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Background: It has long been advised to account for baseline covariates in the analysis of confirmatory randomised trials, with the main statistical justifications being that this increases power and, when a randomisation scheme balanced covariates, permits a valid estimate of experimental error. There are various methods available to account for covariates but it is not clear how to choose among them. Methods: Taking the perspective of writing a statistical analysis plan, we consider how to choose between the three most promising broad approaches: direct adjustment, standardisation and inverse-probability-of-treatment weighting. Results: The three approaches are similar in being asymptotically efficient, in losing efficiency with mis-specified covariate functions, and in handling designed balance. If a marginal estimand is targeted (for example, a risk difference or survival difference), then direct adjustment should be avoided because it involves fitting non-standard models that are subject to convergence issues. Convergence is most likely with IPTW. Robust standard errors used by IPTW are anti-conservative at small sample sizes. All approaches can use similar methods to handle missing covariate data. With missing outcome data, each method has its own way to estimate a treatment effect in the all-randomised population. We illustrate some issues in a reanalysis of GetTested, a randomised trial designed to assess the effectiveness of an electonic sexually-transmitted-infection testing and results service. Conclusions: No single approach is always best: the choice will depend on the trial context. We encourage trialists to consider all three methods more routinely.

Information from various data sources is increasingly available nowadays. However, some of the data sources may produce biased estimation due to commonly encountered biased sampling, population heterogeneity, or model misspecification. This calls for statistical methods to combine information in the presence of biased sources. In this paper, a robust data fusion-extraction method is proposed. The method can produce a consistent estimator of the parameter of interest even if many of the data sources are biased. The proposed estimator is easy to compute and only employs summary statistics, and hence can be applied to many different fields, e.g. meta-analysis, Mendelian randomisation and distributed system. Moreover, the proposed estimator is asymptotically equivalent to the oracle estimator that only uses data from unbiased sources under some mild conditions. Asymptotic normality of the proposed estimator is also established. In contrast to the existing meta-analysis methods, the theoretical properties are guaranteed even if both the number of data sources and the dimension of the parameter diverge as the sample size increases, which ensures the performance of the proposed method over a wide range. The robustness and oracle property is also evaluated via simulation studies. The proposed method is applied to a meta-analysis data set to evaluate the surgical treatment for the moderate periodontal disease, and a Mendelian randomization data set to study the risk factors of head and neck cancer.

In decision modelling with time to event data, parametric models are often used to extrapolate the survivor function. One such model is the piecewise exponential model whereby the hazard function is partitioned into segments, with the hazard constant within the segment and independent between segments and the boundaries of these segments are known as change-points. We present an approach for determining the location and number of change-points in piecewise exponential models. Inference is performed in a Bayesian framework using Markov Chain Monte Carlo (MCMC) where the model parameters can be integrated out of the model and the number of change-points can be sampled as part of the MCMC scheme. We can estimate both the uncertainty in the change-point locations and hazards for a given change-point model and obtain a probabilistic interpretation for the number of change-points. We evaluate model performance to determine changepoint numbers and locations in a simulation study and show the utility of the method using two data sets for time to event data. In a dataset of Glioblastoma patients we use the piecewise exponential model to describe the general trends in the hazard function. In a data set of heart transplant patients, we show the piecewise exponential model produces the best statistical fit and extrapolation amongst other standard parametric models. Piecewise exponential models may be useful for survival extrapolation if a long-term constant hazard trend is clinically plausible. A key advantage of this method is that the number and change-point locations are automatically estimated rather than specified by the analyst.

Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target functions - integrated with respect to a probability measure. Such problems can often be solved by stochastic optimization methods: performing optimization steps with respect to the indexed target function with randomly switched indices. In this work, we study a continuous-time variant of the stochastic gradient descent algorithm for optimization problems with continuous data. This so-called stochastic gradient process consists in a gradient flow minimizing an indexed target function that is coupled with a continuous-time index process determining the index. Index processes are, e.g., reflected diffusions, pure jump processes, or other L\'evy processes on compact spaces. Thus, we study multiple sampling patterns for the continuous data space and allow for data simulated or streamed at runtime of the algorithm. We analyze the approximation properties of the stochastic gradient process and study its longtime behavior and ergodicity under constant and decreasing learning rates. We end with illustrating the applicability of the stochastic gradient process in a polynomial regression problem with noisy functional data, as well as in a physics-informed neural network.

Although deep models achieve high predictive performance, it is difficult for humans to understand the predictions they made. Explainability is important for real-world applications to justify their reliability. Many example-based explanation methods have been proposed, such as representer point selection, where an explanation model defined by a set of training examples is used for explaining a prediction model. For improving the interpretability, reducing the number of examples in the explanation model is important. However, the explanations with fewer examples can be unfaithful since it is difficult to approximate prediction models well by such example-based explanation models. The unfaithful explanations mean that the predictions by the explainable model are different from those by the prediction model. We propose a method for training deep models such that their predictions are faithfully explained by explanation models with a small number of examples. We train the prediction and explanation models simultaneously with a sparse regularizer for reducing the number of examples. The proposed method can be incorporated into any neural network-based prediction models. Experiments using several datasets demonstrate that the proposed method improves faithfulness while keeping the predictive performance.

Cross-validation is the standard approach for tuning parameter selection in many non-parametric regression problems. However its use is less common in change-point regression, perhaps as its prediction error-based criterion may appear to permit small spurious changes and hence be less well-suited to estimation of the number and location of change-points. We show that in fact the problems of cross-validation with squared error loss are more severe and can lead to systematic under- or over-estimation of the number of change-points, and highly suboptimal estimation of the mean function in simple settings where changes are easily detectable. We propose two simple approaches to remedy these issues, the first involving the use of absolute error rather than squared error loss, and the second involving modifying the holdout sets used. For the latter, we provide conditions that permit consistent estimation of the number of change-points for a general change-point estimation procedure. We show these conditions are satisfied for optimal partitioning using new results on its performance when supplied with the incorrect number of change-points. Numerical experiments show that the absolute error approach in particular is competitive with common change-point methods using classical tuning parameter choices when error distributions are well-specified, but can substantially outperform these in misspecified models. An implementation of our methodology is available in the R package crossvalidationCP on CRAN.

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal solutions that correspond to different instances of the linear program. We introduce a new formulation of the problem that, compared to other existing methods, allows the recovery of a less restrictive and generally more appropriate admissible set of cost estimates. It can be shown that this inverse optimization problem yields a finite number of solutions, and we develop an exact two-phase algorithm to determine all such solutions. Moreover, we propose an efficient decomposition algorithm to solve large instances of the problem. The algorithm extends naturally to an online learning environment where it can be used to provide quick updates of the cost estimate as new data becomes available over time. For the online setting, we further develop an effective adaptive sampling strategy that guides the selection of the next samples. The efficacy of the proposed methods is demonstrated in computational experiments involving two applications, customer preference learning and cost estimation for production planning. The results show significant reductions in computation and sampling efforts.

Reliant on too many experiments to learn good actions, current Reinforcement Learning (RL) algorithms have limited applicability in real-world settings, which can be too expensive to allow exploration. We propose an algorithm for batch RL, where effective policies are learned using only a fixed offline dataset instead of online interactions with the environment. The limited data in batch RL produces inherent uncertainty in value estimates of states/actions that were insufficiently represented in the training data. This leads to particularly severe extrapolation when our candidate policies diverge from one that generated the data. We propose to mitigate this issue via two straightforward penalties: a policy-constraint to reduce this divergence and a value-constraint that discourages overly optimistic estimates. Over a comprehensive set of 32 continuous-action batch RL benchmarks, our approach compares favorably to state-of-the-art methods, regardless of how the offline data were collected.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach builds off of techniques for distributionally robust optimization and Owen's empirical likelihood, and we provide a number of finite-sample and asymptotic results characterizing the theoretical performance of the estimator. In particular, we show that our procedure comes with certificates of optimality, achieving (in some scenarios) faster rates of convergence than empirical risk minimization by virtue of automatically balancing bias and variance. We give corroborating empirical evidence showing that in practice, the estimator indeed trades between variance and absolute performance on a training sample, improving out-of-sample (test) performance over standard empirical risk minimization for a number of classification problems.