We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.

Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on regular grids, applicable to a general set of spaces. This is helpful whenever an algorithm *explores* to reduce uncertainty, such as in active learning, Bayesian optimization, reinforcement learning, and marginalization in graphical models. To draw samples from a DPP in practice, existing literature focuses on approximate schemes of low cost, or comparably inefficient exact algorithms like rejection sampling. We point out that, for many settings of relevance to machine learning, it is also possible to draw *exact* samples from DPPs on continuous domains. We start from an intuitive example on the real line, which is then generalized to multivariate real vector spaces. We also compare to previously studied approximations, showing that exact sampling, despite higher cost, can be preferable where precision is needed.

We describe our experience in the development of a probabilistic network for the diagnosis of acute cardiopulmonary diseases. A panel of expert physicians collaborated to specify the qualitative part, that is a directed acyclic graph defining a factorization of the joint probability distribution of domain variables. The quantitative part, that is the set of all conditional probability distributions defined by each factor, was estimated in the Bayesian paradigm: we applied a special formal representation, characterized by a low number of parameters and a parameterization intelligible for physicians, elicited the joint prior distribution of parameters from medical experts, and updated it by conditioning on a dataset of hospital patient records using Markov Chain Monte Carlo simulation. Refinement was cyclically performed until the probabilistic network provided satisfactory Concordance Index values for a selection of acute diseases and reasonable inference on six fictitious patient cases. The probabilistic network can be employed to perform medical diagnosis on a total of 63 diseases (38 acute and 25 chronic) on the basis of up to 167 patient findings.

Bibliographic analysis considers the author's research areas, the citation network and the paper content among other things. In this paper, we combine these three in a topic model that produces a bibliographic model of authors, topics and documents, using a nonparametric extension of a combination of the Poisson mixed-topic link model and the author-topic model. This gives rise to the Citation Network Topic Model (CNTM). We propose a novel and efficient inference algorithm for the CNTM to explore subsets of research publications from CiteSeerX. The publication datasets are organised into three corpora, totalling to about 168k publications with about 62k authors. The queried datasets are made available online. In three publicly available corpora in addition to the queried datasets, our proposed model demonstrates an improved performance in both model fitting and document clustering, compared to several baselines. Moreover, our model allows extraction of additional useful knowledge from the corpora, such as the visualisation of the author-topics network. Additionally, we propose a simple method to incorporate supervision into topic modelling to achieve further improvement on the clustering task.

The Dirichlet process and its extension, the Pitman-Yor process, are stochastic processes that take probability distributions as a parameter. These processes can be stacked up to form a hierarchical nonparametric Bayesian model. In this article, we present efficient methods for the use of these processes in this hierarchical context, and apply them to latent variable models for text analytics. In particular, we propose a general framework for designing these Bayesian models, which are called topic models in the computer science community. We then propose a specific nonparametric Bayesian topic model for modelling text from social media. We focus on tweets (posts on Twitter) in this article due to their ease of access. We find that our nonparametric model performs better than existing parametric models in both goodness of fit and real world applications.

We describe a method for parameter estimation in bipartite probabilistic graphical models for joint prediction of clinical conditions from the electronic medical record. The method does not rely on the availability of gold-standard labels, but rather uses noisy labels, called anchors, for learning. We provide a likelihood-based objective and a moments-based initialization that are effective at learning the model parameters. The learned model is evaluated in a task of assigning a heldout clinical condition to patients based on retrospective analysis of the records, and outperforms baselines which do not account for the noisiness in the labels or do not model the conditions jointly.

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. Gaussian processes (GPs) provide a Bayesian approach to learning such problems in a kernel based framework. We develop Gaussian process models based on pseudo-likelihood to solve sequence labeling problems. The pseudo-likelihood model enables one to capture multiple dependencies among the output components of the sequence without becoming computationally intractable. We use an efficient variational Gaussian approximation method to perform inference in the proposed model. We also provide an iterative algorithm which can effectively make use of the information from the neighboring labels to perform prediction. The ability to capture multiple dependencies makes the proposed approach useful for a wide range of sequence labeling problems. Numerical experiments on some sequence labeling problems in natural language processing demonstrate the usefulness of the proposed approach.

Non-stationary continuous time Bayesian networks are introduced. They allow the parents set of each node to change over continuous time. Three settings are developed for learning non-stationary continuous time Bayesian networks from data: known transition times, known number of epochs and unknown number of epochs. A score function for each setting is derived and the corresponding learning algorithm is developed. A set of numerical experiments on synthetic data is used to compare the effectiveness of non-stationary continuous time Bayesian networks to that of non-stationary dynamic Bayesian networks. Furthermore, the performance achieved by non-stationary continuous time Bayesian networks is compared to that achieved by state-of-the-art algorithms on four real-world datasets, namely drosophila, saccharomyces cerevisiae, songbird and macroeconomics.

The goal of this thesis is to investigate the potential of predictive modelling for football injuries. This work was conducted in close collaboration with Tottenham Hotspurs FC (THFC), the PGA European tour and the participation of Wolverhampton Wanderers (WW). Three investigations were conducted: 1. Predicting the recovery time of football injuries using the UEFA injury recordings: The UEFA recordings is a common standard for recording injuries in professional football. For this investigation, three datasets of UEFA injury recordings were available. Different machine learning algorithms were used in order to build a predictive model. The performance of the machine learning models is then improved by using feature selection conducted through correlation-based subset feature selection and random forests. 2. Predicting injuries in professional football using exposure records: The relationship between exposure (in training hours and match hours) in professional football athletes and injury incidence was studied. A common problem in football is understanding how the training schedule of an athlete can affect the chance of him getting injured. The task was to predict the number of days a player can train before he gets injured. 3. Predicting intrinsic injury incidence using in-training GPS measurements: A significant percentage of football injuries can be attributed to overtraining and fatigue. GPS data collected during training sessions might provide indicators of fatigue, or might be used to detect very intense training sessions which can lead to overtraining. This research used GPS data gathered during training sessions of the first team of THFC, in order to predict whether an injury would take place during a week.

Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables is difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure called globally sparse probabilistic PCA (GSPPCA) that allows to obtain several sparse components with the same sparsity pattern. This allows the practitioner to identify the original variables which are relevant to describe the data. To this end, using Roweis' probabilistic interpretation of PCA and a Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. To avoid the drawbacks of discrete model selection, a simple relaxation of this framework is presented. It allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood is then maximized over this path. This approach is illustrated on real and synthetic data sets. In particular, using unlabeled microarray data, GSPPCA infers much more relevant gene subsets than traditional sparse PCA algorithms.