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Gaussian graphical models are graphs that represent the conditional relationships among multivariate normal variables. The process of uncovering the structure of these graphs is known as structure learning. Despite the fact that Bayesian methods in structure learning offer intuitive and well-founded ways to measure model uncertainty and integrate prior information, frequentist methods are often preferred due to the computational burden of the Bayesian approach. Over the last decade, Bayesian methods have seen substantial improvements, with some now capable of generating accurate estimates of graphs up to a thousand variables in mere minutes. Despite these advancements, a comprehensive review or empirical comparison of all cutting-edge methods has not been conducted. This paper delves into a wide spectrum of Bayesian approaches used in structure learning, evaluates their efficacy through a simulation study, and provides directions for future research. This study gives an exhaustive overview of this dynamic field for both newcomers and experts.

Observational studies are frequently used to estimate the effect of an exposure or treatment on an outcome. To obtain an unbiased estimate of the treatment effect, it is crucial to measure the exposure accurately. A common type of exposure misclassification is recall bias, which occurs in retrospective cohort studies when study subjects may inaccurately recall their past exposure. Specifically, differential recall bias can be problematic when examining the effect of a self-reported binary exposure since the magnitude of recall bias can differ between groups. In this paper, we provide the following contributions: 1) we derive bounds for the average treatment effect (ATE) in the presence of recall bias; 2) we develop several estimation approaches under different identification strategies; 3) we conduct simulation studies to evaluate their performance under several scenarios of model misspecification; 4) we propose a sensitivity analysis method that can examine the robustness of our results with respect to different assumptions; and 5) we apply the proposed framework to an observational study, estimating the effect of childhood physical abuse on adulthood mental health.

Extended resolution shows that auxiliary variables are very powerful in theory. However, attempts to exploit this potential in practice have had limited success. One reasonably effective method in this regard is bounded variable addition (BVA), which automatically reencodes formulas by introducing new variables and eliminating clauses, often significantly reducing formula size. We find motivating examples suggesting that the performance improvement caused by BVA stems not only from this size reduction but also from the introduction of effective auxiliary variables. Analyzing specific packing-coloring instances, we discover that BVA is fragile with respect to formula randomization, relying on variable order to break ties. With this understanding, we augment BVA with a heuristic for breaking ties in a structured way. We evaluate our new preprocessing technique, Structured BVA (SBVA), on more than 29,000 formulas from previous SAT competitions and show that it is robust to randomization. In a simulated competition setting, our implementation outperforms BVA on both randomized and original formulas, and appears to be well-suited for certain families of formulas.

The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional Boussinesq-Abbott system. The problem can be reduced to a transmission problem for this Boussinesq system, in which the transmission conditions between the components of the domain at the left and at the right of the object are determined through the resolution of coupled forced ODEs in time satisfied by the vertical displacement of the object and the average discharge in the portion of the fluid located under the object. We propose a new extended formulation in which these ODEs are complemented by two other forced ODEs satisfied by the trace of the surface elevation at the contact points. The interest of this new extended formulation is that the forcing terms are easy to compute numerically and that the surface elevation at the contact points is furnished for free. Based on this formulation, we propose a second order scheme that involves a generalization of the MacCormack scheme with nonlocal flux and a source term, which is coupled to a second order Heun scheme for the ODEs. In order to validate this scheme, several explicit solutions for this wave-structure interaction problem are derived and can serve as benchmark for future codes. As a byproduct, our method provides a second order scheme for the generation of waves at the entrance of the numerical domain for the Boussinesq-Abbott system.

Large language models(LLMs) have shown excellent text generation capabilities, but there is still much space for improvement in accuracy, sometimes with grammatical errors, semantic inaccuracies, and contextual incoherence, which seriously affect the reliability of the models. These problems may originate from the difficulties and limitations encountered in the pattern extraction stage of large language models. How to utilize the generative power of large language models to generate as many possible patterns that help solve problems and find the optimal patterns from them, so as to use patterns to guide large language models to generate good content, has become a current research hotspot. In this paper, we propose a pattern extraction and selection framework, PatternGPT, which generates rich patterns through the extraction ability of large language models and draws on the idea of federation learning, where multiple agents collaborate with each other to generate diverse patterns. High-quality patterns are selected by defining criteria and optimization algorithms to personalize the guidance of the model generation process. PatternGPT has the advantages of generating diverse and useful patterns, extending relevant knowledge, facilitating efficient pattern use and transfer, and optimizing the quality of generated results and user experience, which provides an effective method for optimizing the text generation capability of large language models and is expected to drive further development in the field of intelligent dialogue and content generation. It is expected to promote further development in the field of intelligent dialogue and content generation.

Electronic health records (EHR) contain narrative notes that provide extensive details on the medical condition and management of patients. Natural language processing (NLP) of clinical notes can use observed frequencies of clinical terms as predictive features for downstream applications such as clinical decision making and patient trajectory prediction. However, due to the vast number of highly similar and related clinical concepts, a more effective modeling strategy is to represent clinical terms as semantic embeddings via representation learning and use the low dimensional embeddings as feature vectors for predictive modeling. To achieve efficient representation, fine-tuning pretrained language models with biomedical knowledge graphs may generate better embeddings for biomedical terms than those from standard language models alone. These embeddings can effectively discriminate synonymous pairs of from those that are unrelated. However, they often fail to capture different degrees of similarity or relatedness for concepts that are hierarchical in nature. To overcome this limitation, we propose HiPrBERT, a novel biomedical term representation model trained on additionally complied data that contains hierarchical structures for various biomedical terms. We modify an existing contrastive loss function to extract information from these hierarchies. Our numerical experiments demonstrate that HiPrBERT effectively learns the pair-wise distance from hierarchical information, resulting in a substantially more informative embeddings for further biomedical applications

Entity linking (EL) for the rapidly growing short text (e.g. search queries and news titles) is critical to industrial applications. Most existing approaches relying on adequate context for long text EL are not effective for the concise and sparse short text. In this paper, we propose a novel framework called Multi-turn Multiple-choice Machine reading comprehension (M3}) to solve the short text EL from a new perspective: a query is generated for each ambiguous mention exploiting its surrounding context, and an option selection module is employed to identify the golden entity from candidates using the query. In this way, M3 framework sufficiently interacts limited context with candidate entities during the encoding process, as well as implicitly considers the dissimilarities inside the candidate bunch in the selection stage. In addition, we design a two-stage verifier incorporated into M3 to address the commonly existed unlinkable problem in short text. To further consider the topical coherence and interdependence among referred entities, M3 leverages a multi-turn fashion to deal with mentions in a sequence manner by retrospecting historical cues. Evaluation shows that our M3 framework achieves the state-of-the-art performance on five Chinese and English datasets for the real-world short text EL.

Automatic KB completion for commonsense knowledge graphs (e.g., ATOMIC and ConceptNet) poses unique challenges compared to the much studied conventional knowledge bases (e.g., Freebase). Commonsense knowledge graphs use free-form text to represent nodes, resulting in orders of magnitude more nodes compared to conventional KBs (18x more nodes in ATOMIC compared to Freebase (FB15K-237)). Importantly, this implies significantly sparser graph structures - a major challenge for existing KB completion methods that assume densely connected graphs over a relatively smaller set of nodes. In this paper, we present novel KB completion models that can address these challenges by exploiting the structural and semantic context of nodes. Specifically, we investigate two key ideas: (1) learning from local graph structure, using graph convolutional networks and automatic graph densification and (2) transfer learning from pre-trained language models to knowledge graphs for enhanced contextual representation of knowledge. We describe our method to incorporate information from both these sources in a joint model and provide the first empirical results for KB completion on ATOMIC and evaluation with ranking metrics on ConceptNet. Our results demonstrate the effectiveness of language model representations in boosting link prediction performance and the advantages of learning from local graph structure (+1.5 points in MRR for ConceptNet) when training on subgraphs for computational efficiency. Further analysis on model predictions shines light on the types of commonsense knowledge that language models capture well.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.