This thesis investigates the applicability of bucket-level filtering techniques in Learned Metric Index. The student will conduct a literature review to understand existing approximate nearest neighbor approaches and other techniques designed to reduce the overhead of linear search, e.g., inverted files, Hierarchical Navigable Small World, or sketches. Appropriate techniques will be experimentally evaluated, and the most promising one will be incorporated into the existing Learned Metric Index codebase. The improved Learned Metric Index will be compared in terms of effectiveness and efficiency with the existing implementation on a subset of embeddings from the LAION-5B image collection to demonstrate its viability on real-world datasets.