Upcoming astronomical surveys will observe billions of galaxies across cosmic time, providing a unique opportunity to map the many pathways of galaxy assembly to an incredibly high resolution. However, the huge amount of data also poses an immediate computational challenge: current tools for inferring parameters from the light of galaxies take $\gtrsim 10$ hours per fit. This is prohibitively expensive. Simulation-based Inference (SBI) is a promising solution. However, it requires simulated data with identical characteristics to the observed data, whereas real astronomical surveys are often highly heterogeneous, with missing observations and variable uncertainties determined by sky and telescope conditions. Here we present a Monte Carlo technique for treating out-of-distribution measurement errors and missing data using standard SBI tools. We show that out-of-distribution measurement errors can be approximated by using standard SBI evaluations, and that missing data can be marginalized over using SBI evaluations over nearby data realizations in the training set. While these techniques slow the inference process from $\sim 1$ sec to $\sim 1.5$ min per object, this is still significantly faster than standard approaches while also dramatically expanding the applicability of SBI. This expanded regime has broad implications for future applications to astronomical surveys.

Designing experiments often requires balancing between learning about the true treatment effects and earning from allocating more samples to the superior treatment. While optimal algorithms for the Multi-Armed Bandit Problem (MABP) provide allocation policies that optimally balance learning and earning, they tend to be computationally expensive. The Gittins Index (GI) is a solution to the MABP that can simultaneously attain optimality and computationally efficiency goals, and it has been recently used in experiments with Bernoulli and Gaussian rewards. For the first time, we present a modification of the GI rule that can be used in experiments with exponentially-distributed rewards. We report its performance in simulated 2- armed and 3-armed experiments. Compared to traditional non-adaptive designs, our novel GI modified design shows operating characteristics comparable in learning (e.g. statistical power) but substantially better in earning (e.g. direct benefits). This illustrates the potential that designs using a GI approach to allocate participants have to improve participant benefits, increase efficiencies, and reduce experimental costs in adaptive multi-armed experiments with exponential rewards.

In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value function converges to the robust average-reward as the discount factor $\gamma$ goes to $1$, and moreover, when $\gamma$ is large, any optimal policy of the robust discounted MDP is also an optimal policy of the robust average-reward. We further design a robust dynamic programming approach, and theoretically characterize its convergence to the optimum. Then, we investigate robust average-reward MDPs directly without using discounted MDPs as an intermediate step. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value iteration algorithm that provably finds its solution, or equivalently, the optimal robust policy.

Creating compelling captions for data visualizations has been a longstanding challenge. Visualization researchers are typically untrained in journalistic reporting and hence the captions that are placed below data visualizations tend to be not overly engaging and rather just stick to basic observations about the data. In this work we explore the opportunities offered by the newly emerging crop of large language models (LLM) which use sophisticated deep learning technology to produce human-like prose. We ask, can these powerful software devices be purposed to produce engaging captions for generic data visualizations like a scatterplot. It turns out that the key challenge lies in designing the most effective prompt for the LLM, a task called prompt engineering. We report on first experiments using the popular LLM GPT-3 and deliver some promising results.

We introduce a sketch-and-solve approach to speed up the Peng-Wei semidefinite relaxation of k-means clustering. When the data is appropriately separated we identify the k-means optimal clustering. Otherwise, our approach provides a high-confidence lower bound on the optimal k-means value. This lower bound is data-driven; it does not make any assumption on the data nor how it is generated. We provide code and an extensive set of numerical experiments where we use this approach to certify approximate optimality of clustering solutions obtained by k-means++.

Universal cross-lingual sentence embeddings map semantically similar cross-lingual sentences into a shared embedding space. Aligning cross-lingual sentence embeddings usually requires supervised cross-lingual parallel sentences. In this work, we propose mSimCSE, which extends SimCSE to multilingual settings and reveal that contrastive learning on English data can surprisingly learn high-quality universal cross-lingual sentence embeddings without any parallel data. In unsupervised and weakly supervised settings, mSimCSE significantly improves previous sentence embedding methods on cross-lingual retrieval and multilingual STS tasks. The performance of unsupervised mSimCSE is comparable to fully supervised methods in retrieving low-resource languages and multilingual STS. The performance can be further enhanced when cross-lingual NLI data is available. Our code is publicly available at https://github.com/yaushian/mSimCSE.

Spectral methods provide consistent estimators for community detection in dense graphs. However, their performance deteriorates as the graphs become sparser. In this work we consider a random graph model that can produce graphs at different levels of sparsity, and we show that graph neural networks can outperform spectral methods on sparse graphs. We illustrate the results with numerical examples in both synthetic and real graphs.

To apply federated learning to drug discovery we developed a novel platform in the context of European Innovative Medicines Initiative (IMI) project MELLODDY (grant n{\deg}831472), which was comprised of 10 pharmaceutical companies, academic research labs, large industrial companies and startups. The MELLODDY platform was the first industry-scale platform to enable the creation of a global federated model for drug discovery without sharing the confidential data sets of the individual partners. The federated model was trained on the platform by aggregating the gradients of all contributing partners in a cryptographic, secure way following each training iteration. The platform was deployed on an Amazon Web Services (AWS) multi-account architecture running Kubernetes clusters in private subnets. Organisationally, the roles of the different partners were codified as different rights and permissions on the platform and administrated in a decentralized way. The MELLODDY platform generated new scientific discoveries which are described in a companion paper.

在模棱两可的机器中，学习的想法是将学习限制为假设类别，在某些群体行动方面，所有功能都是均等的。通常使用不可约说的表示或不变理论来参数化此类函数的空间。在本说明中，我们解释了归因于Malgrange的一般过程，以表达线性空间之间的所有多项式图，这些线性空间相对于组$ G $的作用，鉴于对较大空间的不变多项式的表征。该方法还可以在$ g $是一个紧凑的谎言组的情况下参数光滑的模糊图。

图神经网络（GNN）是非欧盟数据的强大深度学习方法。流行的GNN是通信算法（MPNNS），它们在本地图中汇总并结合了信号。但是，浅的mpnns倾向于错过远程信号，并且在某些异质图上表现不佳，而深度mpnns可能会遇到过度平滑或过度阵型等问题。为了减轻此类问题，现有的工作通常会从欧几里得数据上训练神经网络或修改图形结构中借用归一化技术。然而，这些方法在理论上并不是很好地理解，并且可能会提高整体计算复杂性。在这项工作中，我们从光谱图嵌入中汲取灵感，并提出$ \ texttt {powerembed} $ - 一种简单的层归一化技术来增强mpnns。我们显示$ \ texttt {powerembed} $可以证明图形运算符的顶部 - $ k $引导特征向量，该算子可以防止过度光滑，并且对图形拓扑是不可知的；同时，它产生了从本地功能到全球信号的表示列表，避免了过度阵列。我们将$ \ texttt {powerembed} $应用于广泛的模拟和真实图表，并展示其竞争性能，尤其是对于异性图。