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The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of probability distributions. This can be considered as a first step towards a more general treatment of statistical learning under epistemic uncertainty.

Datasets collecting software mentions from scholarly publications can potentially be used for research into the software that has been used in the published research, as well as into the practice of software citation. Recently, new software mention datasets with different characteristics have been published. We present an approach to assess the usability of such datasets for research on research software. Our approach includes sampling and data preparation, manual annotation for quality and mention characteristics, and annotation analysis. We applied it to two software mention datasets for evaluation based on qualitative observation. Doing this, we were able to find challenges to working with the selected datasets to do research. Main issues refer to the structure of the dataset, the quality of the extracted mentions (54% and 23% of mentions respectively are not to software), and software accessibility. While one dataset does not provide links to mentioned software at all, the other does so in a way that can impede quantitative research endeavors: (1) Links may come from different sources and each point to different software for the same mention. (2) The quality of the automatically retrieved links is generally poor (in our sample, 65.4% link the wrong software). (3) Links exist only for a small subset (in our sample, 20.5%) of mentions, which may lead to skewed or disproportionate samples. However, the greatest challenge and underlying issue in working with software mention datasets is the still suboptimal practice of software citation: Software should not be mentioned, it should be cited following the software citation principles.

Estimands can help clarify the interpretation of treatment effects and ensure that estimators are aligned to the study's objectives. Cluster randomised trials require additional attributes to be defined within the estimand compared to individually randomised trials, including whether treatment effects are marginal or cluster specific, and whether they are participant or cluster average. In this paper, we provide formal definitions of estimands encompassing both these attributes using potential outcomes notation and describe differences between them. We then provide an overview of estimators for each estimand, describe their assumptions, and show consistency (i.e. asymptotically unbiased estimation) for a series of analyses based on cluster level summaries. Then, through a reanalysis of a published cluster randomised trial, we demonstrate that the choice of both estimand and estimator can affect interpretation. For instance, the estimated odds ratio ranged from 1.38 (p=0.17) to 1.83 (p=0.03) depending on the target estimand, and for some estimands, the choice of estimator affected the conclusions by leading to smaller treatment effect estimates. We conclude that careful specification of the estimand, along with an appropriate choice of estimator, are essential to ensuring that cluster randomised trials address the right question.

We propose a simple empirical representation of expectations such that: For a number of samples above a certain threshold, drawn from any probability distribution with finite fourth-order statistic, the proposed estimator outperforms the empirical average when tested against the actual population, with respect to the quadratic loss. For datasets smaller than this threshold, the result still holds, but for a class of distributions determined by their first four statistics. Our approach leverages the duality between distributionally robust and risk-averse optimization.

Group lasso is a commonly used regularization method in statistical learning in which parameters are eliminated from the model according to predefined groups. However, when the groups overlap, optimizing the group lasso penalized objective can be time-consuming on large-scale problems because of the non-separability induced by the overlapping groups. This bottleneck has seriously limited the application of overlapping group lasso regularization in many modern problems, such as gene pathway selection and graphical model estimation. In this paper, we propose a separable penalty as an approximation of the overlapping group lasso penalty. Thanks to the separability, the computation of regularization based on our penalty is substantially faster than that of the overlapping group lasso, especially for large-scale and high-dimensional problems. We show that the penalty is the tightest separable relaxation of the overlapping group lasso norm within the family of $\ell_{q_1}/\ell_{q_2}$ norms. Moreover, we show that the estimator based on the proposed separable penalty is statistically equivalent to the one based on the overlapping group lasso penalty with respect to their error bounds and the rate-optimal performance under the squared loss. We demonstrate the faster computational time and statistical equivalence of our method compared with the overlapping group lasso in simulation examples and a classification problem of cancer tumors based on gene expression and multiple gene pathways.

New biological assays like Perturb-seq link highly parallel CRISPR interventions to a high-dimensional transcriptomic readout, providing insight into gene regulatory networks. Causal gene regulatory networks can be represented by directed acyclic graph (DAGs), but learning DAGs from observational data is complicated by lack of identifiability and a combinatorial solution space. Score-based structure learning improves practical scalability of inferring DAGs. Previous score-based methods are sensitive to error variance structure; on the other hand, estimation of error variance is difficult without prior knowledge of structure. Accordingly, we present $\texttt{dotears}$ [doo-tairs], a continuous optimization framework which leverages observational and interventional data to infer a single causal structure, assuming a linear Structural Equation Model (SEM). $\texttt{dotears}$ exploits structural consequences of hard interventions to give a marginal estimate of exogenous error structure, bypassing the circular estimation problem. We show that $\texttt{dotears}$ is a provably consistent estimator of the true DAG under mild assumptions. $\texttt{dotears}$ outperforms other methods in varied simulations, and in real data infers edges that validate with higher precision and recall than state-of-the-art methods through differential expression tests and high-confidence protein-protein interactions.

In this study, we systematically evaluate the impact of common design choices in Mixture of Experts (MoEs) on validation performance, uncovering distinct influences at token and sequence levels. We also present empirical evidence showing comparable performance between a learned router and a frozen, randomly initialized router, suggesting that learned routing may not be essential. Our study further reveals that Sequence-level routing can result in topic-specific weak expert specialization, in contrast to syntax specialization observed with Token-level routing.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.