在本文中，我们解决了测试两个观察到的树$（t，t'）$是独立采样还是从它们相关的联合分布中进行采样的问题。这个问题我们称为树中的相关检测，在两个相关随机图的图形对齐中起着关键作用。通过图形对准，我们研究了单方面测试的存在条件，即具有I型误差和非呈现能力的消失的测试。对于带有平均$ \ lambda的Poisson后代的相关Galton-Watson模型，我们在（0,1）$中$ s $ s \ s $ s \ in（0,1）$，我们在$ s = \ sqrt { \ alpha} $，其中$ \ alpha \ sim 0.3383 $是Otter的常数。也就是说，我们证明，对于$ s \ leq \ sqrt {\ alpha} $，不存在此类测试，并且每当$ \ sqrt {\ alpha} $，$ \ lambda $ for Empoot Foom Foom时，就存在此类测试。该结果为稀疏制度（$ o（1）$平均节点度）以及Ganassali等人研究的MPALIGN方法的性能提供了有关图形对准问题的新启示。 （2021），Piccioli等。 （2021），特别是Piccioli等人的猜想。 （2021）MPALIGN在相关参数的部分恢复任务中取得成功，提供了平均节点度$ \ lambda $的平均节点$ \ lambda $足够大。

分散的优化在机器学习方面越来越受欢迎，其可伸缩性和效率。直观地，它也应提供更好的隐私保证，因为节点只能观察到网络图中其邻居发送的消息。但是，正式化和量化这一收益是具有挑战性的：现有结果通常仅限于当地差异隐私（LDP）保证忽略权力下放的优势。在这项工作中，我们介绍了成对网络差异隐私，这是一种放松的LDP，该隐藏率捕获了一个事实，即从节点$ u $到节点$ v $的隐私泄漏可能取决于它们在图中的相对位置。然后，我们分析局部噪声注入与固定和随机通信图上的（简单或随机）八卦方案的组合。我们还得出了一种差异化的分散优化算法，该算法在局部梯度下降步骤和八卦平均之间进行交替。我们的结果表明，我们的算法放大隐私保证是图表中节点之间距离的函数，与受信任策展人的隐私性权衡取舍相匹配，直到明确取决于图形拓扑的因素。最后，我们通过有关合成和现实世界数据集的实验来说明我们的隐私收益。

Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We obtain sufficient conditions under which this testing is impossible or feasible. We propose MPAlign, a message-passing algorithm for graph alignment inspired by the tree correlation detection problem. We prove MPAlign to succeed in polynomial time at partial alignment whenever tree detection is feasible. As a result our analysis of tree detection reveals new ranges of parameters for which partial alignment of sparse random graphs is feasible in polynomial time. We then conjecture that graph alignment is not feasible in polynomial time when the associated tree detection problem is impossible. If true, this conjecture together with our sufficient conditions on tree detection impossibility would imply the existence of a hard phase for graph alignment, i.e. a parameter range where alignment cannot be done in polynomial time even though it is known to be feasible in non-polynomial time.

在本文中，我们考虑图对对齐问题，这是恢复的问题，给定两个图形，节点之间的一对一映射，最大化边缘重叠。此问题可以被视为众所周知的图形同构问题的嘈杂版本，并出现在许多应用中，包括社交网络Deanymation和蜂窝生物学。我们这里的焦点是部分恢复，即，我们寻找一个一对一的映射，这对图形的节点的一小部分而不是在所有这些上都是正确的，并且我们假设两个输入图对问题是相关的ERD \ h {o} sr \'enyi参数$（n，q，s）$。我们的主要贡献是在$（n，q，s）$给出必要和充分的条件，在其中部分恢复是可能的，因为节点N $的节点数量的概率很高。特别是，我们表明，在某些额外的假设下，可以在$ NQS = \ \ \θ（1）$制度中实现部分恢复。

Graph Neural Networks (GNNs) have shown great potential in the field of graph representation learning. Standard GNNs define a local message-passing mechanism which propagates information over the whole graph domain by stacking multiple layers. This paradigm suffers from two major limitations, over-squashing and poor long-range dependencies, that can be solved using global attention but significantly increases the computational cost to quadratic complexity. In this work, we propose an alternative approach to overcome these structural limitations by leveraging the ViT/MLP-Mixer architectures introduced in computer vision. We introduce a new class of GNNs, called Graph MLP-Mixer, that holds three key properties. First, they capture long-range dependency and mitigate the issue of over-squashing as demonstrated on the Long Range Graph Benchmark (LRGB) and the TreeNeighbourMatch datasets. Second, they offer better speed and memory efficiency with a complexity linear to the number of nodes and edges, surpassing the related Graph Transformer and expressive GNN models. Third, they show high expressivity in terms of graph isomorphism as they can distinguish at least 3-WL non-isomorphic graphs. We test our architecture on 4 simulated datasets and 7 real-world benchmarks, and show highly competitive results on all of them.

Over the past decade, neural networks have been successful at making predictions from biological sequences, especially in the context of regulatory genomics. As in other fields of deep learning, tools have been devised to extract features such as sequence motifs that can explain the predictions made by a trained network. Here we intend to go beyond explainable machine learning and introduce SEISM, a selective inference procedure to test the association between these extracted features and the predicted phenotype. In particular, we discuss how training a one-layer convolutional network is formally equivalent to selecting motifs maximizing some association score. We adapt existing sampling-based selective inference procedures by quantizing this selection over an infinite set to a large but finite grid. Finally, we show that sampling under a specific choice of parameters is sufficient to characterize the composite null hypothesis typically used for selective inference-a result that goes well beyond our particular framework. We illustrate the behavior of our method in terms of calibration, power and speed and discuss its power/speed trade-off with a simpler data-split strategy. SEISM paves the way to an easier analysis of neural networks used in regulatory genomics, and to more powerful methods for genome wide association studies (GWAS).

Information on the grass growth over a year is essential for some models simulating the use of this resource to feed animals on pasture or at barn with hay or grass silage. Unfortunately, this information is rarely available. The challenge is to reconstruct grass growth from two sources of information: usual daily climate data (rainfall, radiation, etc.) and cumulative growth over the year. We have to be able to capture the effect of seasonal climatic events which are known to distort the growth curve within the year. In this paper, we formulate this challenge as a problem of disaggregating the cumulative growth into a time series. To address this problem, our method applies time series forecasting using climate information and grass growth from previous time steps. Several alternatives of the method are proposed and compared experimentally using a database generated from a grassland process-based model. The results show that our method can accurately reconstruct the time series, independently of the use of the cumulative growth information.

As of 2022, greenhouse gases (GHG) emissions reporting and auditing are not yet compulsory for all companies and methodologies of measurement and estimation are not unified. We propose a machine learning-based model to estimate scope 1 and scope 2 GHG emissions of companies not reporting them yet. Our model, specifically designed to be transparent and completely adapted to this use case, is able to estimate emissions for a large universe of companies. It shows good out-of-sample global performances as well as good out-of-sample granular performances when evaluating it by sectors, by countries or by revenues buckets. We also compare our results to those of other providers and find our estimates to be more accurate. Thanks to the proposed explainability tools using Shapley values, our model is fully interpretable, the user being able to understand which factors split explain the GHG emissions for each particular company.

Robots are traditionally bounded by a fixed embodiment during their operational lifetime, which limits their ability to adapt to their surroundings. Co-optimizing control and morphology of a robot, however, is often inefficient due to the complex interplay between the controller and morphology. In this paper, we propose a learning-based control method that can inherently take morphology into consideration such that once the control policy is trained in the simulator, it can be easily deployed to robots with different embodiments in the real world. In particular, we present the Embodiment-aware Transformer (EAT), an architecture that casts this control problem as conditional sequence modeling. EAT outputs the optimal actions by leveraging a causally masked Transformer. By conditioning an autoregressive model on the desired robot embodiment, past states, and actions, our EAT model can generate future actions that best fit the current robot embodiment. Experimental results show that EAT can outperform all other alternatives in embodiment-varying tasks, and succeed in an example of real-world evolution tasks: stepping down a stair through updating the morphology alone. We hope that EAT will inspire a new push toward real-world evolution across many domains, where algorithms like EAT can blaze a trail by bridging the field of evolutionary robotics and big data sequence modeling.

Dependency hell is a well-known pain point in the development of large software projects and machine learning (ML) code bases are not immune from it. In fact, ML applications suffer from an additional form, namely, "data source dependency hell". This term refers to the central role played by data and its unique quirks that often lead to unexpected failures of ML models which cannot be explained by code changes. In this paper, we present an automated dependency mapping framework that allows MLOps engineers to monitor the whole dependency map of their models in a fast paced engineering environment and thus mitigate ahead of time the consequences of any data source changes (e.g., re-train model, ignore data, set default data etc.). Our system is based on a unified and generic approach, employing techniques from static analysis, from which data sources can be identified reliably for any type of dependency on a wide range of source languages and artefacts. The dependency mapping framework is exposed as a REST web API where the only input is the path to the Git repository hosting the code base. Currently used by MLOps engineers at Microsoft, we expect such dependency map APIs to be adopted more widely by MLOps engineers in the future.