Over the last decade, an approach that has gained a lot of popularity to tackle non-parametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of probability distributions. The main goal of our work is to understand the optimality of two-sample tests constructed based on this approach. First, we show that the popular MMD (maximum mean discrepancy) two-sample test is not optimal in terms of the separation boundary measured in Hellinger distance. Second, we propose a modification to the MMD test based on spectral regularization by taking into account the covariance information (which is not captured by the MMD test) and prove the proposed test to be minimax optimal with a smaller separation boundary than that achieved by the MMD test. Third, we propose an adaptive version of the above test which involves a data-driven strategy to choose the regularization parameter and show the adaptive test to be almost minimax optimal up to a logarithmic factor. Moreover, our results hold for the permutation variant of the test where the test threshold is chosen elegantly through the permutation of the samples. Through numerical experiments on synthetic and real-world data, we demonstrate the superior performance of the proposed test in comparison to the MMD test.

我们考虑在非参数环境中对高阶希尔伯特空间的高阶估计估计。我们提出的估计器缩小了Bochner积分量的$ U $统计估计器，而不是希尔伯特领域的预指定目标元素。根据$ u $统计的内核的退化，我们构建了一致的收缩估计量，并具有快速的收敛速度，并产生了Oracle不平等，比较了$ u $统计估计器的风险及其收缩版。令人惊讶的是，我们表明，通过假设$ u $统计的内核完全退化而设计的收缩估计器也是一致的估计器，即使内核不是完全退化。这项工作涵盖并改进了Krikamol等人，2016年，JMLR和Zhou等，2019，JMVA，它仅处理繁殖的内核Hilbert Space中的平均元素和协方差操作员估计。我们还将结果专注于正常的平均估计，并表明对于$ d \ ge 3 $，拟议的估算器严格根据平均误差的样本平均值进行了改进。

概率分布之间的差异措施是统计推理和机器学习的核心。在许多应用中，在不同的空格上支持感兴趣的分布，需要在数据点之间进行有意义的对应。激励明确地将一致的双向图编码为差异措施，这项工作提出了一种用于匹配的新型不平衡的Monge最佳运输制剂，达到异构体，在不同空间上的分布。我们的配方由于公制空间之间的Gromov-Haussdrow距离而受到了原则放松，并且采用了两个周期一致的地图，将每个分布推向另一个分布。我们研究了拟议的差异的结构性，并且特别表明它将流行的循环一致的生成对抗网络（GaN）框架捕获为特殊情况，从而提供理论解释它。通过计算效率激励，然后我们将差异括起来并将映射限制为参数函数类。由此产生的核化版本被创建为广义最大差异（GMMD）。研究了GMMD的经验估计的收敛速率，并提供了支持我们理论的实验。

我们派生并分析了一种用于估计有限簇树中的所有分裂的通用，递归算法以及相应的群集。我们进一步研究了从内核密度估计器接收级别设置估计时该通用聚类算法的统计特性。特别是，我们推出了有限的样本保证，一致性，收敛率以及用于选择内核带宽的自适应数据驱动策略。对于这些结果，我们不需要与H \“{o}连续性等密度的连续性假设，而是仅需要非参数性质的直观几何假设。

内核方法是强大的学习方法，允许执行非线性数据分析。尽管它们很受欢迎，但在大数据方案中，它们的可伸缩性差。已经提出了各种近似方法，包括随机特征近似，以减轻问题。但是，除了内核脊回归外，大多数这些近似内核方法的统计一致性尚不清楚，其中已证明随机特征近似不仅在计算上有效，而且在统计上与最小值最佳收敛速率一致。在本文中，我们通过研究近似KPCA的计算和统计行为之间的权衡，研究了内核主成分分析（KPCA）中随机特征近似的功效。我们表明，与KPCA相比，与KPCA相比，与KPCA相比，近似KPCA在与基于内核函数基于其对相应的特征面积的投影相关的误差方面是有效的。该分析取决于伯恩斯坦类型的不平等现象，对自我偶和式希尔伯特·史克米特（Hilbert-Schmidt）操作员价值u统计量的运营商和希尔伯特·史克米特（Hilbert-Schmidt）规范取决于独立利益。

Recently, deep networks have shown impressive performance for the segmentation of cardiac Magnetic Resonance Imaging (MRI) images. However, their achievement is proving slow to transition to widespread use in medical clinics because of robustness issues leading to low trust of clinicians to their results. Predicting run-time quality of segmentation masks can be useful to warn clinicians against poor results. Despite its importance, there are few studies on this problem. To address this gap, we propose a quality control method based on the agreement across decoders of a multi-view network, TMS-Net, measured by the cosine similarity. The network takes three view inputs resliced from the same 3D image along different axes. Different from previous multi-view networks, TMS-Net has a single encoder and three decoders, leading to better noise robustness, segmentation performance and run-time quality estimation in our experiments on the segmentation of the left atrium on STACOM 2013 and STACOM 2018 challenge datasets. We also present a way to generate poor segmentation masks by using noisy images generated with engineered noise and Rician noise to simulate undertraining, high anisotropy and poor imaging settings problems. Our run-time quality estimation method show a good classification of poor and good quality segmentation masks with an AUC reaching to 0.97 on STACOM 2018. We believe that TMS-Net and our run-time quality estimation method has a high potential to increase the thrust of clinicians to automatic image analysis tools.

Large Language Models (LLMs) have been the subject of active research, significantly advancing the field of Natural Language Processing (NLP). From BERT to BLOOM, LLMs have surpassed state-of-the-art results in various natural language tasks such as question answering, summarization, and text generation. Many ongoing efforts focus on understanding LLMs' capabilities, including their knowledge of the world, syntax, and semantics. However, extending the textual prowess of LLMs to symbolic reasoning has been slow and predominantly focused on tackling problems related to the mathematical field. In this paper, we explore the use of LLMs for automated planning - a branch of AI concerned with the realization of action sequences (plans) to achieve a goal, typically executed by intelligent agents, autonomous robots, and unmanned vehicles. We introduce Plansformer; an LLM fine-tuned on planning problems and capable of generating plans with favorable behavior in terms of correctness and length with reduced knowledge-engineering efforts. We also demonstrate the adaptability of Plansformer in solving different planning domains with varying complexities, owing to the transfer learning abilities of LLMs. For one configuration of Plansformer, we achieve ~97% valid plans, out of which ~95% are optimal for Towers of Hanoi - a puzzle-solving domain.

Chatbots, or bots for short, are multi-modal collaborative assistants that can help people complete useful tasks. Usually, when chatbots are referenced in connection with elections, they often draw negative reactions due to the fear of mis-information and hacking. Instead, in this paper, we explore how chatbots may be used to promote voter participation in vulnerable segments of society like senior citizens and first-time voters. In particular, we build a system that amplifies official information while personalizing it to users' unique needs transparently. We discuss its design, build prototypes with frequently asked questions (FAQ) election information for two US states that are low on an ease-of-voting scale, and report on its initial evaluation in a focus group. Our approach can be a win-win for voters, election agencies trying to fulfill their mandate and democracy at large.

Atrial Fibrillation (AF) is characterized by disorganised electrical activity in the atria and is known to be sustained by the presence of regions of fibrosis (scars) or functional cellular remodeling, both of which may lead to areas of slow conduction. Estimating the effective conductivity of the myocardium and identifying regions of abnormal propagation is therefore crucial for the effective treatment of AF. We hypothesise that the spatial distribution of tissue conductivity can be directly inferred from an array of concurrently acquired contact electrograms (EGMs). We generate a dataset of simulated cardiac AP propagation using randomised scar distributions and a phenomenological cardiac model and calculate contact electrograms at various positions on the field. A deep neural network, based on a modified U-net architecture, is trained to estimate the location of the scar and quantify conductivity of the tissue with a Jaccard index of $91$%. We adapt a wavelet-based surrogate testing analysis to confirm that the inferred conductivity distribution is an accurate representation of the ground truth input to the model. We find that the root mean square error (RMSE) between the ground truth and our predictions is significantly smaller ($p_{val}=0.007$) than the RMSE between the ground truth and surrogate samples.

自动驾驶汽车必须能够可靠地处理不利的天气条件（例如，雪地）安全运行。在本文中，我们研究了以不利条件捕获的转动传感器输入（即图像）的想法，将其下游任务（例如，语义分割）可以达到高精度。先前的工作主要将其作为未配对的图像到图像翻译问题，因为缺乏在完全相同的相机姿势和语义布局下捕获的配对图像。虽然没有完美对准的图像，但可以轻松获得粗配上的图像。例如，许多人每天在好天气和不利的天气中驾驶相同的路线；因此，在近距离GPS位置捕获的图像可以形成一对。尽管来自重复遍历的数据不太可能捕获相同的前景对象，但我们认为它们提供了丰富的上下文信息来监督图像翻译模型。为此，我们提出了一个新颖的训练目标，利用了粗糙的图像对。我们表明，我们与一致的训练方案可提高更好的图像翻译质量和改进的下游任务，例如语义分割，单眼深度估计和视觉定位。