本文研究了用于训练过度参数化制度中的贝叶斯神经网络（BNN）的变异推理（VI），即当神经元的数量趋于无穷大时。更具体地说，我们考虑过度参数化的两层BNN，并指出平均VI训练中的关键问题。这个问题来自于证据（ELBO）的下限分解为两个术语：一个与模型的可能性函数相对应，第二个对应于kullback-leibler（KL）差异（KL）差异。特别是，我们从理论和经验上都表明，只有当根据观测值和神经元之间的比率适当地重新缩放KL时，在过度参数化制度中，这两个术语之间存在权衡。我们还通过数值实验来说明我们的理论结果，这些实验突出了该比率的关键选择。

机器学习中的许多问题都可以表达为在措施空间上优化凸功能。本文研究了这种无限维度的镜子下降算法的收敛性。通过定向衍生物来定义布雷格曼的差异，我们得出了相对平滑且强烈凸成的功能对的方案的收敛。将我们的结果应用于联合分布和kullback-leibler（kl）差异，我们表明，在连续设置中，Sinkhorn的熵最佳传输的原始迭代对应于镜子下降，我们获得了其（sub）线性收敛的新证明。我们还表明，期望最大化（EM）始终可以正式写作作为镜下下降，并且在固定混合物时优化潜在分布时，我们得出了趋同的收敛速率。

我们解决了在没有观察到的混杂的存在下的因果效应估计的问题，但是观察到潜在混杂因素的代理。在这种情况下，我们提出了两种基于内核的方法，用于非线性因果效应估计：（a）两阶段回归方法，以及（b）最大矩限制方法。我们专注于近端因果学习设置，但是我们的方法可以用来解决以弗雷霍尔姆积分方程为特征的更广泛的逆问题。特别是，我们提供了在非线性环境中解决此问题的两阶段和矩限制方法的统一视图。我们为每种算法提供一致性保证，并证明这些方法在合成数据和模拟现实世界任务的数据上获得竞争结果。特别是，我们的方法优于不适合利用代理变量的早期方法。

Novel topological spin textures, such as magnetic skyrmions, benefit from their inherent stability, acting as the ground state in several magnetic systems. In the current study of atomic monolayer magnetic materials, reasonable initial guesses are still needed to search for those magnetic patterns. This situation underlines the need to develop a more effective way to identify the ground states. To solve this problem, in this work, we propose a genetic-tunneling-driven variance-controlled optimization approach, which combines a local energy minimizer back-end and a metaheuristic global searching front-end. This algorithm is an effective optimization solution for searching for magnetic ground states at extremely low temperatures and is also robust for finding low-energy degenerated states at finite temperatures. We demonstrate here the success of this method in searching for magnetic ground states of 2D monolayer systems with both artificial and calculated interactions from density functional theory. It is also worth noting that the inherent concurrent property of this algorithm can significantly decrease the execution time. In conclusion, our proposed method builds a useful tool for low-dimensional magnetic system energy optimization.

The release of ChatGPT, a language model capable of generating text that appears human-like and authentic, has gained significant attention beyond the research community. We expect that the convincing performance of ChatGPT incentivizes users to apply it to a variety of downstream tasks, including prompting the model to simplify their own medical reports. To investigate this phenomenon, we conducted an exploratory case study. In a questionnaire, we asked 15 radiologists to assess the quality of radiology reports simplified by ChatGPT. Most radiologists agreed that the simplified reports were factually correct, complete, and not potentially harmful to the patient. Nevertheless, instances of incorrect statements, missed key medical findings, and potentially harmful passages were reported. While further studies are needed, the initial insights of this study indicate a great potential in using large language models like ChatGPT to improve patient-centered care in radiology and other medical domains.

Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised dimensionality reduction is described. The method is compared to other methods on synthetic and real data obtained from crashworthiness analyses. The results show a superiority of the here described approach over state of the art surrogate modelling techniques, Polynomial Chaos Expansions and Neural Networks.

Purpose: Tracking the 3D motion of the surgical tool and the patient anatomy is a fundamental requirement for computer-assisted skull-base surgery. The estimated motion can be used both for intra-operative guidance and for downstream skill analysis. Recovering such motion solely from surgical videos is desirable, as it is compliant with current clinical workflows and instrumentation. Methods: We present Tracker of Anatomy and Tool (TAToo). TAToo jointly tracks the rigid 3D motion of patient skull and surgical drill from stereo microscopic videos. TAToo estimates motion via an iterative optimization process in an end-to-end differentiable form. For robust tracking performance, TAToo adopts a probabilistic formulation and enforces geometric constraints on the object level. Results: We validate TAToo on both simulation data, where ground truth motion is available, as well as on anthropomorphic phantom data, where optical tracking provides a strong baseline. We report sub-millimeter and millimeter inter-frame tracking accuracy for skull and drill, respectively, with rotation errors below 1{\deg}. We further illustrate how TAToo may be used in a surgical navigation setting. Conclusion: We present TAToo, which simultaneously tracks the surgical tool and the patient anatomy in skull-base surgery. TAToo directly predicts the motion from surgical videos, without the need of any markers. Our results show that the performance of TAToo compares favorably to competing approaches. Future work will include fine-tuning of our depth network to reach a 1 mm clinical accuracy goal desired for surgical applications in the skull base.

Selecting the number of topics in LDA models is considered to be a difficult task, for which alternative approaches have been proposed. The performance of the recently developed singular Bayesian information criterion (sBIC) is evaluated and compared to the performance of alternative model selection criteria. The sBIC is a generalization of the standard BIC that can be implemented to singular statistical models. The comparison is based on Monte Carlo simulations and carried out for several alternative settings, varying with respect to the number of topics, the number of documents and the size of documents in the corpora. Performance is measured using different criteria which take into account the correct number of topics, but also whether the relevant topics from the DGPs are identified. Practical recommendations for LDA model selection in applications are derived.

Previous work has shown the potential of deep learning to predict renal obstruction using kidney ultrasound images. However, these image-based classifiers have been trained with the goal of single-visit inference in mind. We compare methods from video action recognition (i.e. convolutional pooling, LSTM, TSM) to adapt single-visit convolutional models to handle multiple visit inference. We demonstrate that incorporating images from a patient's past hospital visits provides only a small benefit for the prediction of obstructive hydronephrosis. Therefore, inclusion of prior ultrasounds is beneficial, but prediction based on the latest ultrasound is sufficient for patient risk stratification.

Prostate cancer is the most common cancer in men worldwide and the second leading cause of cancer death in the United States. One of the prognostic features in prostate cancer is the Gleason grading of histopathology images. The Gleason grade is assigned based on tumor architecture on Hematoxylin and Eosin (H&E) stained whole slide images (WSI) by the pathologists. This process is time-consuming and has known interobserver variability. In the past few years, deep learning algorithms have been used to analyze histopathology images, delivering promising results for grading prostate cancer. However, most of the algorithms rely on the fully annotated datasets which are expensive to generate. In this work, we proposed a novel weakly-supervised algorithm to classify prostate cancer grades. The proposed algorithm consists of three steps: (1) extracting discriminative areas in a histopathology image by employing the Multiple Instance Learning (MIL) algorithm based on Transformers, (2) representing the image by constructing a graph using the discriminative patches, and (3) classifying the image into its Gleason grades by developing a Graph Convolutional Neural Network (GCN) based on the gated attention mechanism. We evaluated our algorithm using publicly available datasets, including TCGAPRAD, PANDA, and Gleason 2019 challenge datasets. We also cross validated the algorithm on an independent dataset. Results show that the proposed model achieved state-of-the-art performance in the Gleason grading task in terms of accuracy, F1 score, and cohen-kappa. The code is available at https://github.com/NabaviLab/Prostate-Cancer.