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Deep Learning predictions with measurable confidence are increasingly desirable for real-world problems, especially in high-risk settings. The Conformal Prediction (CP) framework is a versatile solution that automatically guarantees a maximum error rate. However, CP suffers from computational inefficiencies that limit its application to large-scale datasets. In this paper, we propose a novel conformal loss function that approximates the traditionally two-step CP approach in a single step. By evaluating and penalising deviations from the stringent expected CP output distribution, a Deep Learning model may learn the direct relationship between input data and conformal p-values. Our approach achieves significant training time reductions up to 86% compared to Aggregated Conformal Prediction (ACP), an accepted CP approximation variant. In terms of approximate validity and predictive efficiency, we carry out a comprehensive empirical evaluation to show our novel loss function's competitiveness with ACP on the well-established MNIST dataset.

Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked point processes. In this work, we focus on adjusting for mark-point dependence when estimating the mean and covariance functions of the mark process, given independent replicates of the marked point process. We assume that the mark process is a Gaussian process and the point process is a log-Gaussian Cox process, where the mark-point dependence is generated through the dependence between two latent Gaussian processes. Under this framework, naive local linear estimators ignoring the mark-point dependence can be severely biased. We show that this bias can be corrected using a local linear estimator of the cross-covariance function and establish uniform convergence rates of the bias-corrected estimators. Furthermore, we propose a test statistic based on local linear estimators for mark-point independence, which is shown to converge to an asymptotic normal distribution in a parametric $\sqrt{n}$-convergence rate. Model diagnostics tools are developed for key model assumptions and a robust functional permutation test is proposed for a more general class of mark-point processes. The effectiveness of the proposed methods is demonstrated using extensive simulations and applications to two real data examples.

Recently the use of mobile technologies in Ecological Momentary Assessments (EMA) and Interventions (EMI) has made it easier to collect data suitable for intra-individual variability studies in the medical field. Nevertheless, especially when self-reports are used during the data collection process, there are difficulties in balancing data quality and the burden placed on the subjects. In this paper, we address this problem for a specific EMA setting which aims to submit a demanding task to subjects at high/low values of a self-reported variable. We adopt a dynamic approach inspired by control chart methods and design optimization techniques to obtain an EMA triggering mechanism for data collection which takes into account both the individual variability of the self-reported variable and of the adherence rate. We test the algorithm in both a simulation setting and with real, large-scale data from a tinnitus longitudinal study. A Wilcoxon-Mann-Whitney Rank Sum Test shows that the algorithm tends to have both a higher F1 score and utility than a random schedule and a rule-based algorithm with static thresholds, which are the current state-of-the-art approaches. In conclusion, the algorithm is proven effective in balancing data quality and the burden placed on the participants, especially, as the analysis performed suggest, in studies where data collection is impacted by adherence.

Causal inference is a critical research area with multi-disciplinary origins and applications, ranging from statistics, computer science, economics, psychology to public health. In many scientific research, randomized experiments provide a golden standard for estimation of causal effects for decades. However, in many situations, randomized experiments are not feasible in practice so that practitioners need to rely on empirical investigation for causal reasoning. Causal inference via observational data is a challenging task since the knowledge of the treatment assignment mechanism is missing, which typically requires non-testable assumptions to make the inference possible. For several years, great effort has been devoted to the research of causal inference for binary treatments. In practice, it is also common to use observational data on multiple treatment comparisons. Within the potential outcomes framework, we propose a generalized cross-fitting estimator (GCF), which generalizes the doubly robust estimator with cross-fitting for binary treatment to multiple treatment comparisons and provides rigorous proofs on its statistical properties. This estimator permits the use of more flexible machine learning methods to model the nuisance parts, and based on relatively weak assumptions, while there is still a theoretical guarantee for valid statistical inference. We show the asymptotic properties of the GCF estimators, and provide the asymptotic simultaneous confidence intervals that achieve the semiparametric efficiency bound for average treatment effect. The performance of the estimator is accessed through simulation study based on the common evaluation metrics generally considered in the causal inference literature.

Causal effect estimation from observational data is a challenging problem, especially with high dimensional data and in the presence of unobserved variables. The available data-driven methods for tackling the problem either provide an estimation of the bounds of a causal effect (i.e. nonunique estimation) or have low efficiency. The major hurdle for achieving high efficiency while trying to obtain unique and unbiased causal effect estimation is how to find a proper adjustment set for confounding control in a fast way, given the huge covariate space and considering unobserved variables. In this paper, we approach the problem as a local search task for finding valid adjustment sets in data. We establish the theorems to support the local search for adjustment sets, and we show that unique and unbiased estimation can be achieved from observational data even when there exist unobserved variables. We then propose a data-driven algorithm that is fast and consistent under mild assumptions. We also make use of a frequent pattern mining method to further speed up the search of minimal adjustment sets for causal effect estimation. Experiments conducted on extensive synthetic and real-world datasets demonstrate that the proposed algorithm outperforms the state-of-the-art criteria/estimators in both accuracy and time-efficiency.

Precision medicine for chronic diseases such as multiple sclerosis (MS) involves choosing a treatment which best balances efficacy and side effects/preferences for individual patients. Making this choice as early as possible is important, as delays in finding an effective therapy can lead to irreversible disability accrual. To this end, we present the first deep neural network model for individualized treatment decisions from baseline magnetic resonance imaging (MRI) (with clinical information if available) for MS patients. Our model (a) predicts future new and enlarging T2 weighted (NE-T2) lesion counts on follow-up MRI on multiple treatments and (b) estimates the conditional average treatment effect (CATE), as defined by the predicted future suppression of NE-T2 lesions, between different treatment options relative to placebo. Our model is validated on a proprietary federated dataset of 1817 multi-sequence MRIs acquired from MS patients during four multi-centre randomized clinical trials. Our framework achieves high average precision in the binarized regression of future NE-T2 lesions on five different treatments, identifies heterogeneous treatment effects, and provides a personalized treatment recommendation that accounts for treatment-associated risk (e.g. side effects, patient preference, administration difficulties).

Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real data set to estimate the extremal quantile treatment effect of college education on wage.

Predictive coding (PC) is an influential theory in computational neuroscience, which argues that the cortex forms unsupervised world models by implementing a hierarchical process of prediction error minimization. PC networks (PCNs) are trained in two phases. First, neural activities are updated to optimize the network's response to external stimuli. Second, synaptic weights are updated to consolidate this change in activity -- an algorithm called \emph{prospective configuration}. While previous work has shown how in various limits, PCNs can be found to approximate backpropagation (BP), recent work has demonstrated that PCNs operating in this standard regime, which does not approximate BP, nevertheless obtain competitive training and generalization performance to BP-trained networks while outperforming them on tasks such as online, few-shot, and continual learning, where brains are known to excel. Despite this promising empirical performance, little is understood theoretically about the properties and dynamics of PCNs in this regime. In this paper, we provide a comprehensive theoretical analysis of the properties of PCNs trained with prospective configuration. We first derive analytical results concerning the inference equilibrium for PCNs and a previously unknown close connection relationship to target propagation (TP). Secondly, we provide a theoretical analysis of learning in PCNs as a variant of generalized expectation-maximization and use that to prove the convergence of PCNs to critical points of the BP loss function, thus showing that deep PCNs can, in theory, achieve the same generalization performance as BP, while maintaining their unique advantages.

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.

With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse healthcare data. A major limitation of existing methods has been the focus on grid-like data; however, the structure of physiological recordings are often irregular and unordered which makes it difficult to conceptualise them as a matrix. As such, graph neural networks have attracted significant attention by exploiting implicit information that resides in a biological system, with interactive nodes connected by edges whose weights can be either temporal associations or anatomical junctions. In this survey, we thoroughly review the different types of graph architectures and their applications in healthcare. We provide an overview of these methods in a systematic manner, organized by their domain of application including functional connectivity, anatomical structure and electrical-based analysis. We also outline the limitations of existing techniques and discuss potential directions for future research.