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The Horvitz-Thompson (H-T) estimator is widely used for estimating various types of average treatment effects under network interference. We systematically investigate the optimality properties of H-T estimator under network interference, by embedding it in the class of all linear estimators. In particular, we show that in presence of any kind of network interference, H-T estimator is in-admissible in the class of all linear estimators when using a completely randomized and a Bernoulli design. We also show that the H-T estimator becomes admissible under certain restricted randomization schemes termed as ``fixed exposure designs''. We give examples of such fixed exposure designs. It is well known that the H-T estimator is unbiased when correct weights are specified. Here, we derive the weights for unbiased estimation of various causal effects, and illustrate how they depend not only on the design, but more importantly, on the assumed form of interference (which in many real world situations is unknown at design stage), and the causal effect of interest.

Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input. The worst-case robustness against these so-called adversarial examples can be quantified by the Lipschitz constant of the neural network. In this paper, we study upper and lower bounds for the Lipschitz constant of random ReLU neural networks. Specifically, we assume that the weights and biases follow a generalization of the He initialization, where general symmetric distributions for the biases are permitted. For shallow neural networks, we characterize the Lipschitz constant up to an absolute numerical constant. For deep networks with fixed depth and sufficiently large width, our established bounds differ by a factor that is logarithmic in the width.

When two stiff inclusions are closely located, the gradient of the solution may become arbitrarily large as the distance between two inclusions tends to zero. Since blow-up of the gradient occurs in the narrow region, fine meshes should be required to compute the gradient. Thus, it is a challenging problem to numerically compute the gradient. Recent studies have shown that the major singularity can be extracted in an explicit way, so it suffices to compute the residual term for which only regular meshes are required. In this paper, we show through numerical simulations that the characterization of the singular term method can be efficiently used for the computation of the gradient when two strongly convex stiff domains of general shapes are closely located.

Inspired by the success of WaveNet in multi-subject speech synthesis, we propose a novel neural network based on causal convolutions for multi-subject motion modeling and generation. The network can capture the intrinsic characteristics of the motion of different subjects, such as the influence of skeleton scale variation on motion style. Moreover, after fine-tuning the network using a small motion dataset for a novel skeleton that is not included in the training dataset, it is able to synthesize high-quality motions with a personalized style for the novel skeleton. The experimental results demonstrate that our network can model the intrinsic characteristics of motions well and can be applied to various motion modeling and synthesis tasks.

Experimental and observational studies often lead to spurious association between the outcome and independent variables describing the intervention, because of confounding to third-party factors. Even in randomized clinical trials, confounding might be unavoidable due to small sample sizes. Practically, this poses a problem, because it is either expensive to re-design and conduct a new study or even impossible to alleviate the contribution of some confounders due to e.g. ethical concerns. Here, we propose a method to consistently derive hypothetical studies that retain as many of the dependencies in the original study as mathematically possible, while removing any association of observed confounders to the independent variables. Using historic studies, we illustrate how the confounding-free scenario re-estimates the effect size of the intervention. The new effect size estimate represents a concise prediction in the hypothetical scenario which paves a way from the original data towards the design of future studies.

Learning from human feedback (LHF) -- and in particular learning from pairwise preferences -- has recently become a crucial ingredient in training large language models (LLMs), and has been the subject of much research. Most recent works frame it as a reinforcement learning problem, where a reward function is learned from pairwise preference data and the LLM is treated as a policy which is adapted to maximize the rewards, often under additional regularization constraints. We propose an alternative interpretation which centers on the generative process for pairwise preferences and treats LHF as a density estimation problem. We provide theoretical and empirical results showing that for a family of generative processes defined via preference behavior distribution equations, training a reward function on pairwise preferences effectively models an annotator's implicit preference distribution. Finally, we discuss and present findings on "annotator misspecification" -- failure cases where wrong modeling assumptions are made about annotator behavior, resulting in poorly-adapted models -- suggesting that approaches that learn from pairwise human preferences could have trouble learning from a population of annotators with diverse viewpoints.

Decreased myocardial capillary density has been reported as an important histopathological feature associated with various heart disorders. Quantitative assessment of cardiac capillarization typically involves double immunostaining of cardiomyocytes (CMs) and capillaries in myocardial slices. In contrast, single immunostaining of basement membrane components is a straightforward approach to simultaneously label CMs and capillaries, presenting fewer challenges in background staining. However, subsequent image analysis always requires manual work in identifying and segmenting CMs and capillaries. Here, we developed an image analysis tool, AutoQC, to automatically identify and segment CMs and capillaries in immunofluorescence images of collagen type IV, a predominant basement membrane protein within the myocardium. In addition, commonly used capillarization-related measurements can be derived from segmentation masks. AutoQC features a weakly supervised instance segmentation algorithm by leveraging the power of a pre-trained segmentation model via prompt engineering. AutoQC outperformed YOLOv8-Seg, a state-of-the-art instance segmentation model, in both instance segmentation and capillarization assessment. Furthermore, the training of AutoQC required only a small dataset with bounding box annotations instead of pixel-wise annotations, leading to a reduced workload during network training. AutoQC provides an automated solution for quantifying cardiac capillarization in basement-membrane-immunostained myocardial slices, eliminating the need for manual image analysis once it is trained.

Spatio-temporal pathogen spread is often partially observed at the metapopulation scale. Available data correspond to proxies and are incomplete, censored and heterogeneous. Moreover, representing such biological systems often leads to complex stochastic models. Such complexity together with data characteristics make the analysis of these systems a challenge. Our objective was to develop a new inference procedure to estimate key parameters of stochastic metapopulation models of animal disease spread from longitudinal and spatial datasets, while accurately accounting for characteristics of census data. We applied our procedure to provide new knowledge on the regional spread of \emph{Mycobacterium avium} subsp. \emph{paratuberculosis} (\emph{Map}), which causes bovine paratuberculosis, a worldwide endemic disease. \emph{Map} spread between herds through trade movements was modeled with a stochastic mechanistic model. Comprehensive data from 2005 to 2013 on cattle movements in 12,857 dairy herds in Brittany (western France) and partial data on animal infection status in 2,278 herds sampled from 2007 to 2013 were used. Inference was performed using a new criterion based on a Monte-Carlo approximation of a composite likelihood, coupled to a numerical optimization algorithm (Nelder-Mead Simplex-like). Our criterion showed a clear superiority to alternative ones in identifying the right parameter values, as assessed by an empirical identifiability on simulated data. Point estimates and profile likelihoods allowed us to establish the initial state of the system, identify the risk of pathogen introduction from outside the metapopulation, and confirm the assumption of the low sensitivity of the diagnostic test. Our inference procedure could easily be applied to other spatio-temporal infection dynamics, especially when ABC-like methods face challenges in defining relevant summary statistics.

Breast cancer remains a global challenge, causing over 1 million deaths globally in 2018. To achieve earlier breast cancer detection, screening x-ray mammography is recommended by health organizations worldwide and has been estimated to decrease breast cancer mortality by 20-40%. Nevertheless, significant false positive and false negative rates, as well as high interpretation costs, leave opportunities for improving quality and access. To address these limitations, there has been much recent interest in applying deep learning to mammography; however, obtaining large amounts of annotated data poses a challenge for training deep learning models for this purpose, as does ensuring generalization beyond the populations represented in the training dataset. Here, we present an annotation-efficient deep learning approach that 1) achieves state-of-the-art performance in mammogram classification, 2) successfully extends to digital breast tomosynthesis (DBT; "3D mammography"), 3) detects cancers in clinically-negative prior mammograms of cancer patients, 4) generalizes well to a population with low screening rates, and 5) outperforms five-out-of-five full-time breast imaging specialists by improving absolute sensitivity by an average of 14%. Our results demonstrate promise towards software that can improve the accuracy of and access to screening mammography worldwide.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.