Dealing with missing data is an important problem in statistical analysis that is often addressed with imputation procedures. The performance and validity of such methods are of great importance for their application in empirical studies. While the prevailing method of Multiple Imputation by Chained Equations (MICE) with Predictive Mean Matching (PMM) is considered standard in the social science literature, the increase in complex datasets may require more advanced approaches based on machine learning. In particular, tree-based imputation methods have emerged as very competitive approaches. However, the performance and validity are not completely understood, particularly compared to the standard MICE PMM. This is especially true for inference in linear models. In this study, we investigate the impact of various imputation methods on coefficient estimation, Type I error, and power, to gain insights that can help empirical researchers deal with missingness more effectively. We explore MICE PMM alongside different tree-based methods, such as MICE with Random Forest (RF), Chained Random Forests with and without PMM (missRanger), and Extreme Gradient Boosting (MIXGBoost), conducting a realistic simulation study using the German National Educational Panel Study (NEPS) as the original data source. Our results reveal that Random Forest-based imputations, especially MICE RF and missRanger with PMM, consistently perform better in most scenarios. Standard MICE PMM shows partially increased bias and overly conservative test decisions, particularly with non-true zero coefficients. Our results thus underscore the potential advantages of tree-based imputation methods, albeit with a caveat that all methods perform worse with an increased missingness, particularly missRanger.
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Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as the solution of convex minimisation problems that can be solved with first-order algorithms. We demonstrate the validity of our approach by testing it on two inverse problem case studies in machine learning and image processing: sparse coefficient estimation of a polynomial via LASSO regression and recovering an image from a subset of the coefficients of its discrete Fourier transform. We further demonstrate that the proposed approach can easily be modified to solve the machine learning task of identifying the optimal sampling pattern in the Fourier domain for a given image and variational regularisation method, which has applications in the context of sparsity promoting reconstruction from magnetic resonance imaging data.
LLMs have become increasingly capable at accomplishing a range of specialized-tasks and can be utilized to expand equitable access to medical knowledge. Most medical LLMs have involved extensive fine-tuning, leveraging specialized medical data and significant, thus costly, amounts of computational power. Many of the top performing LLMs are proprietary and their access is limited to very few research groups. However, open-source (OS) models represent a key area of growth for medical LLMs due to significant improvements in performance and an inherent ability to provide the transparency and compliance required in healthcare. We present OpenMedLM, a prompting platform which delivers state-of-the-art (SOTA) performance for OS LLMs on medical benchmarks. We evaluated a range of OS foundation LLMs (7B-70B) on four medical benchmarks (MedQA, MedMCQA, PubMedQA, MMLU medical-subset). We employed a series of prompting strategies, including zero-shot, few-shot, chain-of-thought (random selection and kNN selection), and ensemble/self-consistency voting. We found that OpenMedLM delivers OS SOTA results on three common medical LLM benchmarks, surpassing the previous best performing OS models that leveraged computationally costly extensive fine-tuning. The model delivers a 72.6% accuracy on the MedQA benchmark, outperforming the previous SOTA by 2.4%, and achieves 81.7% accuracy on the MMLU medical-subset, establishing itself as the first OS LLM to surpass 80% accuracy on this benchmark. Our results highlight medical-specific emergent properties in OS LLMs which have not yet been documented to date elsewhere, and showcase the benefits of further leveraging prompt engineering to improve the performance of accessible LLMs for medical applications.
Understanding a surgical scene is crucial for computer-assisted surgery systems to provide any intelligent assistance functionality. One way of achieving this scene understanding is via scene segmentation, where every pixel of a frame is classified and therefore identifies the visible structures and tissues. Progress on fully segmenting surgical scenes has been made using machine learning. However, such models require large amounts of annotated training data, containing examples of all relevant object classes. Such fully annotated datasets are hard to create, as every pixel in a frame needs to be annotated by medical experts and, therefore, are rarely available. In this work, we propose a method to combine multiple partially annotated datasets, which provide complementary annotations, into one model, enabling better scene segmentation and the use of multiple readily available datasets. Our method aims to combine available data with complementary labels by leveraging mutual exclusive properties to maximize information. Specifically, we propose to use positive annotations of other classes as negative samples and to exclude background pixels of binary annotations, as we cannot tell if they contain a class not annotated but predicted by the model. We evaluate our method by training a DeepLabV3 on the publicly available Dresden Surgical Anatomy Dataset, which provides multiple subsets of binary segmented anatomical structures. Our approach successfully combines 6 classes into one model, increasing the overall Dice Score by 4.4% compared to an ensemble of models trained on the classes individually. By including information on multiple classes, we were able to reduce confusion between stomach and colon by 24%. Our results demonstrate the feasibility of training a model on multiple datasets. This paves the way for future work further alleviating the need for one large, fully segmented datasets.
Data for which a set of objects is described by multiple distinct feature sets (called views) is known as multi-view data. When missing values occur in multi-view data, all features in a view are likely to be missing simultaneously. This leads to very large quantities of missing data which, especially when combined with high-dimensionality, makes the application of conditional imputation methods computationally infeasible. We introduce a new imputation method based on the existing stacked penalized logistic regression (StaPLR) algorithm for multi-view learning. It performs imputation in a dimension-reduced space to address computational challenges inherent to the multi-view context. We compare the performance of the new imputation method with several existing imputation algorithms in simulated data sets. The results show that the new imputation method leads to competitive results at a much lower computational cost, and makes the use of advanced imputation algorithms such as missForest and predictive mean matching possible in settings where they would otherwise be computationally infeasible.
We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on Gaussian priors, leading to convenient conjugate formulae for posterior inference. We review recent results providing theoretical guarantees on the quality of the resulting posterior-based estimation and uncertainty quantification, and we discuss the application of the theory to the important classes of Gaussian series priors defined on the Dirichlet-Laplacian eigenbasis and Mat\'ern process priors. We provide an implementation of posterior inference for both classes of priors, and investigate its performance in a numerical simulation study.
Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this contribution, we provide a rigorous justification of these approaches for a two-layers neural network model called the committee machine. We also introduce a version of the approximate message passing (AMP) algorithm for the committee machine that allows to perform optimal learning in polynomial time for a large set of parameters. We find that there are regimes in which a low generalization error is information-theoretically achievable while the AMP algorithm fails to deliver it, strongly suggesting that no efficient algorithm exists for those cases, and unveiling a large computational gap.
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if "bad" elements (elements that violate the shape regularity or maximum angle condition) are covered virtually by "good" simplices. A numerical experiment confirms the theoretical result.
The approach to analysing compositional data has been dominated by the use of logratio transformations, to ensure exact subcompositional coherence and, in some situations, exact isometry as well. A problem with this approach is that data zeros, found in most applications, have to be replaced to allow the logarithmic transformation. An alternative new approach, called the `chiPower' transformation, which allows data zeros, is to combine the standardization inherent in the chi-square distance in correspondence analysis, with the essential elements of the Box-Cox power transformation. The chiPower transformation is justified because it} defines between-sample distances that tend to logratio distances for strictly positive data as the power parameter tends to zero, and are then equivalent to transforming to logratios. For data with zeros, a value of the power can be identified that brings the chiPower transformation as close as possible to a logratio transformation, without having to substitute the zeros. Especially in the area of high-dimensional data, this alternative approach can present such a high level of coherence and isometry as to be a valid approach to the analysis of compositional data. Furthermore, in a supervised learning context, if the compositional variables serve as predictors of a response in a modelling framework, for example generalized linear models, then the power can be used as a tuning parameter in optimizing the accuracy of prediction through cross-validation. The chiPower-transformed variables have a straightforward interpretation, since they are each identified with single compositional parts, not ratios.
The categorical Gini covariance is a dependence measure between a numerical variable and a categorical variable. The Gini covariance measures dependence by quantifying the difference between the conditional and unconditional distributional functions. A value of zero for the categorical Gini covariance implies independence of the numerical variable and the categorical variable. We propose a non-parametric test for testing the independence between a numerical and categorical variable using the categorical Gini covariance. We used the theory of U-statistics to find the test statistics and study the properties. The test has an asymptotic normal distribution. As the implementation of a normal-based test is difficult, we develop a jackknife empirical likelihood (JEL) ratio test for testing independence. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed JEL-based test. We illustrate the test procedure using real a data set.
A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method to model weak discontinuities using nonconforming finite-element meshes. The essence of LET is in treating the elements that are cut by an interface as simple laminates of the two phases, and this idea is here extended to propagating interfaces so that the volume fraction of the phases and the lamination orientation vary accordingly. In the proposed LET-PF approach, the phase-field variable (order parameter), which is governed by an evolution equation of the Ginzburg-Landau type, plays the role of a level-set function that implicitly defines the position of the (sharp) interface. The mechanical equilibrium subproblem is then solved using the semisharp LET technique. Performance of LET-PF is illustrated by numerical examples. In particular, it is shown that, for the problems studied, LET-PF exhibits higher accuracy than the conventional phase-field method so that, for instance, qualitatively correct results can be obtained using a significantly coarser mesh, and thus at a lower computational cost.
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