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Many applications comprise of sequences of event data with the time of occurrence of the events. Models for predicting time of occurrence play a significant role in a diverse set of applications like social networks, financial transactions, healthcare, and human mobility. Recent works have introduced neural network based point process for modeling event-times, and were shown to provide state-of-the-art performance in predicting event-times. However, neural networks are poor at quantifying predictive uncertainty and tend to produce overconfident predictions during extrapolation. A proper uncertainty quantification is crucial for many practical applications. Therefore, we propose a novel point process model, Bayesian Neural Hawkes process which leverages uncertainty modelling capability of Bayesian models and generalization capability of the neural networks. The model is capable of predicting epistemic uncertainty over the event occurrence time and its effectiveness is demonstrated for on simulated and real-world datasets.

The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In recent years several continuous limits in the number of iteration and particles have been performed in order to study properties of the method. In particular, a one--dimensional linear stability analysis reveals possible drawbacks in the phase space of moments provided by the continuous limits of the EKI, but observed also in the multi--dimensional setting. In this work we address this issue by introducing a stabilization of the dynamics which leads to a method with globally asymptotically stable solutions. We illustrate the performance of the stabilized version by using test inverse problems from the literature and comparing it with the classical continuous limit formulation of the method.

In this paper, we propose Latent Relation Language Models (LRLMs), a class of language models that parameterizes the joint distribution over the words in a document and the entities that occur therein via knowledge graph relations. This model has a number of attractive properties: it not only improves language modeling performance, but is also able to annotate the posterior probability of entity spans for a given text through relations. Experiments demonstrate empirical improvements over both a word-based baseline language model and a previous approach that incorporates knowledge graph information. Qualitative analysis further demonstrates the proposed model's ability to learn to predict appropriate relations in context.

This paper proposes a neural sequence-to-sequence text-to-speech (TTS) model which can control latent attributes in the generated speech that are rarely annotated in the training data, such as speaking style, accent, background noise, and recording conditions. The model is formulated as a conditional generative model based on the variational autoencoder (VAE) framework, with two levels of hierarchical latent variables. The first level is a categorical variable, which represents attribute groups (e.g. clean/noisy) and provides interpretability. The second level, conditioned on the first, is a multivariate Gaussian variable, which characterizes specific attribute configurations (e.g. noise level, speaking rate) and enables disentangled fine-grained control over these attributes. This amounts to using a Gaussian mixture model (GMM) for the latent distribution. Extensive evaluation demonstrates its ability to control the aforementioned attributes. In particular, we train a high-quality controllable TTS model on real found data, which is capable of inferring speaker and style attributes from a noisy utterance and use it to synthesize clean speech with controllable speaking style.

The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails to model data with a latent hyperspherical structure. To address this issue we propose using a von Mises-Fisher (vMF) distribution instead, leading to a hyperspherical latent space. Through a series of experiments we show how such a hyperspherical VAE, or $\mathcal{S}$-VAE, is more suitable for capturing data with a hyperspherical latent structure, while outperforming a normal, $\mathcal{N}$-VAE, in low dimensions on other data types.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.

Topic models have been widely explored as probabilistic generative models of documents. Traditional inference methods have sought closed-form derivations for updating the models, however as the expressiveness of these models grows, so does the difficulty of performing fast and accurate inference over their parameters. This paper presents alternative neural approaches to topic modelling by providing parameterisable distributions over topics which permit training by backpropagation in the framework of neural variational inference. In addition, with the help of a stick-breaking construction, we propose a recurrent network that is able to discover a notionally unbounded number of topics, analogous to Bayesian non-parametric topic models. Experimental results on the MXM Song Lyrics, 20NewsGroups and Reuters News datasets demonstrate the effectiveness and efficiency of these neural topic models.

Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.

We propose a new approach to inverse reinforcement learning (IRL) based on the deep Gaussian process (deep GP) model, which is capable of learning complicated reward structures with few demonstrations. Our model stacks multiple latent GP layers to learn abstract representations of the state feature space, which is linked to the demonstrations through the Maximum Entropy learning framework. Incorporating the IRL engine into the nonlinear latent structure renders existing deep GP inference approaches intractable. To tackle this, we develop a non-standard variational approximation framework which extends previous inference schemes. This allows for approximate Bayesian treatment of the feature space and guards against overfitting. Carrying out representation and inverse reinforcement learning simultaneously within our model outperforms state-of-the-art approaches, as we demonstrate with experiments on standard benchmarks ("object world","highway driving") and a new benchmark ("binary world").

In this paper, we develop the continuous time dynamic topic model (cDTM). The cDTM is a dynamic topic model that uses Brownian motion to model the latent topics through a sequential collection of documents, where a "topic" is a pattern of word use that we expect to evolve over the course of the collection. We derive an efficient variational approximate inference algorithm that takes advantage of the sparsity of observations in text, a property that lets us easily handle many time points. In contrast to the cDTM, the original discrete-time dynamic topic model (dDTM) requires that time be discretized. Moreover, the complexity of variational inference for the dDTM grows quickly as time granularity increases, a drawback which limits fine-grained discretization. We demonstrate the cDTM on two news corpora, reporting both predictive perplexity and the novel task of time stamp prediction.