Similarity measure for sparse time course data based on Gaussian processes

We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in sparse time series, such as those found in various biological settings, e.g., gene transcriptomics. We show that the GP measure is equivalent to the Euclidean distance when the noise variance in the GP is negligible compared to the noise variance of the signal. Our numerical experiments on both synthetic and real data show improved performance of the GP similarity when used in conjunction with two distance-based clustering methods.

Graph-based Topic Extraction from Vector Embeddings of Text Documents: Application to a Corpus of News Articles

Production of news content is growing at an astonishing rate. To help manage and monitor the sheer amount of text, there is an increasing need to develop efficient methods that can provide insights into emerging content areas, and stratify unstructured corpora of text into `topics' that stem intrinsically from content similarity. Here we present an unsupervised framework that brings together powerful vector embeddings from natural language processing with tools from multiscale graph partitioning that can reveal natural partitions at different resolutions without making a priori assumptions about the number of clusters in the corpus. We show the advantages of graph-based clustering through end-to-end comparisons with other popular clustering and topic modelling methods, and also evaluate different text vector embeddings, from classic Bag-of-Words to Doc2Vec to the recent transformers based model Bert. This comparative work is showcased through an analysis of a corpus of US news coverage during the presidential election year of 2016.

BART-based inference for Poisson processes

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non parametric regression and classification. Here we introduce a BART scheme for estimating the intensity of inhomogeneous Poisson Processes. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. Our approach enables full posterior inference of the intensity in a nonparametric regression setting. We demonstrate the performance of our scheme through simulation studies on synthetic and real datasets in one and two dimensions, and compare our approach to alternative approaches.

Geometric graphs from data to aid classification tasks with graph convolutional networks

Classification is a classic problem in data analytics and has been approached from many different angles, including machine learning. Traditionally, machine learning methods classify samples based solely on their features. This paradigm is evolving. Recent developments on Graph Convolutional Networks have shown that explicitly using information not directly present in the features to represent a type of relationship between samples can improve the classification performance by a significant margin. However, graphs are not often immediately present in data sets, thus limiting the applicability of Graph Convolutional Networks. In this paper, we explore if graphs extracted from the features themselves can aid classification performance. First, we show that constructing optimal geometric graphs directly from data features can aid classification tasks on both synthetic and real-world data sets from different domains. Second, we introduce two metrics to characterize optimal graphs: i) by measuring the alignment between the subspaces spanned by the features convolved with the graph and the ground truth; and ii) ratio of class separation in the output activations of Graph Convolutional Networks: this shows that the optimal graph maximally separates classes. Finally, we find that sparsifying the optimal graph can potentially improve classification performance.

Semi-supervised classification on graphs using explicit diffusion dynamics

Classification tasks based on feature vectors can be significantly improved by including within deep learning a graph that summarises pairwise relationships between the samples. Intuitively, the graph acts as a conduit to channel and bias the inference of class labels. Here, we study classification methods that consider the graph as the originator of an explicit graph diffusion. We show that appending graph diffusion to feature-based learning as an \textit{a posteriori} refinement achieves state-of-the-art classification accuracy. This method, which we call Graph Diffusion Reclassification (GDR), uses overshooting events of a diffusive graph dynamics to reclassify individual nodes. The method uses intrinsic measures of node influence, which are distinct for each node, and allows the evaluation of the relationship and importance of features and graph for classification. We also present diff-GCN, a simple extension of Graph Convolutional Neural Network (GCN) architectures that leverages explicit diffusion dynamics, and allows the natural use of directed graphs. To showcase our methods, we use benchmark datasets of documents with associated citation data.

Graph-based data clustering via multiscale community detection

We present a graph-theoretical approach to data clustering, which combines the creation of a graph from the data with Markov Stability, a multiscale community detection framework. We show how the multiscale capabilities of the method allow the estimation of the number of clusters, as well as alleviating the sensitivity to the parameters in graph construction. We use both synthetic and benchmark real datasets to compare and evaluate several graph construction methods and clustering algorithms, and show that multiscale graph-based clustering achieves improved performance compared to popular clustering methods without the need to set externally the number of clusters.

Extracting information from free text through unsupervised graph-based clustering: an application to patient incident records

The large volume of text in electronic healthcare records often remains underused due to a lack of methodologies to extract interpretable content. Here we present an unsupervised framework for the analysis of free text that combines text-embedding with paragraph vectors and graph-theoretical multiscale community detection. We analyse text from a corpus of patient incident reports from the National Health Service in England to find content-based clusters of reports in an unsupervised manner and at different levels of resolution. Our unsupervised method extracts groups with high intrinsic textual consistency and compares well against categories hand-coded by healthcare personnel. We also show how to use our content-driven clusters to improve the supervised prediction of the degree of harm of the incident based on the text of the report. Finally, we discuss future directions to monitor reports over time, and to detect emerging trends outside pre-existing categories.

Learning spatiotemporal signals using a recurrent spiking network that discretizes time

Learning to produce spatiotemporal sequences is a common task the brain has to solve. While many sequential behaviours differ superficially, the underlying organization of the computation might be similar. The way the brain learns these tasks remains unknown as current computational models do not typically use realistic biologically-plausible learning. Here, we propose a model where a spiking recurrent network drives a read-out layer. Plastic synapses follow common Hebbian learning rules. The dynamics of the recurrent network is constrained to encode time while the read-out neurons encode space. Space is then linked with time through Hebbian learning. Here we demonstrate that the model is able to learn spatiotemporal dynamics on a timescale that is behaviorally relevant. Learned sequences are robustly replayed during a regime of spontaneous activity.

Quantifying the alignment of graph and features in deep learning

We show that the classification performance of Graph Convolutional Networks is related to the alignment between features, graph and ground truth, which we quantify using a subspace alignment measure corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces associated with features, graph and ground truth. The proposed measure is based on the principal angles between subspaces and has both spectral and geometrical interpretations. We showcase the relationship between the subspace alignment measure and the classification performance through the study of limiting cases of Graph Convolutional Networks as well as systematic randomizations of both features and graph structure applied to a constructive example and several examples of citation networks of different origin. The analysis also reveals the relative importance of the graph and features for classification purposes.

From Free Text to Clusters of Content in Health Records: An Unsupervised Graph Partitioning Approach

Electronic Healthcare records contain large volumes of unstructured data in different forms. Free text constitutes a large portion of such data, yet this source of richly detailed information often remains under-used in practice because of a lack of suitable methodologies to extract interpretable content in a timely manner. Here we apply network-theoretical tools to the analysis of free text in Hospital Patient Incident reports in the English National Health Service, to find clusters of reports in an unsupervised manner and at different levels of resolution based directly on the free text descriptions contained within them. To do so, we combine recently developed deep neural network text-embedding methodologies based on paragraph vectors with multi-scale Markov Stability community detection applied to a similarity graph of documents obtained from sparsified text vector similarities. We showcase the approach with the analysis of incident reports submitted in Imperial College Healthcare NHS Trust, London. The multiscale community structure reveals levels of meaning with different resolution in the topics of the dataset, as shown by relevant descriptive terms extracted from the groups of records, as well as by comparing a posteriori against hand-coded categories assigned by healthcare personnel. Our content communities exhibit good correspondence with well-defined hand-coded categories, yet our results also provide further medical detail in certain areas as well as revealing complementary descriptors of incidents beyond the external classification. We also discuss how the method can be used to monitor reports over time and across different healthcare providers, and to detect emerging trends that fall outside of pre-existing categories.