Translation-based embedding models have gained significant attention in link prediction tasks for knowledge graphs. TransE is the primary model among translation-based embeddings and is well-known for its low complexity and high efficiency. Therefore, most of the earlier works have modified the score function of the TransE approach in order to improve the performance of link prediction tasks. Nevertheless, proven theoretically and experimentally, the performance of TransE strongly depends on the loss function. Margin Ranking Loss (MRL) has been one of the earlier loss functions which is widely used for training TransE. However, the scores of positive triples are not necessarily enforced to be sufficiently small to fulfill the translation from head to tail by using relation vector (original assumption of TransE). To tackle this problem, several loss functions have been proposed recently by adding upper bounds and lower bounds to the scores of positive and negative samples. Although highly effective, previously developed models suffer from an expansion in search space for a selection of the hyperparameters (in particular the upper and lower bounds of scores) on which the performance of the translation-based models is highly dependent. In this paper, we propose a new loss function dubbed Adaptive Margin Loss (AML) for training translation-based embedding models. The formulation of the proposed loss function enables an adaptive and automated adjustment of the margin during the learning process. Therefore, instead of obtaining two values (upper bound and lower bound), only the center of a margin needs to be determined. During learning, the margin is expanded automatically until it converges. In our experiments on a set of standard benchmark datasets including Freebase and WordNet, the effectiveness of AML is confirmed for training TransE on link prediction tasks.
In order to fulfill the gap of MRL in assigning high scores to positive samples, a limited-based scoring function has been proposed @cite_17 . This method limits the score of positive samples by adding an upper-bound ( @math ). It is represented as limited-based scoring loss illustrated in fig:sota . In this way, the scores of positive samples are forced to stay before the upper bound which significantly improves the performance of translation-based KGE models @cite_17 @cite_10 @cite_3 . revises the MRL by adding a term ( @math ) to limit maximum value of positive score: The possible combination of variables for @math and @math is wide with a complexity of @math . Considering that, the setting of ( @math ) is yet a manual task in experiments, the model and the results suffer from the difficulty of finding an optimum setting by trying all possible combinations.
@cite_10 @cite_3 @cite_17
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In knowledge graph embedding models, the margin-based ranking loss as the common loss function is usually used to encourage discrimination between golden triplets and incorrect triplets, which has proved effective in many translation-based models for knowledge graph embedding. However, we find that the loss function cannot ensure the fact that the scoring of correct triplets must be low enough to fulfill the translation. In this paper, we present a limit-based scoring loss to provide lower scoring of a golden triplet, and then to extend two basic translation models TransE and TransH, separately to TransE-RS and TransH-RS by combining limit-based scoring loss with margin-based ranking loss. Both the presented models have low complexities of parameters benefiting for application on large scale graphs. In experiments, we evaluate our models on two typical tasks including triplet classification and link prediction, and also analyze the scoring distributions of positive and negative triplets by different models. Experimental results show that the introduced limit-based scoring loss is effective to improve the capacities of knowledge graph embedding. This paper explores the preference-based top- @math rank aggregation problem. Suppose that a collection of items is repeatedly compared in pairs, and one wishes to recover a consistent ordering that emphasizes the top- @math ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce (BTL) model that postulates a set of latent preference scores underlying all items, where the odds of paired comparisons depend only on the relative scores of the items involved. We characterize the minimax limits on identifiability of top- @math ranked items, in the presence of random and non-adaptive sampling. Our results highlight a separation measure that quantifies the gap of preference scores between the @math and @math ranked items. The minimum sample complexity required for reliable top- @math ranking scales inversely with the separation measure irrespective of other preference distribution metrics. To approach this minimax limit, we propose a nearly linear-time ranking scheme, called , that returns the indices of the top- @math items in accordance to a careful score estimate. In a nutshell, Spectral MLE starts with an initial score estimate with minimal squared loss (obtained via a spectral method), and then successively refines each component with the assistance of coordinate-wise MLEs. Encouragingly, Spectral MLE allows perfect top- @math item identification under minimal sample complexity. The practical applicability of Spectral MLE is further corroborated by numerical experiments. Most existing weakly supervised localization (WSL) approaches learn detectors by finding positive bounding boxes based on features learned with image-level supervision. However, those features do not contain spatial location related information and usually provide poor-quality positive samples for training a detector. To overcome this issue, we propose a deep self-taught learning approach, which makes the detector learn the object-level features reliable for acquiring tight positive samples and afterwards re-train itself based on them. Consequently, the detector progressively improves its detection ability and localizes more informative positive samples. To implement such self-taught learning, we propose a seed sample acquisition method via image-to-object transferring and dense subgraph discovery to find reliable positive samples for initializing the detector. An online supportive sample harvesting scheme is further proposed to dynamically select the most confident tight positive samples and train the detector in a mutual boosting way. To prevent the detector from being trapped in poor optima due to overfitting, we propose a new relative improvement of predicted CNN scores for guiding the self-taught learning process. Extensive experiments on PASCAL 2007 and 2012 show that our approach outperforms the state-of-the-arts, strongly validating its effectiveness. Most existing weakly supervised localization (WSL) approaches learn detectors by finding positive bounding boxes based on features learned with image-level supervision. However, those features do not contain spatial location related information and usually provide poor-quality positive samples for training a detector. To overcome this issue, we propose a deep self-taught learning approach, which makes the detector learn the object-level features reliable for acquiring tight positive samples and afterwards re-train itself based on them. Consequently, the detector progressively improves its detection ability and localizes more informative positive samples. To implement such self-taught learning, we propose a seed sample acquisition method via image-to-object transferring and dense subgraph discovery to find reliable positive samples for initializing the detector. An online supportive sample harvesting scheme is further proposed to dynamically select the most confident tight positive samples and train the detector in a mutual boosting way. To prevent the detector from being trapped in poor optima due to overfitting, we propose a new relative improvement of predicted CNN scores for guiding the self-taught learning process. Extensive experiments on PASCAL 2007 and 2012 show that our approach outperforms the state-of-the-arts, strongly validating its effectiveness.