This paper presents recent developments in model selection and model averaging for parametric and nonparametric models. While there is extensive literature on model selection under parametric settings, we present recently developed results in the context of nonparametric models. In applications, estimation and inference are often conducted under the selected model without considering the uncertainty from the selection process. This often leads to inefficiency in results and misleading confidence intervals. Thus an alternative to model selection is model averaging where the estimated model is the weighted sum of all the submodels. This reduces model uncertainty. In recent years, there has been significant interest in model averaging and some important developments have taken place in this area. We present results for both the parametric and nonparametric cases. Some possible topics for future research are also indicated.

Multi-hop knowledge graph question answer (KGQA) is a challenging task because it requires reasoning over multiple edges of the knowledge graph (KG) to arrive at the right answer. However, KGs are often incomplete with many missing links, posing additional challenges for multi-hop KGQA. Recent research on multi-hop KGQA attempted to deal with KG sparsity with relevant external texts. In our work, we propose a multi-hop KGQA model based on relation knowledge enhancement (RKE-KGQA), which fuses both label and text relations through global attention for relation knowledge augmentation. It is well known that the relation between entities can be represented by labels in the knowledge graph or texts in the text corpus, and multi-hop KGQA needs to jump across different entities through relations. First, we assign an activation probability to each entity, then calculate a score for the enhancement relation, and then transfer the score through the activated relations and, finally, obtain the answer. We carry out extensive experiments on three datasets and demonstrate that RKE-KGQA achieves the outperformance result.

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In recent years, the suggestion of combining models as an alternative to selecting a single model from a frequentist prospective has been advanced in a number of studies. In this paper, we propose a new semi-parametric estimator of regression coe¢ cients, which is in the form of a feasible generalized ridge estimator by Hoerl and Kennard (1970b) but with di¤erent biasing factors. We prove that the generalized ridge estimator is algebraically identical to the model average estimator. Further, the biasing factors that determine the properties of both the generalized ridge and semi-parametric estimators are directly linked to the weights used in model averaging. These are interesting results for the interpretations and applications of both semi-parametric and ridge estimators. Furthermore, we demonstrate that these estimators based on model averaging weights can have properties superior to the well-known feasible generalized ridge estimator in a large region of the parameter space. Two empirical examples are presented.

Multi-modal entity alignment refers to identifying equivalent entities between two different multi-modal knowledge graphs that consist of multi-modal information such as structural triples and descriptive images. Most previous multi-modal entity alignment methods have mainly used corresponding encoders of each modality to encode entity information and then perform feature fusion to obtain the multi-modal joint representation. However, this approach does not fully utilize the multi-modal information of aligned entities. To address this issue, we propose MEAFE, a multi-modal entity alignment method based on feature enhancement. The MEAFE adopts the multi-modal pre-trained model, OCR model, and GATv2 network to enhance the model’s ability to extract useful features in entity structure triplet information and image description, respectively, thereby generating more effective multi-modal representations. Secondly, it further adds modal distribution information of the entity to enhance the model’s understanding and modeling ability of the multi-modal information. Experiments on bilingual and cross-graph multi-modal datasets demonstrate that the proposed method outperforms models that use traditional feature extraction methods.