In ecological and environmental contexts, management actions must sometimes be chosen urgently. Value of information (VoI) analysis provides a quantitative toolkit for projecting the improved management outcomes expected after making additional measurements. However, traditional VoI analysis reports metrics as expected values (i.e. risk-neutral). This can be problematic because expected values hide uncertainties in projections. The true value of a measurement will only be known after the measurement's outcome is known, leaving large uncertainty in the measurement's value before it is performed. As a result, the expected value metrics produced in traditional VoI analysis may not align with the priorities of a risk-averse decision-maker who wants to avoid low-value measurement outcomes. In the present work, we introduce four new VoI metrics that can address a decision-maker's risk-aversion to different measurement outcomes. We demonstrate the benefits of the new metrics with two ecological case studies for which traditional VoI analysis has been previously applied. Using the new metrics, we also demonstrate a clear mathematical link between the often-separated environmental decision-making disciplines of VoI and optimal design of experiments. This mathematical link has the potential to catalyse future collaborations between ecologists and statisticians to work together to quantitatively address environmental decision-making questions of fundamental importance. Overall, the introduced VoI metrics complement existing metrics to provide decision-makers with a comprehensive view of the value of, and risks associated with, a proposed monitoring or measurement activity. This is critical for improved environmental outcomes when decisions must be urgently made.
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Correspondence analysis (CA) is a popular technique to visualize the relationship between two categorical variables. CA uses the data from a two-way contingency table and is affected by the presence of outliers. The supplementary points method is a popular method to handle outliers. Its disadvantage is that the information from entire rows or columns is removed. However, outliers can be caused by cells only. In this paper, a reconstitution algorithm is introduced to cope with such cells. This algorithm can reduce the contribution of cells in CA instead of deleting entire rows or columns. Thus the remaining information in the row and column involved can be used in the analysis. The reconstitution algorithm is compared with two alternative methods for handling outliers, the supplementary points method and MacroPCA. It is shown that the proposed strategy works well.
Asymptotic analysis for covariance parameter estimation of Gaussian processes with functional inputs
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend these theoretical guarantees to encompass scenarios accounting for approximation errors in the inputs, which allows robustness of practical implementations relying on conventional sampling methods or projections onto a functional basis. Loosely speaking, both consistency and normality hold when the approximation error becomes negligible, a condition that is often achieved as the number of samples or basis functions becomes large. These later asymptotic properties are illustrated through analytical examples, including one that covers the case of non-randomly perturbed grids, as well as several numerical illustrations.
Benchmarks have emerged as the central approach for evaluating Large Language Models (LLMs). The research community often relies on a model's average performance across the test prompts of a benchmark to evaluate the model's performance. This is consistent with the assumption that the test prompts within a benchmark represent a random sample from a real-world distribution of interest. We note that this is generally not the case; instead, we hold that the distribution of interest varies according to the specific use case. We find that (1) the correlation in model performance across test prompts is non-random, (2) accounting for correlations across test prompts can change model rankings on major benchmarks, (3) explanatory factors for these correlations include semantic similarity and common LLM failure points.
We present a generic algorithm for scoring pose estimation methods that rely on single image semantic analysis. The algorithm employs a lightweight putative shape representation using a combination of multiple Gaussian Processes. Each Gaussian Process (GP) yields distance normal distributions from multiple reference points in the object's coordinate system to its surface, thus providing a geometric evaluation framework for scoring predicted poses. Our confidence measure comprises the average mixture probability of pixel back-projections onto the shape template. In the reported experiments, we compare the accuracy of our GP based representation of objects versus the actual geometric models and demonstrate the ability of our method to capture the influence of outliers as opposed to the corresponding intrinsic measures that ship with the segmentation and pose estimation methods.
In Bayesian theory, the role of information is central. The influence exerted by prior information on posterior outcomes often jeopardizes Bayesian studies, due to the potentially subjective nature of the prior choice. In modeling where a priori knowledge is lacking, the reference prior theory emerges as a proficient tool. Based on the criterion of mutual information, this theory makes it possible to construct a non-informative prior whose choice can be qualified as objective. In this paper, we contribute to the enrichment of reference prior theory. Indeed, we unveil an original analogy between reference prior theory and Global Sensitivity Analysis, from which we propose a natural generalization of the mutual information definition. Leveraging dissimilarity measures between probability distributions, such as f-divergences, we provide a formalized framework for what we term generalized reference priors. Our main result offers a limit of mutual information, simplifying the definition of reference priors as its maximal arguments. This approach opens a new way that facilitates the theoretical derivation of reference priors under constraints or within specific classes. In the absence of constraints, we further prove that the Jeffreys prior maximizes the generalized mutual information considered.
Predicting postoperative risk can inform effective care management & planning. We explored large language models (LLMs) in predicting postoperative risk through clinical texts using various tuning strategies. Records spanning 84,875 patients from Barnes Jewish Hospital (BJH) between 2018 & 2021, with a mean duration of follow-up based on the length of postoperative ICU stay less than 7 days, were utilized. Methods were replicated on the MIMIC-III dataset. Outcomes included 30-day mortality, pulmonary embolism (PE) & pneumonia. Three domain adaptation & finetuning strategies were implemented for three LLMs (BioGPT, ClinicalBERT & BioClinicalBERT): self-supervised objectives; incorporating labels with semi-supervised fine-tuning; & foundational modelling through multi-task learning. Model performance was compared using the AUROC & AUPRC for classification tasks & MSE & R2 for regression tasks. Cohort had a mean age of 56.9 (sd: 16.8) years; 50.3% male; 74% White. Pre-trained LLMs outperformed traditional word embeddings, with absolute maximal gains of 38.3% for AUROC & 14% for AUPRC. Adapting models through self-supervised finetuning further improved performance by 3.2% for AUROC & 1.5% for AUPRC Incorporating labels into the finetuning procedure further boosted performances, with semi-supervised finetuning improving by 1.8% for AUROC & 2% for AUPRC & foundational modelling improving by 3.6% for AUROC & 2.6% for AUPRC compared to self-supervised finetuning. Pre-trained clinical LLMs offer opportunities for postoperative risk predictions with unseen data, & further improvements from finetuning suggests benefits in adapting pre-trained models to note-specific perioperative use cases. Incorporating labels can further boost performance. The superior performance of foundational models suggests the potential of task-agnostic learning towards the generalizable LLMs in perioperative care.
Calls to make scientific research more open have gained traction with a range of societal stakeholders. Open Science practices include but are not limited to the early sharing of results via preprints and openly sharing outputs such as data and code to make research more reproducible and extensible. Existing evidence shows that adopting Open Science practices has effects in several domains. In this study, we investigate whether adopting one or more Open Science practices leads to significantly higher citations for an associated publication, which is one form of academic impact. We use a novel dataset known as Open Science Indicators, produced by PLOS and DataSeer, which includes all PLOS publications from 2018 to 2023 as well as a comparison group sampled from the PMC Open Access Subset. In total, we analyze circa 122'000 publications. We calculate publication and author-level citation indicators and use a broad set of control variables to isolate the effect of Open Science Indicators on received citations. We show that Open Science practices are adopted to different degrees across scientific disciplines. We find that the early release of a publication as a preprint correlates with a significant positive citation advantage of about 20.2% on average. We also find that sharing data in an online repository correlates with a smaller yet still positive citation advantage of 4.3% on average. However, we do not find a significant citation advantage for sharing code. Further research is needed on additional or alternative measures of impact beyond citations. Our results are likely to be of interest to researchers, as well as publishers, research funders, and policymakers.
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity and dimensionality of the problems. In particular, covariance matrices in many cases are numerically unstable and linear algebra shows that often such matrices cannot be inverted accurately on a finite precision computer. A common ad hoc approach to stabilizing a matrix is application of a so-called nugget. However, this can change the model and introduce error to the original solution. It is well known from numerical analysis that ill-conditioned matrices cannot be accurately inverted. In this paper we develop a multilevel computational method that scales well with the number of observations and dimensions. A multilevel basis is constructed adapted to a kD-tree partitioning of the observations. Numerically unstable covariance matrices with large condition numbers can be transformed into well conditioned multilevel ones without compromising accuracy. Moreover, it is shown that the multilevel prediction exactly solves the Best Linear Unbiased Predictor (BLUP) and Generalized Least Squares (GLS) model, but is numerically stable. The multilevel method is tested on numerically unstable problems of up to 25 dimensions. Numerical results show speedups of up to 42,050 times for solving the BLUP problem, but with the same accuracy as the traditional iterative approach. For very ill-conditioned cases the speedup is infinite. In addition, decay estimates of the multilevel covariance matrices are derived based on high dimensional interpolation techniques from the field of numerical analysis. This work lies at the intersection of statistics, uncertainty quantification, high performance computing and computational applied mathematics.
In contemporary problems involving genetic or neuroimaging data, thousands of hypotheses need to be tested. Due to their high power, and finite sample guarantees on type-1 error under weak assumptions, Monte-Carlo permutation tests are often considered as gold standard for these settings. However, the enormous computational effort required for (thousands of) permutation tests is a major burden. Recently, Fischer and Ramdas (2024) constructed a permutation test for a single hypothesis in which the permutations are drawn sequentially one-by-one and the testing process can be stopped at any point without inflating the type I error. They showed that the number of permutations can be substantially reduced (under null and alternative) while the power remains similar. We show how their approach can be modified to make it suitable for a broad class of multiple testing procedures. In particular, we discuss its use with the Benjamini-Hochberg procedure and illustrate the application on a large dataset.
Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential future research directions.
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