The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming-Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion.
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Document-based Question-Answering (QA) tasks are crucial for precise information retrieval. While some existing work focus on evaluating large language model's performance on retrieving and answering questions from documents, assessing the LLMs' performance on QA types that require exact answer selection from predefined options and numerical extraction is yet to be fully assessed. In this paper, we specifically focus on this underexplored context and conduct empirical analysis of LLMs (GPT-4 and GPT 3.5) on question types, including single-choice, yes-no, multiple-choice, and number extraction questions from documents. We use the Cogtale dataset for evaluation, which provide human expert-tagged responses, offering a robust benchmark for precision and factual grounding. We found that LLMs, particularly GPT-4, can precisely answer many single-choice and yes-no questions given relevant context, demonstrating their efficacy in information retrieval tasks. However, their performance diminishes when confronted with multiple-choice and number extraction formats, lowering the overall performance of the model on this task, indicating that these models may not be reliable for the task. This limits the applications of LLMs on applications demanding precise information extraction from documents, such as meta-analysis tasks. However, these findings hinge on the assumption that the retrievers furnish pertinent context necessary for accurate responses, emphasizing the need for further research on the efficacy of retriever mechanisms in enhancing question-answering performance. Our work offers a framework for ongoing dataset evaluation, ensuring that LLM applications for information retrieval and document analysis continue to meet evolving standards.
Approximate inference methods like the Laplace method, Laplace approximations and variational methods, amongst others, are popular methods when exact inference is not feasible due to the complexity of the model or the abundance of data. In this paper we propose a hybrid approximate method called Low-Rank Variational Bayes correction (VBC), that uses the Laplace method and subsequently a Variational Bayes correction in a lower dimension, to the joint posterior mean. The cost is essentially that of the Laplace method which ensures scalability of the method, in both model complexity and data size. Models with fixed and unknown hyperparameters are considered, for simulated and real examples, for small and large datasets.
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is satisfied with high probability. This work describes an extension of such methods which supports adaptive sampling to satisfy general error criteria for functions of a common array of expectations. Although several functions involving multiple expectations are being evaluated, only one random sequence is required, albeit sometimes of larger dimension than the underlying randomness. These enhanced Monte Carlo and Quasi-Monte Carlo algorithms are implemented in the QMCPy Python package with support for economic and parallel function evaluation. We exemplify these capabilities on problems from machine learning and global sensitivity analysis.
Recently, advancements in large language models (LLMs) have shown an unprecedented ability across various language tasks. This paper investigates the potential application of LLMs to slot filling with noisy ASR transcriptions, via both in-context learning and task-specific fine-tuning. Dedicated prompt designs and fine-tuning approaches are proposed to improve the robustness of LLMs for slot filling with noisy ASR transcriptions. Moreover, a linearised knowledge injection (LKI) scheme is also proposed to integrate dynamic external knowledge into LLMs. Experiments were performed on SLURP to quantify the performance of LLMs, including GPT-3.5-turbo, GPT-4, LLaMA-13B and Vicuna-13B (v1.1 and v1.5) with different ASR error rates. The use of the proposed fine-tuning together with the LKI scheme for LLaMA-13B achieved an 8.3% absolute SLU-F1 improvement compared to the strong Flan-T5-base baseline system on a limited data setup.
We propose an individual claims reserving model based on the conditional Aalen--Johansen estimator, as developed in Bladt and Furrer (2023b). In our approach, we formulate a multi-state problem, where the underlying variable is the individual claim size, rather than time. The states in this model represent development periods, and we estimate the cumulative density function of individual claim costs using the conditional Aalen--Johansen method as transition probabilities to an absorbing state. Our methodology reinterprets the concept of multi-state models and offers a strategy for modeling the complete curve of individual claim costs. To illustrate our approach, we apply our model to both simulated and real datasets. Having access to the entire dataset enables us to support the use of our approach by comparing the predicted total final cost with the actual amount, as well as evaluating it in terms of the continuously ranked probability score, as discussed in Gneiting and A. E. Raftery (2007)
Entity resolution (ER) is the process of identifying records that refer to the same entities within one or across multiple databases. Numerous techniques have been developed to tackle ER challenges over the years, with recent emphasis placed on machine and deep learning methods for the matching phase. However, the quality of the benchmark datasets typically used in the experimental evaluations of learning-based matching algorithms has not been examined in the literature. To cover this gap, we propose four different approaches to assessing the difficulty and appropriateness of 13 established datasets: two theoretical approaches, which involve new measures of linearity and existing measures of complexity, and two practical approaches: the difference between the best non-linear and linear matchers, as well as the difference between the best learning-based matcher and the perfect oracle. Our analysis demonstrates that most of the popular datasets pose rather easy classification tasks. As a result, they are not suitable for properly evaluating learning-based matching algorithms. To address this issue, we propose a new methodology for yielding benchmark datasets. We put it into practice by creating four new matching tasks, and we verify that these new benchmarks are more challenging and therefore more suitable for further advancements in the field.
Altermagnetism, a new magnetic phase, has been theoretically proposed and experimentally verified to be distinct from ferromagnetism and antiferromagnetism. Although altermagnets have been found to possess many exotic physical properties, the very limited availability of known altermagnetic materials (e.g., 14 confirmed materials) hinders the study of such properties. Hence, discovering more types of altermagnetic materials is crucial for a comprehensive understanding of altermagnetism and thus facilitating new applications in the next-generation information technologies, e.g., storage devices and high-sensitivity sensors. Here, we report 25 new altermagnetic materials that cover metals, semiconductors, and insulators, discovered by an AI search engine unifying symmetry analysis, graph neural network pre-training, optimal transport theory, and first-principles electronic structure calculation. The wide range of electronic structural characteristics reveals that various novel physical properties manifest in these newly discovered altermagnetic materials, e.g., anomalous Hall effect, anomalous Kerr effect, and topological property. Noteworthy, we discovered 8 i-wave altermagnetic materials for the first time. Overall, the AI search engine performs much better than human experts and suggests a set of new altermagnetic materials with unique properties, outlining its potential for accelerated discovery of the materials with targeting properties.
We explore a specific type of distribution shift called domain expertise, in which training is limited to a subset of all possible labels. This setting is common among specialized human experts, or specific focused studies. We show how the standard approach to distribution shift, which involves re-weighting data, can result in paradoxical disagreements among differing domain expertise. We also demonstrate how standard adjustments for causal inference lead to the same paradox. We prove that the characteristics of these paradoxes exactly mimic another set of paradoxes which arise among sets of voter preferences.
The satisfiability problem is NP-complete but there are subclasses where all the instances are satisfiable. For this, restrictions on the shape of the formula are made. Darman and D\"ocker show that the subclass MONOTONE $3$-SAT-($k$,1) with $k \geq 5$ proves to be NP-complete and pose the open question whether instances of MONOTONE $3$-SAT-(3,1) are satisfiable. This paper shows that all instances of MONOTONE $3$-SAT-(3,1) are satisfiable using the new concept of a color-structures.
Image segmentation methods have been utilized to determine the particle size distribution of crushed ores. Due to the complex working environment, high-powered computing equipment is difficult to deploy. At the same time, the ore distribution is stacked, and it is difficult to identify the complete features. To address this issue, an effective box-supervised technique with texture features is provided for ore image segmentation that can identify complete and independent ores. Firstly, a ghost feature pyramid network (Ghost-FPN) is proposed to process the features obtained from the backbone to reduce redundant semantic information and computation generated by complex networks. Then, an optimized detection head is proposed to obtain the feature to maintain accuracy. Finally, Lab color space (Lab) and local binary patterns (LBP) texture features are combined to form a fusion feature similarity-based loss function to improve accuracy while incurring no loss. Experiments on MS COCO have shown that the proposed fusion features are also worth studying on other types of datasets. Extensive experimental results demonstrate the effectiveness of the proposed method, which achieves over 50 frames per second with a small model size of 21.6 MB. Meanwhile, the method maintains a high level of accuracy compared with the state-of-the-art approaches on ore image dataset. The source code is available at \url{//github.com/MVME-HBUT/OREINST}.
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