Learning predictive models from small high-dimensional data sets is a key problem in high-dimensional statistics. Expert knowledge elicitation can help, and a strong line of work focuses on directly eliciting informative prior distributions for parameters. This either requires considerable statistical expertise or is laborious, as the emphasis has been on accuracy and not on efficiency of the process. Another line of work queries about importance of features one at a time, assuming them to be independent and hence missing covariance information. In contrast, we propose eliciting expert knowledge about pairwise feature similarities, to borrow statistical strength in the predictions, and using sequential decision making techniques to minimize the effort of the expert. Empirical results demonstrate improvement in predictive performance on both simulated and real data, in high-dimensional linear regression tasks, where we learn the covariance structure with a Gaussian process, based on sequential elicitation.

Recently much attention has been paid to deep generative models, since they have been used to great success for variational inference, generation of complex data types, and more. In most all of these settings, the goal has been to find a particular member of that model family: optimized parameters index a distribution that is close (via a divergence or classification metric) to a target distribution. Much less attention, however, has been paid to the problem of learning a model itself. Here we introduce a two-network architecture and optimization procedure for learning intractable exponential family models (not a single distribution from those models). These exponential families are learned accurately, allowing operations like posterior inference to be executed directly and generically with an input choice of natural parameters, rather than performing inference via optimization for each particular distribution within that model.

Deep fundamental factor models are developed to interpret and capture non-linearity, interaction effects and non-parametric shocks in financial econometrics. Uncertainty quantification provides interpretability with interval estimation, ranking of factor importances and estimation of interaction effects. Estimating factor realizations under either homoscedastic or heteroscedastic error is also available. With no hidden layers we recover a linear factor model and for one or more hidden layers, uncertainty bands for the sensitivity to each input naturally arise from the network weights. To illustrate our methodology, we construct a six-factor model of assets in the S\&P 500 index and generate information ratios that are three times greater than generalized linear regression. We show that the factor importances are materially different from the linear factor model when accounting for non-linearity. Finally, we conclude with directions for future research

This report first provides a brief overview of a number of supervised learning algorithms for regression tasks. Among those are neural networks, regression trees, and the recently introduced Nexting. Nexting has been presented in the context of reinforcement learning where it was used to predict a large number of signals at different timescales. In the second half of this report, we apply the algorithms to historical weather data in order to evaluate their suitability to forecast a local weather trend. Our experiments did not identify one clearly preferable method, but rather show that choosing an appropriate algorithm depends on the available side information. For slowly varying signals and a proficient number of training samples, Nexting achieved good results in the studied cases.

We present a modelling framework for the investigation of prototype-based classifiers in non-stationary environments. Specifically, we study Learning Vector Quantization (LVQ) systems trained from a stream of high-dimensional, clustered data.We consider standard winner-takes-all updates known as LVQ1. Statistical properties of the input data change on the time scale defined by the training process. We apply analytical methods borrowed from statistical physics which have been used earlier for the exact description of learning in stationary environments. The suggested framework facilitates the computation of learning curves in the presence of virtual and real concept drift. Here we focus on timedependent class bias in the training data. First results demonstrate that, while basic LVQ algorithms are suitable for the training in non-stationary environments, weight decay as an explicit mechanism of forgetting does not improve the performance under the considered drift processes.

Machine learning algorithms are increasingly involved in sensitive decision-making process with adversarial implications on individuals. This paper presents mdfa, an approach that identifies the characteristics of the victims of a classifier's discrimination. We measure discrimination as a violation of multi-differential fairness. Multi-differential fairness is a guarantee that a black box classifier's outcomes do not leak information on the sensitive attributes of a small group of individuals. We reduce the problem of identifying worst-case violations to matching distributions and predicting where sensitive attributes and classifier's outcomes coincide. We apply mdfa to a recidivism risk assessment classifier and demonstrate that individuals identified as African-American with little criminal history are three-times more likely to be considered at high risk of violent recidivism than similar individuals but not African-American.

In many competitive sports and games (such as tennis, basketball, chess and electronic sports), the most useful definition of a competitor's skill is the propensity of that competitor to win against an opponent. It is often difficult to measure this skill explicitly: take basketball for example, a team's skill depends on the abilities of its players in terms of shooting accuracy, physical fitness, mental preparation, but also on the team's cohesion and coordination, on its strategy, on the enthusiasm of its fans, and a number of other intangible factors. However, it is easy to observe this skill implicitly through the outcomes of matches. In this setting, probabilistic models of pairwise-comparison outcomes provide an elegant and effective approach to quantifying skill and to predicting future match outcomes given past data. These models, pioneered by Zermelo [1928] in the context of chess (and by Thurstone [1927] in the context of psychophysics), have been studied for almost a century. They posit that each competitor i (i.e., a team or player) is characterized by a latent score s R and that the outcome probabilities of a match between i and j are a function of

Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for modeling and representing discrete structures in data distributions, for example class membership or discrete symmetries. To address this difficulty, we present a normalizing flow architecture which relies on domain partitioning using locally invertible functions, and possesses both real and discrete valued latent variables. This Real and Discrete (RAD) approach retains the desirable normalizing flow properties of exact sampling, exact inference, and analytically computable probabilities, while at the same time allowing simultaneous modeling of both continuous and discrete structure in a data distribution.

The emergence of an ageing population is a significant public health concern. This has led to an increase in the number of people living with progressive neurodegenerative disorders like dementia. Consequently, the strain this is places on health and social care services means providing 24-hour monitoring is not sustainable. Technological intervention is being considered, however no solution exists to non-intrusively monitor the independent living needs of patients with dementia. As a result many patients hit crisis point before intervention and support is provided. In parallel, patient care relies on feedback from informal carers about significant behavioural changes. Yet, not all people have a social support network and early intervention in dementia care is often missed. The smart meter rollout has the potential to change this. Using machine learning and signal processing techniques, a home energy supply can be disaggregated to detect which home appliances are turned on and off. This will allow Activities of Daily Living (ADLs) to be assessed, such as eating and drinking, and observed changes in routine to be detected for early intervention. The primary aim is to help reduce deterioration and enable patients to stay in their homes for longer. A Support Vector Machine (SVM) and Random Decision Forest classifier are modelled using data from three test homes. The trained models are then used to monitor two patients with dementia during a six-month clinical trial undertaken in partnership with Mersey Care NHS Foundation Trust. In the case of load disaggregation for appliance detection, the SVM achieved (AUC=0.86074, Sen=0.756 and Spec=0.92838). While the Decision Forest achieved (AUC=0.9429, Sen=0.9634 and Spec=0.9634). ADLs are also analysed to identify the behavioural patterns of the occupant while detecting alterations in routine.

In epidemiology, identifying the effect of exposure variables in relation to a time-to-event outcome is a classical research area of practical importance. Incorporating propensity score in the Cox regression model, as a measure to control for confounding, has certain advantages when outcome is rare. However, in situations involving exposure measured with moderate to substantial error, identifying the exposure effect using propensity score in Cox models remains a challenging yet unresolved problem. In this paper, we propose an estimating equation method to correct for the exposure misclassification-caused bias in the estimation of exposure-outcome associations. We also discuss the asymptotic properties and derive the asymptotic variances of the proposed estimators. We conduct a simulation study to evaluate the performance of the proposed estimators in various settings. As an illustration, we apply our method to correct for the misclassification-caused bias in estimating the association of PM2.5 level with lung cancer mortality using a nationwide prospective cohort, the Nurses' Health Study (NHS). The proposed methodology can be applied using our user-friendly R function published online.