All reinforcement learning algorithms must handle the trade-off between exploration and exploitation. Many state-of-the-art deep reinforcement learning methods use noise in the action selection, such as Gaussian noise in policy gradient methods or $\epsilon$-greedy in Q-learning. While these methods are appealing due to their simplicity, they do not explore the state space in a methodical manner. We present an approach that uses a model to derive reward bonuses as a means of intrinsic motivation to improve model-free reinforcement learning. A key insight of our approach is that this dynamics model can be learned in the latent feature space of a value function, representing the dynamics of the agent and the environment. This method is both theoretically grounded and computationally advantageous, permitting the efficient use of Bayesian information-theoretic methods in high-dimensional state spaces. We evaluate our method on several continuous control tasks, focusing on improving exploration.

Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have low detection power for subtle, emerging irregularities. Additionally, recent detection techniques based on subset scanning make strong independence assumptions and suffer degraded performance in correlated data. We introduce methods for identifying anomalous patterns in non-iid data by combining Gaussian processes with novel log-likelihood ratio statistic and subset scanning techniques. Our approaches are powerful, interpretable, and can integrate information across multiple data streams. We illustrate their performance on numeric simulations and three open source spatiotemporal datasets of opioid overdose deaths, 311 calls, and storm reports.

We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a set of transition rate matrices that, for reasons of conjugacy, is easy to find. To determine the hyperparameters for our set of priors, we reconsider the problem in discrete time, where we can use the well-known Imprecise Dirichlet Model. In particular, we show how the limit of the resulting discrete-time estimators is a continuous-time estimator. It corresponds to a specific choice of hyperparameters and has an exceptionally simple closed-form expression.

In the cost per click (CPC) pricing model, an advertiser pays an ad network only when a user clicks on an ad; in turn, the ad network gives a share of that revenue to the publisher where the ad was impressed. Still, advertisers may be unsatisfied with ad networks charging them for "valueless" clicks, or so-called accidental clicks. [...] Charging advertisers for such clicks is detrimental in the long term as the advertiser may decide to run their campaigns on other ad networks. In addition, machine-learned click models trained to predict which ad will bring the highest revenue may overestimate an ad click-through rate, and as a consequence negatively impacting revenue for both the ad network and the publisher. In this work, we propose a data-driven method to detect accidental clicks from the perspective of the ad network. We collect observations of time spent by users on a large set of ad landing pages - i.e., dwell time. We notice that the majority of per-ad distributions of dwell time fit to a mixture of distributions, where each component may correspond to a particular type of clicks, the first one being accidental. We then estimate dwell time thresholds of accidental clicks from that component. Using our method to identify accidental clicks, we then propose a technique that smoothly discounts the advertiser's cost of accidental clicks at billing time. Experiments conducted on a large dataset of ads served on Yahoo mobile apps confirm that our thresholds are stable over time, and revenue loss in the short term is marginal. We also compare the performance of an existing machine-learned click model trained on all ad clicks with that of the same model trained only on non-accidental clicks. There, we observe an increase in both ad click-through rate (+3.9%) and revenue (+0.2%) on ads served by the Yahoo Gemini network when using the latter. [...]

Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorised likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This approximation is clearly limited as demonstrated by observing a residual image from a VAE reconstruction, which often possess a high level of structure. This paper demonstrates a novel scheme to incorporate a structured Gaussian likelihood prediction network within the VAE that allows the residual correlations to be modelled. Our novel architecture, with minimal increase in complexity, incorporates the covariance matrix prediction within the VAE. We also propose a new mechanism for allowing structured uncertainty on color images. Furthermore, we provide a scheme for effectively training this model, and include some suggestions for improving performance in terms of efficiency or modelling longer range correlations. The advantage of our approach is illustrated on the CelebA face data and the LSUN outdoor churches dataset, with substantial improvements in terms of samples over traditional VAE and better reconstructions.

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier features. This sparse representation induces global rather than local constraints on the function space and is computationally efficient. This allows us to formulate a grid-free approximation that scales well with the number of data points and the size of the domain. We demonstrate that this allows MCMC approximations to the non-Gaussian posterior. We also find that, in practice, Fourier features have more consistent optimization behavior than previous approaches. Our approximate Bayesian method can fit over 100,000 events with complex spatiotemporal patterns in three dimensions on a single GPU.

Presbyterian reverend Thomas Bayes had no reason to suspect he'd make any lasting contribution to humankind. Born in England at the beginning of the 18th century, Bayes was a quiet and questioning man. He published only two works in his lifetime. In 1731, he wrote a defense of God's--and the British monarchy's--"divine benevolence," and in 1736, an anonymous defense of the logic of Isaac Newton's calculus. Yet an argument he wrote before his death in 1761 would shape the course of history.