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Longitudinal and survival sub-models are two building blocks for joint modelling of longitudinal and time to event data. Extensive research indicates separate analysis of these two processes could result in biased outputs due to their associations. Conditional independence between measurements of biomarkers and event time process given latent classes or random effects is a common approach for characterising the association between the two sub-models while taking the heterogeneity among the population into account. However, this assumption is tricky to validate because of the unobservable latent variables. Thus a Gaussian copula joint model with random effects is proposed to accommodate the scenarios where the conditional independence assumption is questionable. In our proposed model, the conventional joint model assuming conditional independence is a special case when the association parameter in the Gaussian copula shrinks to zero. Simulation studies and real data application are carried out to evaluate the performance of our proposed model. In addition, personalised dynamic predictions of survival probabilities are obtained based on the proposed model and comparisons are made to the predictions obtained under the conventional joint model.

Despite the recent progress in the field of causal inference, to date there is no agreed upon methodology to glean treatment effect estimation from observational data. The consequence on clinical practice is that, when lacking results from a randomized trial, medical personnel is left without guidance on what seems to be effective in a real-world scenario. This article proposes a pragmatic methodology to obtain preliminary but robust estimation of treatment effect from observational studies, to provide front-line clinicians with a degree of confidence in their treatment strategy. Our study design is applied to an open problem, the estimation of treatment effect of the proning maneuver on COVID-19 Intensive Care patients.

Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the form of a lookup table or carried out on demand, to apply a goodness-of-fit test. Stephens (1970) provided remarkable simple and useful transformations of several classic goodness-of-fit test statistics that stabilized their exact-$n$ critical values for varying sample sizes $n$. However, detail on the accuracy of these and subsequent transformations in yielding exact $p$-values, or even deep understanding on the derivation of several transformations, is still scarce nowadays. We illuminate and automatize, using modern tools, the latter stabilization approach to (i) expand its scope of applicability and (ii) yield semi-continuous exact $p$-values, as opposed to exact critical values for fixed significance levels. We show improvements on the stabilization accuracy of the exact null distributions of the Kolmogorov-Smirnov, Cram\'er-von Mises, Anderson-Darling, Kuiper, and Watson test statistics. In addition, we provide a parameter-dependent exact-$n$ stabilization for several novel statistics for testing uniformity on the hypersphere of arbitrary dimension. A data application in astronomy illustrates the benefits of the advocated stabilization for quickly analyzing small-to-moderate sequentially-measured samples.

This paper proposes a new RWO-Sampling (Random Walk Over-Sampling) based on graphs for imbalanced datasets. In this method, two schemes based on under-sampling and over-sampling methods are introduced to keep the proximity information robust to noises and outliers. After constructing the first graph on minority class, RWO-Sampling will be implemented on selected samples, and the rest will remain unchanged. The second graph is constructed for the majority class, and the samples in a low-density area (outliers) are removed. Finally, in the proposed method, samples of the majority class in a high-density area are selected, and the rest are eliminated. Furthermore, utilizing RWO-sampling, the boundary of minority class is increased though the outliers are not raised. This method is tested, and the number of evaluation measures is compared to previous methods on nine continuous attribute datasets with different over-sampling rates and one data set for the diagnosis of COVID-19 disease. The experimental results indicated the high efficiency and flexibility of the proposed method for the classification of imbalanced data

A matrix formalism for the determination of the best estimator in certain simulation-based parameter estimation problems will be presented and discussed. The equations, termed as the Linear Template Fit, combine a linear regression with a least square method and its optimization. The Linear Template Fit employs only predictions that are calculated beforehand and which are provided for a few values of the parameter of interest. Therefore, the Linear Template Fit is particularly suited for parameter estimation with computationally intensive simulations that are otherwise often limited in their usability for statistical inference, or for performance critical applications. Equations for error propagation are discussed, and the analytic form provides comprehensive insights into the parameter estimation problem. Furthermore, the quickly-converging algorithm of the Quadratic Template Fit will be presented, which is suitable for a non-linear dependence on the parameters. As an example application, a determination of the strong coupling constant, $\alpha_s(m_Z)$, from inclusive jet cross section data at the CERN Large Hadron Collider is studied and compared with previously published results.

Time series forecasting is widely used in business intelligence, e.g., forecast stock market price, sales, and help the analysis of data trend. Most time series of interest are macroscopic time series that are aggregated from microscopic data. However, instead of directly modeling the macroscopic time series, rare literature studied the forecasting of macroscopic time series by leveraging data on the microscopic level. In this paper, we assume that the microscopic time series follow some unknown mixture probabilistic distributions. We theoretically show that as we identify the ground truth latent mixture components, the estimation of time series from each component could be improved because of lower variance, thus benefitting the estimation of macroscopic time series as well. Inspired by the power of Seq2seq and its variants on the modeling of time series data, we propose Mixture of Seq2seq (MixSeq), an end2end mixture model to cluster microscopic time series, where all the components come from a family of Seq2seq models parameterized by different parameters. Extensive experiments on both synthetic and real-world data show the superiority of our approach.

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.

While existing work in robust deep learning has focused on small pixel-level $\ell_p$ norm-based perturbations, this may not account for perturbations encountered in several real world settings. In many such cases although test data might not be available, broad specifications about the types of perturbations (such as an unknown degree of rotation) may be known. We consider a setup where robustness is expected over an unseen test domain that is not i.i.d. but deviates from the training domain. While this deviation may not be exactly known, its broad characterization is specified a priori, in terms of attributes. We propose an adversarial training approach which learns to generate new samples so as to maximize exposure of the classifier to the attributes-space, without having access to the data from the test domain. Our adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial perturbations, and the outer minimization finding model parameters by optimizing the loss on adversarial perturbations generated from the inner maximization. We demonstrate the applicability of our approach on three types of naturally occurring perturbations -- object-related shifts, geometric transformations, and common image corruptions. Our approach enables deep neural networks to be robust against a wide range of naturally occurring perturbations. We demonstrate the usefulness of the proposed approach by showing the robustness gains of deep neural networks trained using our adversarial training on MNIST, CIFAR-10, and a new variant of the CLEVR dataset.

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g. spectral clustering) without requiring any changes to the latter or affecting its computational complexity. Our implementation is available online.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.