A practical algorithm to calculate Cap Discrepancy
Uniform distribution of the points has been of interest to researchers for a long time and has applications in different areas of Mathematics and Computer Science. One of the well-known measures to evaluate the uniformity of a given distribution is Discrepancy, which assesses the difference between the Uniform distribution and the empirical distribution given by putting mass points at the points of the given set. While Discrepancy is very useful to measure uniformity, it is computationally challenging to be calculated accurately. We introduce the concept of directed Discrepancy based on which we have developed an algorithm, called Directional Discrepancy, that can offer accurate approximation for the cap Discrepancy of a finite set distributed on the unit Sphere, $\mathbb{S}^2.$ We also analyze the time complexity of the Directional Discrepancy algorithm precisely; and practically evaluate its capacity by calculating the Cap Discrepancy of a specific distribution, Polar Coordinates, which aims to distribute points uniformly on the Sphere.
Code (1)
Similar Papers 제목 키워드 기반
DWMD: Dimensional Weighted Orderwise Moment Discrepancy for Domain-specific Hidden Representation Matching
Knowledge transfer from a source domain to a different but semantically related target domain has long been an important topic in the context of unsupervised domain adaptation (UDA). A key challenge in this field is esta…
Domain AdaptationTransfer LearningUnsupervised Domain AdaptationvalidDomain Discrepancy Aware Distillation for Model Aggregation in Federated Learning
Knowledge distillation has recently become popular as a method of model aggregation on the server for federated learning. It is generally assumed that there are abundant public unlabeled data on the server. However, in r…
Federated LearningKnowledge DistillationOrder Matters: Improving Domain Adaptation by Reordering Data
Domain shift remains a key challenge in deploying machine learning models to the real world. Unsupervised domain adaptation (UDA) aims to address this by minimising domain discrepancy during training, but the discrepancy…
Unsupervised Domain AdaptationImage ClassificationConsistency and Discrepancy-Based Contrastive Tripartite Graph Learning for Recommendations
Tripartite graph-based recommender systems markedly diverge from traditional models by recommending unique combinations such as user groups and item bundles. Despite their effectiveness, these systems exacerbate the long…
Contrastive LearningGraph LearningRecommendation SystemsEvaluating Transferability in Retrieval Tasks: An Approach Using MMD and Kernel Methods
Retrieval tasks play central roles in real-world machine learning systems such as search engines recommender systems and retrieval-augmented generation (RAG). Achieving decent performance in these tasks often require…
RAGRecommendation SystemsRetrievalRetrieval-augmented Generation+1