现代对高斯工艺的近似适合“高数据”，其成本在观测值的数量中缩放，但在``宽数据''上表现不佳，在输入功能的数量方面缩小了很差。也就是说，随着输入功能的数量的增长，良好的预测性能需要汇总变量及其相关成本的数量才能快速增长。我们引入了一个内核，该内核允许汇总变量的数量通过输入功能的数量成倍增长，但在观测数和输入功能的数量中仅需要线性成本。通过引入B \'ezier Buttress来实现此缩放，该块允许在无需计算矩阵倒置或决定因素的情况下进行近似推断。我们表明，我们的内核与高斯流程回归中一些最常用的内核具有非常相似的相似之处，并从经验上证明了内核可以扩展到高大和宽的数据集的能力。

贝叶斯后期和模型证据的计算通常需要数值整合。贝叶斯正交（BQ）是一种基于替代模型的数值整合方法，能够具有出色的样品效率，但其缺乏并行化阻碍了其实际应用。在这项工作中，我们提出了一种并行的（批次）BQ方法，该方法采用了核正素的技术，该技术具有证明是指数的收敛速率。另外，与嵌套采样一样，我们的方法允许同时推断后期和模型证据。重新选择了来自BQ替代模型的样品，通过内核重组算法获得一组稀疏的样品，需要可忽略的额外时间来增加批处理大小。从经验上讲，我们发现我们的方法显着优于在包括锂离子电池分析在内的各种现实世界数据集中，最先进的BQ技术和嵌套采样的采样效率。

空间变压器网络（STNS）估计图像变换，可以通过“放大”图像中的相关区域来改善下游任务。但是，STN很难训练，并且对转型的错误预测敏感。为了避免这些局限性，我们提出了一种概率扩展，该扩展估计了随机转化而不是确定性的转换。边缘化转换使我们能够以多个姿势考虑每个图像，这使本地化任务变得更加容易，并且培训更加健壮。作为另一个好处，随机转换充当了局部，学习的数据增强，可改善下游任务。我们在标准成像基准和充满挑战的现实数据集中显示，这两种属性可改善分类性能，鲁棒性和模型校准。我们进一步证明，该方法通过改善时间序列数据的模型性能来推广到非视觉域。

The performance of the Deep Learning (DL) models depends on the quality of labels. In some areas, the involvement of human annotators may lead to noise in the data. When these corrupted labels are blindly regarded as the ground truth (GT), DL models suffer from performance deficiency. This paper presents a method that aims to learn a confident model in the presence of noisy labels. This is done in conjunction with estimating the uncertainty of multiple annotators. We robustly estimate the predictions given only the noisy labels by adding entropy or information-based regularizer to the classifier network. We conduct our experiments on a noisy version of MNIST, CIFAR-10, and FMNIST datasets. Our empirical results demonstrate the robustness of our method as it outperforms or performs comparably to other state-of-the-art (SOTA) methods. In addition, we evaluated the proposed method on the curated dataset, where the noise type and level of various annotators depend on the input image style. We show that our approach performs well and is adept at learning annotators' confusion. Moreover, we demonstrate how our model is more confident in predicting GT than other baselines. Finally, we assess our approach for segmentation problem and showcase its effectiveness with experiments.

Landing an unmanned aerial vehicle unmanned aerial vehicle (UAV) on top of an unmanned surface vehicle (USV) in harsh open waters is a challenging problem, owing to forces that can damage the UAV due to a severe roll and/or pitch angle of the USV during touchdown. To tackle this, we propose a novel model predictive control (MPC) approach enabling a UAV to land autonomously on a USV in these harsh conditions. The MPC employs a novel objective function and an online decomposition of the oscillatory motion of the vessel to predict, attempt, and accomplish the landing during near-zero tilt of the landing platform. The nonlinear prediction of the motion of the vessel is performed using visual data from an onboard camera. Therefore, the system does not require any communication with the USV or a control station. The proposed method was analyzed in numerous robotics simulations in harsh and extreme conditions and further validated in various real-world scenarios.

We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifold of point clouds. Our theory provides theoretical guarantees and explicit bounds on the functional form of the graph Laplacian, in the case when it acts on functions defined close to singularities of the underlying manifold. We also propose methods that can be used to estimate these geometric properties of the point cloud, which are based on the theoretical guarantees.

Nearly all jurisdictions in the United States require a professional license exam, commonly referred to as "the Bar Exam," as a precondition for law practice. To even sit for the exam, most jurisdictions require that an applicant completes at least seven years of post-secondary education, including three years at an accredited law school. In addition, most test-takers also undergo weeks to months of further, exam-specific preparation. Despite this significant investment of time and capital, approximately one in five test-takers still score under the rate required to pass the exam on their first try. In the face of a complex task that requires such depth of knowledge, what, then, should we expect of the state of the art in "AI?" In this research, we document our experimental evaluation of the performance of OpenAI's `text-davinci-003` model, often-referred to as GPT-3.5, on the multistate multiple choice (MBE) section of the exam. While we find no benefit in fine-tuning over GPT-3.5's zero-shot performance at the scale of our training data, we do find that hyperparameter optimization and prompt engineering positively impacted GPT-3.5's zero-shot performance. For best prompt and parameters, GPT-3.5 achieves a headline correct rate of 50.3% on a complete NCBE MBE practice exam, significantly in excess of the 25% baseline guessing rate, and performs at a passing rate for both Evidence and Torts. GPT-3.5's ranking of responses is also highly-correlated with correctness; its top two and top three choices are correct 71% and 88% of the time, respectively, indicating very strong non-entailment performance. While our ability to interpret these results is limited by nascent scientific understanding of LLMs and the proprietary nature of GPT, we believe that these results strongly suggest that an LLM will pass the MBE component of the Bar Exam in the near future.

The future of population-based breast cancer screening is likely personalized strategies based on clinically relevant risk models. Mammography-based risk models should remain robust to domain shifts caused by different populations and mammographic devices. Modern risk models do not ensure adaptation across vendor-domains and are often conflated to unintentionally rely on both precursors of cancer and systemic/global mammographic information associated with short- and long-term risk, respectively, which might limit performance. We developed a robust, cross-vendor model for long-term risk assessment. An augmentation-based domain adaption technique, based on flavorization of mammographic views, ensured generalization to an unseen vendor-domain. We trained on samples without diagnosed/potential malignant findings to learn systemic/global breast tissue features, called mammographic texture, indicative of future breast cancer. However, training so may cause erratic convergence. By excluding noise-inducing samples and designing a case-control dataset, a robust ensemble texture model was trained. This model was validated in two independent datasets. In 66,607 Danish women with flavorized Siemens views, the AUC was 0.71 and 0.65 for prediction of interval cancers within two years (ICs) and from two years after screening (LTCs), respectively. In a combination with established risk factors, the model's AUC increased to 0.68 for LTCs. In 25,706 Dutch women with Hologic-processed views, the AUCs were not different from the AUCs in Danish women with flavorized views. The results suggested that the model robustly estimated long-term risk while adapting to an unseen processed vendor-domain. The model identified 8.1% of Danish women accounting for 20.9% of ICs and 14.2% of LTCs.

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but the quality bar for medical and clinical applications is high. Today, attempts to assess models' clinical knowledge typically rely on automated evaluations on limited benchmarks. There is no standard to evaluate model predictions and reasoning across a breadth of tasks. To address this, we present MultiMedQA, a benchmark combining six existing open question answering datasets spanning professional medical exams, research, and consumer queries; and HealthSearchQA, a new free-response dataset of medical questions searched online. We propose a framework for human evaluation of model answers along multiple axes including factuality, precision, possible harm, and bias. In addition, we evaluate PaLM (a 540-billion parameter LLM) and its instruction-tuned variant, Flan-PaLM, on MultiMedQA. Using a combination of prompting strategies, Flan-PaLM achieves state-of-the-art accuracy on every MultiMedQA multiple-choice dataset (MedQA, MedMCQA, PubMedQA, MMLU clinical topics), including 67.6% accuracy on MedQA (US Medical License Exam questions), surpassing prior state-of-the-art by over 17%. However, human evaluation reveals key gaps in Flan-PaLM responses. To resolve this we introduce instruction prompt tuning, a parameter-efficient approach for aligning LLMs to new domains using a few exemplars. The resulting model, Med-PaLM, performs encouragingly, but remains inferior to clinicians. We show that comprehension, recall of knowledge, and medical reasoning improve with model scale and instruction prompt tuning, suggesting the potential utility of LLMs in medicine. Our human evaluations reveal important limitations of today's models, reinforcing the importance of both evaluation frameworks and method development in creating safe, helpful LLM models for clinical applications.

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, also a novel primal-dual Langevin algorithm for sampling from non-smooth distributions is introduced in this work.