Many decision in clinical science and epidemiology -- estimating probability of technical success for a clinical trial, assessing comparative effectiveness of two therapies, imputing a placebo effect onto natural history data -- rely on combining sources of information about a clinical cohort that comes from different kinds of studies. Specifically we contrast patient-level sources that provide granular pictures of individual disease course (clinical trial, registries, or electronic health records) with aggregate sources such as published clinical trial results and the TFLs (tables figures and listings). One strategy for combining aggregate with patient-level data sources is to bring each into a common format for a unified analysis. If one wants to maintain the analytic flexibility of patient-level data, then a natural solution is to convert the aggregate data information into a simulated patient-level dataset that recapitulate those aggregate statistics. This is an under-determined inverse problem in that there are many such datasets, and it cannot be well specified without further constraints. FRESH(Fusion of Recent Evidence with Subject Histories) provides a well-defined method for solving this problem, and therefore providing maximal analytic flexibility.

Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial dependencies between groups of more than two variables can play a significant role in the analysis and modelling of such systems, yet extracting such high-order interactions from data remains challenging. Here, we introduce a hierarchy of d-order interaction measures, increasingly inclusive of possible factorisations of the joint probability distribution, and define non-parametric, kernel-based tests to establish systematically the statistical significance of d-order interactions. We also establish mathematical links with lattice theory, which elucidate the derivation of the interaction measures and their composite permutation tests; clarify the connection of simplicial complexes with kernel matrix centring; and provide a means to enhance computational efficiency. We illustrate our results numerically with validations on synthetic data, and through an application to neuroimaging data.

Active learning sequentially selects the best instance for labeling by optimizing an acquisition function to enhance data/label efficiency. The selection can be either from a discrete instance set (pool-based scenario) or a continuous instance space (query synthesis scenario). In this work, we study both active learning scenarios for Gaussian Process Classification (GPC). The existing active learning strategies that maximize the Estimated Error Reduction (EER) aim at reducing the classification error after training with the new acquired instance in a onestep-look-ahead manner. The computation of EER-based acquisition functions is typically prohibitive as it requires retraining the GPC with every new query.

GCNGAT Algorithmγη Tγη T Thanos 0.4 0.01 1000 0.4 0.01 1000 BanditSampler 0.4 0.01 N/A 0.4 0.01 N/A Table 5: The detailed sampling hyperparameters for Squirrel.

We use Law(X) to denote the distribution of random variable X. When ν is a probability distribution for over set Ω and Ais a subset of Ω, we use ν(A) to denote the probability that the random variable X belongs to A, when X is sampled from distribution ν. Similarly, the marginal distribution on the next N random variables for fγ,r#ν is fγ,r#ν2. We thus proved equation (22) and Lemma 3 is proved. Lemma 4 Suppose Z1( |A) and Z2( |A) are two conditional distribution with range RN, and for all values of a Ω, Wp(Law(Z1(a)),Law(Z2(a))) c (23) where Z1(a) Z1( |A= a), and Z2(a) Z2( |A= a).