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We introduce isotonic conditional laws (ICL) which extend the classical notion of conditional laws by the additional requirement that there exists an isotonic relationship between the random variable of interest and the conditioning random object. We show existence and uniqueness of ICL building on conditional expectations given $\sigma$-lattices. ICL corresponds to a classical conditional law if and only if the latter is already isotonic. ICL is motivated from a statistical point of view by showing that ICL emerges equivalently as the minimizer of an expected score where the scoring rule may be taken from a large class comprising the continuous ranked probability score (CRPS). Furthermore, ICL is calibrated in the sense that it is invariant to certain conditioning operations, and the corresponding event probabilities and quantiles are simultaneously optimal with respect to all relevant scoring functions. We develop a new notion of general conditional functionals given $\sigma$-lattices which is of independent interest.

Language models, especially pre-trained large language models, have showcased remarkable abilities as few-shot in-context learners (ICL), adept at adapting to new tasks with just a few demonstrations in the input context. However, the model's ability to perform ICL is sensitive to the choice of the few-shot demonstrations. Instead of using a fixed set of demonstrations, one recent development is to retrieve demonstrations tailored to each input query. The implementation of demonstration retrieval is relatively straightforward, leveraging existing databases and retrieval systems. This not only improves the efficiency and scalability of the learning process but also has been shown to reduce biases inherent in manual example selection. In light of the encouraging results and growing research in ICL with retrieved demonstrations, we conduct an extensive review of studies in this area. In this survey, we discuss and compare different design choices for retrieval models, retrieval training procedures, and inference algorithms.

In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with respect to general preorders and provide a representation theorem for such functionals. The results are illustrated for different stochastic orders in the literature, including the usual stochastic order, the increasing convex/concave order, and the dispersive order.

Generative models for multimodal data permit the identification of latent factors that may be associated with important determinants of observed data heterogeneity. Common or shared factors could be important for explaining variation across modalities whereas other factors may be private and important only for the explanation of a single modality. Multimodal Variational Autoencoders, such as MVAE and MMVAE, are a natural choice for inferring those underlying latent factors and separating shared variation from private. In this work, we investigate their capability to reliably perform this disentanglement. In particular, we highlight a challenging problem setting where modality-specific variation dominates the shared signal. Taking a cross-modal prediction perspective, we demonstrate limitations of existing models, and propose a modification how to make them more robust to modality-specific variation. Our findings are supported by experiments on synthetic as well as various real-world multi-omics data sets.

The question of whether people's experience in the world shapes conceptual representation and lexical semantics is longstanding. Word-association, feature-listing and similarity rating tasks aim to address this question but require a subjective interpretation of the latent dimensions identified. In this study, we introduce a supervised representational-alignment method that (i) determines whether two groups of individuals share the same basis of a certain category, and (ii) explains in what respects they differ. In applying this method, we show that congenital blindness induces conceptual reorganization in both a-modal and sensory-related verbal domains, and we identify the associated semantic shifts. We first apply supervised feature-pruning to a language model (GloVe) to optimize prediction accuracy of human similarity judgments from word embeddings. Pruning identifies one subset of retained GloVe features that optimizes prediction of judgments made by sighted individuals and another subset that optimizes judgments made by blind. A linear probing analysis then interprets the latent semantics of these feature-subsets by learning a mapping from the retained GloVe features to 65 interpretable semantic dimensions. We applied this approach to seven semantic domains, including verbs related to motion, sight, touch, and amodal verbs related to knowledge acquisition. We find that blind individuals more strongly associate social and cognitive meanings to verbs related to motion or those communicating non-speech vocal utterances (e.g., whimper, moan). Conversely, for amodal verbs, they demonstrate much sparser information. Finally, for some verbs, representations of blind and sighted are highly similar. The study presents a formal approach for studying interindividual differences in word meaning, and the first demonstration of how blindness impacts conceptual representation of everyday verbs.

This article is concerned with the multilevel Monte Carlo (MLMC) methods for approximating expectations of some functions of the solution to the Heston 3/2-model from mathematical finance, which takes values in $(0, \infty)$ and possesses superlinearly growing drift and diffusion coefficients. To discretize the SDE model, a new Milstein-type scheme is proposed to produce independent sample paths. The proposed scheme can be explicitly solved and is positivity-preserving unconditionally, i.e., for any time step-size $h>0$. This positivity-preserving property for large discretization time steps is particularly desirable in the MLMC setting. Furthermore, a mean-square convergence rate of order one is proved in the non-globally Lipschitz regime, which is not trivial, as the diffusion coefficient grows super-linearly. The obtained order-one convergence in turn promises the desired relevant variance of the multilevel estimator and justifies the optimal complexity $\mathcal{O}(\epsilon^{-2})$ for the MLMC approach, where $\epsilon > 0$ is the required target accuracy. Numerical experiments are finally reported to confirm the theoretical findings.

Learning better sentence embeddings leads to improved performance for natural language understanding tasks including semantic textual similarity (STS) and natural language inference (NLI). As prior studies leverage large-scale labeled NLI datasets for fine-tuning masked language models to yield sentence embeddings, task performance for languages other than English is often left behind. In this study, we directly compared two data augmentation techniques as potential solutions for monolingual STS: (a) cross-lingual transfer that exploits English resources alone as training data to yield non-English sentence embeddings as zero-shot inference, and (b) machine translation that coverts English data into pseudo non-English training data in advance. In our experiments on monolingual STS in Japanese and Korean, we find that the two data techniques yield performance on par. Rather, we find a superiority of the Wikipedia domain over the NLI domain for these languages, in contrast to prior studies that focused on NLI as training data. Combining our findings, we demonstrate that the cross-lingual transfer of Wikipedia data exhibits improved performance, and that native Wikipedia data can further improve performance for monolingual STS.

Language models (LMs) show promise as tools for communicating science to the general public by simplifying and summarizing complex language. Because models can be prompted to generate text for a specific audience (e.g., college-educated adults), LMs might be used to create multiple versions of plain language summaries for people with different familiarities of scientific topics. However, it is not clear what the benefits and pitfalls of adaptive plain language are. When is simplifying necessary, what are the costs in doing so, and do these costs differ for readers with different background knowledge? Through three within-subjects studies in which we surface summaries for different envisioned audiences to participants of different backgrounds, we found that while simpler text led to the best reading experience for readers with little to no familiarity in a topic, high familiarity readers tended to ignore certain details in overly plain summaries (e.g., study limitations). Our work provides methods and guidance on ways of adapting plain language summaries beyond the single "general" audience.

For languages with no annotated resources, transferring knowledge from rich-resource languages is an effective solution for named entity recognition (NER). While all existing methods directly transfer from source-learned model to a target language, in this paper, we propose to fine-tune the learned model with a few similar examples given a test case, which could benefit the prediction by leveraging the structural and semantic information conveyed in such similar examples. To this end, we present a meta-learning algorithm to find a good model parameter initialization that could fast adapt to the given test case and propose to construct multiple pseudo-NER tasks for meta-training by computing sentence similarities. To further improve the model's generalization ability across different languages, we introduce a masking scheme and augment the loss function with an additional maximum term during meta-training. We conduct extensive experiments on cross-lingual named entity recognition with minimal resources over five target languages. The results show that our approach significantly outperforms existing state-of-the-art methods across the board.