A simple model to study subspace clustering is the high-dimensional $k$-Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction error in this model in the high-dimensional regime with extensive sparsity, i.e. when the fraction of non-zero components of the cluster means $\rho$, as well as the ratio $\alpha$ between the number of samples and the dimension are fixed, while the dimension diverges. We identify the information-theoretic threshold below which obtaining a positive correlation with the true cluster means is statistically impossible. Additionally, we investigate the performance of the approximate message passing (AMP) algorithm analyzed via its state evolution, which is conjectured to be optimal among polynomial algorithm for this task. We identify in particular the existence of a statistical-to-computational gap between the algorithm that require a signal-to-noise ratio $\lambda_{\text{alg}} \ge k / \sqrt{\alpha} $ to perform better than random, and the information theoretic threshold at $\lambda_{\text{it}} \approx \sqrt{-k \rho \log{\rho}} / \sqrt{\alpha}$. Finally, we discuss the case of sub-extensive sparsity $\rho$ by comparing the performance of the AMP with other sparsity-enhancing algorithms, such as sparse-PCA and diagonal thresholding.

我们考虑内核分类的问题。内核回归的作品表明，预测误差的衰减率与大量数据集的样品数量的数量有两个数量：数据集的容量和来源。在这项工作中，我们计算了高斯设计下错误分类（预测）错误的衰减率，以满足源和容量假设的数据集。我们得出了两个标准内核分类设置的源和容量系数的函数，即边缘最大化支持向量机（SVM）和脊分类，并将两种方法对比。结果，我们发现该类别的数据集已知的最差案例频率松散。最后，我们表明，在实际数据集中还观察到了这项工作中介绍的费率。

与经典线性模型不同，非线性生成模型在统计学习的文献中被稀疏地解决。这项工作旨在引起对这些模型及其保密潜力的关注。为此，我们调用了复制方法，以在反相反的问题中得出渐近归一化的横熵，其生成模型由具有通用协方差函数的高斯随机场描述。我们的推导进一步证明了贝叶斯估计量的渐近统计解耦，并为给定的非线性模型指定了解耦设置。复制解决方案描述了严格的非线性模型建立了全有或全无的相变：存在一个关键负载，最佳贝叶斯推断从完美的学习变为不相关的学习。基于这一发现，我们设计了一种新的安全编码方案，该方案可实现窃听通道的保密能力。这个有趣的结果意味着，严格的非线性生成模型是完美的，没有任何安全编码。我们通过分析说明性模型的完全安全和可靠的推论来证明后一种陈述是合理的。

多级分类问题的广义线性模型是现代机器学习任务的基本构建块之一。在本手稿中，我们通过具有任何凸损耗和正规化的经验风险最小化（ERM）来描述与通用手段和协方士的k $高斯的混合。特别是，我们证明了表征ERM估计的精确渐近剂，以高维度，在文献中扩展了关于高斯混合分类的几个先前结果。我们举例说明我们在统计学习中的两个兴趣任务中的两个任务：a）与稀疏手段的混合物进行分类，我们研究了$ \ ell_2 $的$ \ ell_1 $罚款的效率; b）Max-Margin多级分类，在那里我们在$ k> 2 $的多级逻辑最大似然估计器上表征了相位过渡。最后，我们讨论了我们的理论如何超出合成数据的范围，显示在不同的情况下，高斯混合在真实数据集中密切地捕获了分类任务的学习曲线。

在本手稿中，我们考虑在高斯设计下的内核Ridge回归（KRR）。根据特征的幂律衰减，在各种作品中报告了KRR过度概括误差衰减的指数。然而，这些衰变是为虚拟化的不同设置提供，即在无噪声案例中，在恒定正则化和嘈杂的最佳正则化案例中。中介设置已留下了大幅上未公布的。在这项工作中，我们统一并扩展了这一工作，提供了所有制度的表征和可以在噪声和正则化相互作用方面观察到的超出误差衰减率。特别是，我们展示了随着样本复杂性增加了无噪音指数与其嘈杂值之间的嘈杂设置中的过渡。最后，我们说明了如何在真实数据集上观察到该交叉。

教师 - 学生模型提供了一个框架，其中可以以封闭形式描述高维监督学习的典型情况。高斯I.I.D的假设然而，可以认为典型教师 - 学生模型的输入数据可以被认为过于限制，以捕获现实数据集的行为。在本文中，我们介绍了教师和学生可以在不同的空格上行动的模型的高斯协变态概括，以固定的，而是通用的特征映射。虽然仍处于封闭形式的仍然可解决，但这种概括能够捕获广泛的现实数据集的学习曲线，从而兑现师生框架的潜力。我们的贡献是两倍：首先，我们证明了渐近培训损失和泛化误差的严格公式。其次，我们呈现了许多情况，其中模型的学习曲线捕获了使用内​​核回归和分类学习的现实数据集之一，其中盒出开箱特征映射，例如随机投影或散射变换，或者与散射变换预先学习的 - 例如通过培训多层神经网络学到的特征。我们讨论了框架的权力和局限性。

Neural style transfer is a deep learning technique that produces an unprecedentedly rich style transfer from a style image to a content image and is particularly impressive when it comes to transferring style from a painting to an image. It was originally achieved by solving an optimization problem to match the global style statistics of the style image while preserving the local geometric features of the content image. The two main drawbacks of this original approach is that it is computationally expensive and that the resolution of the output images is limited by high GPU memory requirements. Many solutions have been proposed to both accelerate neural style transfer and increase its resolution, but they all compromise the quality of the produced images. Indeed, transferring the style of a painting is a complex task involving features at different scales, from the color palette and compositional style to the fine brushstrokes and texture of the canvas. This paper provides a solution to solve the original global optimization for ultra-high resolution images, enabling multiscale style transfer at unprecedented image sizes. This is achieved by spatially localizing the computation of each forward and backward passes through the VGG network. Extensive qualitative and quantitative comparisons show that our method produces a style transfer of unmatched quality for such high resolution painting styles.

The number of international benchmarking competitions is steadily increasing in various fields of machine learning (ML) research and practice. So far, however, little is known about the common practice as well as bottlenecks faced by the community in tackling the research questions posed. To shed light on the status quo of algorithm development in the specific field of biomedical imaging analysis, we designed an international survey that was issued to all participants of challenges conducted in conjunction with the IEEE ISBI 2021 and MICCAI 2021 conferences (80 competitions in total). The survey covered participants' expertise and working environments, their chosen strategies, as well as algorithm characteristics. A median of 72% challenge participants took part in the survey. According to our results, knowledge exchange was the primary incentive (70%) for participation, while the reception of prize money played only a minor role (16%). While a median of 80 working hours was spent on method development, a large portion of participants stated that they did not have enough time for method development (32%). 25% perceived the infrastructure to be a bottleneck. Overall, 94% of all solutions were deep learning-based. Of these, 84% were based on standard architectures. 43% of the respondents reported that the data samples (e.g., images) were too large to be processed at once. This was most commonly addressed by patch-based training (69%), downsampling (37%), and solving 3D analysis tasks as a series of 2D tasks. K-fold cross-validation on the training set was performed by only 37% of the participants and only 50% of the participants performed ensembling based on multiple identical models (61%) or heterogeneous models (39%). 48% of the respondents applied postprocessing steps.

State-of-the-art brain tumor segmentation is based on deep learning models applied to multi-modal MRIs. Currently, these models are trained on images after a preprocessing stage that involves registration, interpolation, brain extraction (BE, also known as skull-stripping) and manual correction by an expert. However, for clinical practice, this last step is tedious and time-consuming and, therefore, not always feasible, resulting in skull-stripping faults that can negatively impact the tumor segmentation quality. Still, the extent of this impact has never been measured for any of the many different BE methods available. In this work, we propose an automatic brain tumor segmentation pipeline and evaluate its performance with multiple BE methods. Our experiments show that the choice of a BE method can compromise up to 15.7% of the tumor segmentation performance. Moreover, we propose training and testing tumor segmentation models on non-skull-stripped images, effectively discarding the BE step from the pipeline. Our results show that this approach leads to a competitive performance at a fraction of the time. We conclude that, in contrast to the current paradigm, training tumor segmentation models on non-skull-stripped images can be the best option when high performance in clinical practice is desired.

Reinforcement learning is a machine learning approach based on behavioral psychology. It is focused on learning agents that can acquire knowledge and learn to carry out new tasks by interacting with the environment. However, a problem occurs when reinforcement learning is used in critical contexts where the users of the system need to have more information and reliability for the actions executed by an agent. In this regard, explainable reinforcement learning seeks to provide to an agent in training with methods in order to explain its behavior in such a way that users with no experience in machine learning could understand the agent's behavior. One of these is the memory-based explainable reinforcement learning method that is used to compute probabilities of success for each state-action pair using an episodic memory. In this work, we propose to make use of the memory-based explainable reinforcement learning method in a hierarchical environment composed of sub-tasks that need to be first addressed to solve a more complex task. The end goal is to verify if it is possible to provide to the agent the ability to explain its actions in the global task as well as in the sub-tasks. The results obtained showed that it is possible to use the memory-based method in hierarchical environments with high-level tasks and compute the probabilities of success to be used as a basis for explaining the agent's behavior.