Time series models such as dynamical systems are frequently fitted to a cohort of data, ignoring variation between individual entities such as patients. In this paper we show how these models can be personalised to an individual level while retaining statistical power, via use of multi-task learning (MTL). To our knowledge this is a novel development of MTL which applies to time series both with and without control inputs. The modelling framework is demonstrated on a physiological drug response problem which results in improved predictive accuracy and uncertainty estimation over existing state-of-the-art models.

Understanding the nature of representations learned by supervised machine learning models is a significant goal in the machine learning community. We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features conditioned on intermediate model representations. Insights into the invariances learned by supervised models can be gained by viewing samples from these inversion models. In addition, we can use these inversion models to estimate the mutual information between a model's inputs and its intermediate representations, thus quantifying the amount of information preserved by the network at different stages. Using this method we examine the types of information preserved at different layers of convolutional neural networks, and explore the invariances induced by different architectural choices. Finally we show that the mutual information between inputs and network layers decreases over the course of training, supporting recent work by Shwartz-Ziv and Tishby (2017) on the information bottleneck theory of deep learning.

Latent variable models can be used to probabilistically "fill-in" missing data entries. The variational autoencoder architecture (Kingma and Welling, 2014; Rezende et al., 2014) includes a "recognition" or "encoder" network that infers the latent variables given the data variables. However, it is not clear how to handle missing data variables in this network. We show how to calculate exactly the latent posterior distribution for the factor analysis (FA) model in the presence of missing data, and note that this solution exhibits a non-trivial dependence on the pattern of missingness. Experiments compare the effectiveness of various approaches to filling in the missing data.

Model criticism is usually carried out by assessing if replicated data generated under the fitted model looks similar to the observed data, see e.g. Gelman, Carlin, Stern, and Rubin (2004, p. 165). This paper presents a method for latent variable models by pulling back the data into the space of latent variables, and carrying out model criticism in that space. Making use of a model's structure enables a more direct assessment of the assumptions made in the prior and likelihood. We demonstrate the method with examples of model criticism in latent space applied to ANOVA, factor analysis, linear dynamical systems and Gaussian processes.

Bedside monitors in Intensive Care Units (ICUs) frequently sound incorrectly, slowing response times and desensitising nurses to alarms (Chambrin, 2001), causing true alarms to be missed (Hug et al., 2011). We compare sliding window predictors with recurrent predictors to classify patient state-of-health from ICU multivariate time series; we report slightly improved performance for the RNN for three out of four targets.

This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a mid-level image representation, called a region tree, in which regions are recursively split into subregions until superpixels are reached. Given the region tree, image segmentation is formalized as sampling cuts in the tree from the model. Inference for the cuts is exact, and formulated using dynamic programming. Our tree-cut model can be tuned to sample segmentations at a particular scale of interest out of many possible multiscale image segmentations. This generalizes the common notion that there should be only one correct segmentation per image. Also, it allows moving beyond the standard single-scale evaluation, where the segmentation result for an image is averaged against the corresponding set of coarse and fine human annotations, to conduct a scale-specific evaluation. Our quantitative results are comparable to those of the leading gPb-owt-ucm method, with the notable advantage that we additionally produce a distribution over all possible tree-consistent segmentations of the image.

Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a dataset of n examples. Several approximation methods have been proposed, but there is a lack of understanding of the relative merits of the different approximations, and in what situations they are most useful. We recommend assessing the quality of the predictions obtained as a function of the compute time taken, and comparing to standard baselines (e.g., Subset of Data and FITC). We empirically investigate four different approximation algorithms on four different prediction problems, and make our code available to encourage future comparisons.

We consider data which are images containing views of multiple objects. Our task is to learn about each of the objects present in the images. This task can be approached as a factorial learning problem, where each image must be explained by instantiating a model for each of the objects present with the correct instantiation parameters. A major problem with learning a factorial model is that as the number of objects increases, there is a combinatorial explosion of the number of configurations that need to be considered. We develop a method to extract object models sequentially from the data by making use of a robust statistical method, thus avoiding the combinatorial explosion, and present results showing successful extraction of objects from real images.

We consider data which are images containing views of multiple objects. Our task is to learn about each of the objects present in the images. This task can be approached as a factorial learning problem, where each image must be explained by instantiating a model for each of the objects present with the correct instantiation parameters. A major problem with learning a factorial model is that as the number of objects increases, there is a combinatorial explosion of the number of configurations that need to be considered. We develop a method to extract object models sequentially from the data by making use of a robust statistical method, thus avoiding the combinatorial explosion, and present results showing successful extraction of objects from real images.

We consider data which are images containing views of multiple objects. Our task is to learn about each of the objects present in the images. This task can be approached as a factorial learning problem, where each image must be explained by instantiating a model for each of the objects present with the correct instantiation parameters. A major problem with learning a factorial model is that as the number of objects increases, there is a combinatorial explosion of the number of configurations that need to be considered. We develop a method to extract object models sequentially from the data by making use of a robust statistical method, thus avoiding thecombinatorial explosion, and present results showing successful extraction of objects from real images.