我们考虑强大的线性回归模型$ \ boldsymbol {y} = x \ beta^* + \ boldsymbol {\ eta} $，其中一个对手忽略了design $ x \ in \ mathbb {r}^r}^n \ times D } $可以选择$ \ boldsymbol {\ eta} $以损坏所有观测值的（可能消失的）$ \ boldsymbol {y} $以任意方式。最近的工作[DLN+21，DNS21]引入了有效的算法，以持续恢复参数矢量。这些算法至关重要地依赖于设计矩阵非常广泛（如果其列跨度远非任何稀疏矢量，矩阵就可以很好地扩展）。在本文中，我们表明存在一个缺乏良好性的设计矩阵家族，因此从理论上讲，在上述稳健线性回归模型中，参数向量的持续恢复是不可能的。我们进一步研究了随机矩阵的良好表现的平均案例时间复杂性。我们表明，如果观察值的数量在环境维度上是二次的，则可以有效地证明给定的$ n $ by-by-by-by-by-by-d $ d $ d $高斯矩阵是否会很好地扩展。当观察数为$ O（d^2）$时，我们通过显示出相同认证问题的计算硬度的严格证据来补充这一结果。

我们开发了第一个快速频谱算法，用于分解$ \ mathbb {r}^d $排名到$ o的随机三阶张量。我们的算法仅涉及简单的线性代数操作，并且可以在当前矩阵乘法时间下在时间$ o（d^{6.05}）$中恢复所有组件。在这项工作之前，只能通过方形的总和[MA，Shi，Steurer 2016]实现可比的保证。相反，快速算法[Hopkins，Schramm，Shi，Steurer 2016]只能分解排名最多的张量（D^{4/3}/\ text {polylog}（d））$。我们的算法结果取决于两种关键成分。将三阶张量的清洁提升到六阶张量，可以用张量网络的语言表示。将张量网络仔细分解为一系列矩形矩阵乘法，这使我们能够快速实现该算法。

我们开发了一种高效的随机块模型中的弱恢复算法。该算法与随机块模型的Vanilla版本的最佳已知算法的统计保证匹配。从这个意义上讲，我们的结果表明，随机块模型没有稳健性。我们的工作受到最近的银行，Mohanty和Raghavendra（SODA 2021）的工作，为相应的区别问题提供了高效的算法。我们的算法及其分析显着脱离了以前的恢复。关键挑战是我们算法的特殊优化景观：种植的分区可能远非最佳意义，即完全不相关的解决方案可以实现相同的客观值。这种现象与PCA的BBP相转变的推出效应有关。据我们所知，我们的算法是第一个在非渐近设置中存在这种推出效果的鲁棒恢复。我们的算法是基于凸优化的框架的实例化（与平方和不同的不同），这对于其他鲁棒矩阵估计问题可能是有用的。我们的分析的副产物是一种通用技术，其提高了任意强大的弱恢复算法的成功（输入的随机性）从恒定（或缓慢消失）概率以指数高概率。

我们开发机器以设计有效的可计算和一致的估计，随着观察人数而达到零的估计误差，因为观察的次数增长，当面对可能损坏的答复，除了样本的所有品，除了每种量之外的ALL。作为具体示例，我们调查了两个问题：稀疏回归和主成分分析（PCA）。对于稀疏回归，我们实现了最佳样本大小的一致性$ n \ gtrsim（k \ log d）/ \ alpha ^ $和最佳错误率$ o（\ sqrt {（k \ log d）/（n \ cdot \ alpha ^ 2））$ N $是观察人数，$ D $是尺寸的数量，$ k $是参数矢量的稀疏性，允许在数量的数量中为逆多项式进行逆多项式样品。在此工作之前，已知估计是一致的，当Inliers $ \ Alpha $ IS $ O（1 / \ log \ log n）$，即使是（非球面）高斯设计矩阵时也是一致的。结果在弱设计假设下持有，并且在这种一般噪声存在下仅被D'Orsi等人最近以密集的设置（即一般线性回归）显示。 [DNS21]。在PCA的上下文中，我们在参数矩阵上的广泛尖端假设下获得最佳错误保证（通常用于矩阵完成）。以前的作品可以仅在假设下获得非琐碎的保证，即与最基于的测量噪声以$ n $（例如，具有方差1 / n ^ 2 $的高斯高斯）。为了设计我们的估算，我们用非平滑的普通方（如$ \ ell_1 $ norm或核规范）装备Huber丢失，并以一种新的方法来分析损失的新方法[DNS21]的方法[DNS21]。功能。我们的机器似乎很容易适用于各种估计问题。

我们研究了稀疏张量主成分分析的问题：给定张量$ \ pmb y = \ pmb w + \ lambda x ^ {\ otimes p} $ with $ \ pmb w \ in \ otimes ^ p \ mathbb {r} ^ n $拥有iid高斯条目，目标是恢复$ k $ -parse单位矢量$ x \ in \ mathbb {r} ^ n $。该模型捕获稀疏PCA（其Wigner形式）和张量PCA。对于$ k \ leq \ sqrt {n} $的高稀疏制度，我们介绍了一系列平滑地插值在简单的多项式算法和指数时穷举搜索算法之间的算法。对于任何$ 1 \ leq t \ leq k $，我们的算法恢复了信噪比$ \ lambda \ geq \ tilde {\ mathcal {o}}（\ sqrt {t} \ cdot（k / t ）^ {p / 2}）$时间$ \ tilde {\ mathcal {o}}（n ^ {p + t}）$，捕获矩阵设置的最先进的保证（在两者中多项式时间和子指数时间制度）。我们的结果自然地延伸到$ r $ distinct $ k $ -parse信号的案例与不相交的支持，保证与尖峰的数量无关。即使在稀疏PCA的局限性情况下，已知的算法也仅恢复$ \ lambda \ geq \ tilde {\ mathcal {o}}（k \ cdot r）$的稀疏向量，而我们的算法需要$ \ lambda \ geq \ tilde { \ mathcal {o}}（k）$。最后，通过分析低度似然比，我们将这些算法结果补充，具体证据说明信噪比和运行时间之间的权衡。该下限捕获稀疏PCA和张量PCA的已知下限。在这一普通模型中，我们在标准数量$ N $，稀疏$ k $的样本数量之间观察更复杂的三方权衡，以及张力电源$ p $。

An Anomaly Detection (AD) System for Self-diagnosis has been developed for Multiphase Flow Meter (MPFM). The system relies on machine learning algorithms for time series forecasting, historical data have been used to train a model and to predict the behavior of a sensor and, thus, to detect anomalies.

Diffusion models have achieved justifiable popularity by attaining state-of-the-art performance in generating realistic objects from seemingly arbitrarily complex data distributions, including when conditioning generation on labels. Unfortunately, however, their iterative nature renders them very computationally inefficient during the sampling process. For the multi-class conditional generation problem, we propose a novel, structurally unique framework of diffusion models which are hierarchically branched according to the inherent relationships between classes. In this work, we demonstrate that branched diffusion models offer major improvements in efficiently generating samples from multiple classes. We also showcase several other advantages of branched diffusion models, including ease of extension to novel classes in a continual-learning setting, and a unique interpretability that offers insight into these generative models. Branched diffusion models represent an alternative paradigm to their traditional linear counterparts, and can have large impacts in how we use diffusion models for efficient generation, online learning, and scientific discovery.

In the era of digital healthcare, the huge volumes of textual information generated every day in hospitals constitute an essential but underused asset that could be exploited with task-specific, fine-tuned biomedical language representation models, improving patient care and management. For such specialized domains, previous research has shown that fine-tuning models stemming from broad-coverage checkpoints can largely benefit additional training rounds over large-scale in-domain resources. However, these resources are often unreachable for less-resourced languages like Italian, preventing local medical institutions to employ in-domain adaptation. In order to reduce this gap, our work investigates two accessible approaches to derive biomedical language models in languages other than English, taking Italian as a concrete use-case: one based on neural machine translation of English resources, favoring quantity over quality; the other based on a high-grade, narrow-scoped corpus natively written in Italian, thus preferring quality over quantity. Our study shows that data quantity is a harder constraint than data quality for biomedical adaptation, but the concatenation of high-quality data can improve model performance even when dealing with relatively size-limited corpora. The models published from our investigations have the potential to unlock important research opportunities for Italian hospitals and academia. Finally, the set of lessons learned from the study constitutes valuable insights towards a solution to build biomedical language models that are generalizable to other less-resourced languages and different domain settings.

Crop type maps are critical for tracking agricultural land use and estimating crop production. Remote sensing has proven an efficient and reliable tool for creating these maps in regions with abundant ground labels for model training, yet these labels remain difficult to obtain in many regions and years. NASA's Global Ecosystem Dynamics Investigation (GEDI) spaceborne lidar instrument, originally designed for forest monitoring, has shown promise for distinguishing tall and short crops. In the current study, we leverage GEDI to develop wall-to-wall maps of short vs tall crops on a global scale at 10 m resolution for 2019-2021. Specifically, we show that (1) GEDI returns can reliably be classified into tall and short crops after removing shots with extreme view angles or topographic slope, (2) the frequency of tall crops over time can be used to identify months when tall crops are at their peak height, and (3) GEDI shots in these months can then be used to train random forest models that use Sentinel-2 time series to accurately predict short vs. tall crops. Independent reference data from around the world are then used to evaluate these GEDI-S2 maps. We find that GEDI-S2 performed nearly as well as models trained on thousands of local reference training points, with accuracies of at least 87% and often above 90% throughout the Americas, Europe, and East Asia. Systematic underestimation of tall crop area was observed in regions where crops frequently exhibit low biomass, namely Africa and South Asia, and further work is needed in these systems. Although the GEDI-S2 approach only differentiates tall from short crops, in many landscapes this distinction goes a long way toward mapping the main individual crop types. The combination of GEDI and Sentinel-2 thus presents a very promising path towards global crop mapping with minimal reliance on ground data.

Algorithms and technologies are essential tools that pervade all aspects of our daily lives. In the last decades, health care research benefited from new computer-based recruiting methods, the use of federated architectures for data storage, the introduction of innovative analyses of datasets, and so on. Nevertheless, health care datasets can still be affected by data bias. Due to data bias, they provide a distorted view of reality, leading to wrong analysis results and, consequently, decisions. For example, in a clinical trial that studied the risk of cardiovascular diseases, predictions were wrong due to the lack of data on ethnic minorities. It is, therefore, of paramount importance for researchers to acknowledge data bias that may be present in the datasets they use, eventually adopt techniques to mitigate them and control if and how analyses results are impacted. This paper proposes a method to address bias in datasets that: (i) defines the types of data bias that may be present in the dataset, (ii) characterizes and quantifies data bias with adequate metrics, (iii) provides guidelines to identify, measure, and mitigate data bias for different data sources. The method we propose is applicable both for prospective and retrospective clinical trials. We evaluate our proposal both through theoretical considerations and through interviews with researchers in the health care environment.