{"title":"Beyond the top six.","description":"A recommendation list can be individually relevant and collectively repetitive. Explore the trade-off before calling a ranking good.","theme":"teal","kind":"Recommender systems","cases":[{"id":"specialist","name":"The ML specialist","title":"Useful is not always diverse.","unit":"Synthetic scores · 0–1","parameter":"Relevance weight λ","x":[0.0,0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1.0],"series":[{"label":"Mean relevance","values":[0.3636273,0.5887515,0.5887515,0.5904929,0.5904929,0.5904929,0.5904929,0.5920467,0.5944139,0.6044416,0.6188521,0.9901594,0.9901594,0.9902895,0.9902895,0.9904424,0.9904424,0.9904424,0.9904424,0.9904424,0.9904424]},{"label":"Pairwise diversity","values":[0.7275567,0.7167305,0.7167305,0.7010089,0.7010089,0.7010089,0.7010089,0.6970108,0.6908444,0.6754936,0.6557893,0.0054026,0.0054026,0.0052094,0.0052094,0.0049866,0.0049866,0.0049866,0.0049866,0.0049866,0.0049866]},{"label":"Topic coverage","values":[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25]}],"snapshots":[{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Product analytics · A worked example",0.341],[6,"Engineering · Design notes",0.264]],"note":"This slate covers 4 of 4 topics. λ=0.00: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · A practical guide",0.981],[6,"Machine learning · Beyond the basics",0.975]],"note":"This slate covers 4 of 4 topics. λ=0.05: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · A practical guide",0.981],[6,"Machine learning · Beyond the basics",0.975]],"note":"This slate covers 4 of 4 topics. λ=0.10: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · A practical guide",0.981],[6,"Machine learning · Design notes",0.986]],"note":"This slate covers 4 of 4 topics. λ=0.15: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · A practical guide",0.981],[6,"Machine learning · Design notes",0.986]],"note":"This slate covers 4 of 4 topics. λ=0.20: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · A practical guide",0.981],[6,"Machine learning · Design notes",0.986]],"note":"This slate covers 4 of 4 topics. λ=0.25: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · A practical guide",0.981],[6,"Machine learning · Design notes",0.986]],"note":"This slate covers 4 of 4 topics. λ=0.30: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Engineering · Common pitfalls",0.169],[3,"Product analytics · Common pitfalls",0.224],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · A practical guide",0.981],[6,"Machine learning · The trade-offs",0.995]],"note":"This slate covers 4 of 4 topics. λ=0.35: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Product analytics · Common pitfalls",0.224],[3,"Engineering · Common pitfalls",0.169],[4,"Research methods · Beyond the basics",0.187],[5,"Machine learning · The trade-offs",0.995],[6,"Machine learning · A field checklist",0.995]],"note":"This slate covers 4 of 4 topics. λ=0.40: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Product analytics · Common pitfalls",0.224],[3,"Engineering · Common pitfalls",0.169],[4,"Research methods · An evaluation guide",0.248],[5,"Machine learning · The trade-offs",0.995],[6,"Machine learning · A field checklist",0.995]],"note":"This slate covers 4 of 4 topics. λ=0.45: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Product analytics · An illustrated primer",0.258],[3,"Engineering · An illustrated primer",0.228],[4,"Research methods · Design notes",0.24],[5,"Machine learning · The trade-offs",0.995],[6,"Machine learning · A field checklist",0.995]],"note":"This slate covers 4 of 4 topics. λ=0.50: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · An illustrated primer",0.982]],"note":"This slate covers 1 of 4 topics. λ=0.55: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · An illustrated primer",0.982]],"note":"This slate covers 1 of 4 topics. λ=0.60: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · A reproducible lab",0.983]],"note":"This slate covers 1 of 4 topics. λ=0.65: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · A reproducible lab",0.983]],"note":"This slate covers 1 of 4 topics. λ=0.70: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · Questions to ask",0.984]],"note":"This slate covers 1 of 4 topics. λ=0.75: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · Questions to ask",0.984]],"note":"This slate covers 1 of 4 topics. λ=0.80: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · Questions to ask",0.984]],"note":"This slate covers 1 of 4 topics. λ=0.85: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Design notes",0.986],[5,"Machine learning · Common pitfalls",0.986],[6,"Machine learning · Questions to ask",0.984]],"note":"This slate covers 1 of 4 topics. λ=0.90: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Common pitfalls",0.986],[5,"Machine learning · Design notes",0.986],[6,"Machine learning · Questions to ask",0.984]],"note":"This slate covers 1 of 4 topics. λ=0.95: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Machine learning · A worked example",0.997],[2,"Machine learning · The trade-offs",0.995],[3,"Machine learning · A field checklist",0.995],[4,"Machine learning · Common pitfalls",0.986],[5,"Machine learning · Design notes",0.986],[6,"Machine learning · Questions to ask",0.984]],"note":"This slate covers 1 of 4 topics. λ=1.00: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."}],"columns":["Rank","Recommended reading · fictional titles","Relevance"],"caption":"The actual six-item slate at the selected λ","context":"48 fictional reading items across four topics. Change λ to trade relevance against redundancy; change the reader to alter preferences.","readout":"Relevance is cosine similarity to a synthetic preference vector. Diversity is one minus mean pairwise cosine similarity. Coverage is unique topics divided by four. 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The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Machine learning · An illustrated primer",0.299],[3,"Engineering · The trade-offs",0.623],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Engineering · A worked example",0.718]],"note":"This slate covers 4 of 4 topics. λ=0.05: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Machine learning · An illustrated primer",0.299],[3,"Engineering · The trade-offs",0.623],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A worked example",0.821]],"note":"This slate covers 4 of 4 topics. λ=0.10: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Machine learning · An illustrated primer",0.299],[3,"Engineering · The trade-offs",0.623],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A worked example",0.821]],"note":"This slate covers 4 of 4 topics. λ=0.15: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · The trade-offs",0.623],[3,"Machine learning · Beyond the basics",0.271],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A short case study",0.839]],"note":"This slate covers 4 of 4 topics. λ=0.20: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · The trade-offs",0.623],[3,"Machine learning · Beyond the basics",0.271],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A short case study",0.839]],"note":"This slate covers 4 of 4 topics. λ=0.25: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · The trade-offs",0.623],[3,"Machine learning · Beyond the basics",0.271],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A short case study",0.839]],"note":"This slate covers 4 of 4 topics. λ=0.30: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · The trade-offs",0.623],[3,"Machine learning · A reproducible lab",0.299],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A short case study",0.839]],"note":"This slate covers 4 of 4 topics. λ=0.35: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · The trade-offs",0.623],[3,"Machine learning · A reproducible lab",0.299],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A short case study",0.839]],"note":"This slate covers 4 of 4 topics. λ=0.40: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · The trade-offs",0.623],[3,"Machine learning · A reproducible lab",0.299],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · A short case study",0.839]],"note":"This slate covers 4 of 4 topics. λ=0.45: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · The trade-offs",0.623],[3,"Machine learning · A field checklist",0.391],[4,"Research methods · An illustrated primer",0.19],[5,"Product analytics · A short case study",0.839],[6,"Product analytics · Beyond the basics",0.838]],"note":"This slate covers 4 of 4 topics. λ=0.50: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · Beyond the basics",0.713],[3,"Machine learning · The trade-offs",0.376],[4,"Research methods · A reproducible lab",0.224],[5,"Product analytics · A short case study",0.839],[6,"Product analytics · Beyond the basics",0.838]],"note":"This slate covers 4 of 4 topics. λ=0.55: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · Beyond the basics",0.713],[3,"Machine learning · The trade-offs",0.376],[4,"Product analytics · A short case study",0.839],[5,"Product analytics · Beyond the basics",0.838],[6,"Product analytics · A field checklist",0.827]],"note":"This slate covers 3 of 4 topics. λ=0.60: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · Beyond the basics",0.713],[3,"Product analytics · A short case study",0.839],[4,"Product analytics · Beyond the basics",0.838],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · Design notes",0.828]],"note":"This slate covers 2 of 4 topics. λ=0.65: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · Design notes",0.718],[3,"Product analytics · A short case study",0.839],[4,"Product analytics · Beyond the basics",0.838],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · Design notes",0.828]],"note":"This slate covers 2 of 4 topics. λ=0.70: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · Design notes",0.718],[3,"Product analytics · A short case study",0.839],[4,"Product analytics · Beyond the basics",0.838],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · Design notes",0.828]],"note":"This slate covers 2 of 4 topics. λ=0.75: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · Design notes",0.718],[3,"Product analytics · A short case study",0.839],[4,"Product analytics · Beyond the basics",0.838],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · Design notes",0.828]],"note":"This slate covers 2 of 4 topics. λ=0.80: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Engineering · Design notes",0.718],[3,"Product analytics · A short case study",0.839],[4,"Product analytics · Beyond the basics",0.838],[5,"Product analytics · Design notes",0.828],[6,"Product analytics · A field checklist",0.827]],"note":"This slate covers 2 of 4 topics. λ=0.85: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Product analytics · A short case study",0.839],[3,"Product analytics · Beyond the basics",0.838],[4,"Product analytics · Design notes",0.828],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · Questions to ask",0.822]],"note":"This slate covers 1 of 4 topics. λ=0.90: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Product analytics · A short case study",0.839],[3,"Product analytics · Beyond the basics",0.838],[4,"Product analytics · Design notes",0.828],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · Questions to ask",0.822]],"note":"This slate covers 1 of 4 topics. λ=0.95: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Product analytics · An illustrated primer",0.84],[2,"Product analytics · A short case study",0.839],[3,"Product analytics · Beyond the basics",0.838],[4,"Product analytics · Design notes",0.828],[5,"Product analytics · A field checklist",0.827],[6,"Product analytics · Questions to ask",0.822]],"note":"This slate covers 1 of 4 topics. λ=1.00: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."}],"columns":["Rank","Recommended reading · fictional titles","Relevance"],"caption":"The actual six-item slate at the selected λ","context":"48 fictional reading items across four topics. Change λ to trade relevance against redundancy; change the reader to alter preferences.","readout":"Relevance is cosine similarity to a synthetic preference vector. Diversity is one minus mean pairwise cosine similarity. Coverage is unique topics divided by four. 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The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · Beyond the basics",0.554],[3,"Engineering · Design notes",0.507],[4,"Product analytics · An evaluation guide",0.503],[5,"Machine learning · Design notes",0.653],[6,"Product analytics · An illustrated primer",0.6]],"note":"This slate covers 4 of 4 topics. λ=0.05: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · Beyond the basics",0.554],[3,"Engineering · Design notes",0.507],[4,"Product analytics · An evaluation guide",0.503],[5,"Machine learning · The trade-offs",0.675],[6,"Research methods · An illustrated primer",0.709]],"note":"This slate covers 4 of 4 topics. λ=0.10: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · Beyond the basics",0.554],[3,"Engineering · Design notes",0.507],[4,"Product analytics · An evaluation guide",0.503],[5,"Research methods · An illustrated primer",0.709],[6,"Machine learning · The trade-offs",0.675]],"note":"This slate covers 4 of 4 topics. λ=0.15: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · Beyond the basics",0.554],[3,"Engineering · Design notes",0.507],[4,"Product analytics · An evaluation guide",0.503],[5,"Research methods · An illustrated primer",0.709],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.20: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A short case study",0.572],[3,"Engineering · Design notes",0.507],[4,"Product analytics · An evaluation guide",0.503],[5,"Research methods · An illustrated primer",0.709],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.25: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A short case study",0.572],[3,"Engineering · Design notes",0.507],[4,"Product analytics · An evaluation guide",0.503],[5,"Research methods · An illustrated primer",0.709],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.30: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A short case study",0.572],[3,"Engineering · Design notes",0.507],[4,"Product analytics · An evaluation guide",0.503],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.35: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A field checklist",0.64],[3,"Product analytics · Common pitfalls",0.498],[4,"Engineering · A reproducible lab",0.472],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.40: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A field checklist",0.64],[3,"Product analytics · Common pitfalls",0.498],[4,"Engineering · A reproducible lab",0.472],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.45: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A field checklist",0.64],[3,"Product analytics · A short case study",0.613],[4,"Engineering · A short case study",0.512],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.50: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A field checklist",0.64],[3,"Product analytics · A short case study",0.613],[4,"Engineering · A worked example",0.549],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.55: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A field checklist",0.64],[3,"Product analytics · A short case study",0.613],[4,"Engineering · A worked example",0.549],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.60: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A worked example",0.661],[3,"Product analytics · A short case study",0.613],[4,"Engineering · A worked example",0.549],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.65: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A worked example",0.661],[3,"Product analytics · A short case study",0.613],[4,"Engineering · A worked example",0.549],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.70: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · A worked example",0.661],[3,"Product analytics · A worked example",0.621],[4,"Engineering · A worked example",0.549],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.75: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · The trade-offs",0.675],[3,"Product analytics · A worked example",0.621],[4,"Engineering · A worked example",0.549],[5,"Research methods · A worked example",0.722],[6,"Research methods · The trade-offs",0.719]],"note":"This slate covers 4 of 4 topics. λ=0.80: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · The trade-offs",0.675],[3,"Product analytics · A worked example",0.621],[4,"Research methods · A worked example",0.722],[5,"Research methods · The trade-offs",0.719],[6,"Research methods · Questions to ask",0.718]],"note":"This slate covers 3 of 4 topics. λ=0.85: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Machine learning · The trade-offs",0.675],[3,"Research methods · A worked example",0.722],[4,"Research methods · The trade-offs",0.719],[5,"Research methods · Questions to ask",0.718],[6,"Research methods · A field checklist",0.714]],"note":"This slate covers 2 of 4 topics. λ=0.90: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Research methods · A worked example",0.722],[3,"Research methods · The trade-offs",0.719],[4,"Research methods · Questions to ask",0.718],[5,"Machine learning · The trade-offs",0.675],[6,"Research methods · A field checklist",0.714]],"note":"This slate covers 2 of 4 topics. λ=0.95: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."},{"rows":[[1,"Research methods · An evaluation guide",0.742],[2,"Research methods · A worked example",0.722],[3,"Research methods · The trade-offs",0.719],[4,"Research methods · Questions to ask",0.718],[5,"Research methods · A field checklist",0.714],[6,"Research methods · A reproducible lab",0.712]],"note":"This slate covers 1 of 4 topics. λ=1.00: λ=1 ranks only relevance; lower λ penalizes similarity to items already selected. The first item is always the highest-scoring candidate."}],"columns":["Rank","Recommended reading · fictional titles","Relevance"],"caption":"The actual six-item slate at the selected λ","context":"48 fictional reading items across four topics. Change λ to trade relevance against redundancy; change the reader to alter preferences.","readout":"Relevance is cosine similarity to a synthetic preference vector. Diversity is one minus mean pairwise cosine similarity. Coverage is unique topics divided by four. The curves are deterministic, not confidence estimates.","note":""}],"config":{"seed":20260927,"candidates":48,"slateSize":6,"lambdaGrid":[0.0,0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1.0]},"method":["The existing recsys.mmr_rerank implementation greedily selects six items. After the highest-relevance first item, it maximizes λ × relevance − (1−λ) × maximum similarity to the selected slate.","Candidate embeddings are positive perturbations of four topic axes, then L2-normalized. Reader vectors are fixed and normalized; the seed controls candidate perturbations. All titles and reader preferences are fictional.","Relevance, pairwise diversity and topic coverage have different meanings despite sharing a 0–1 scale. They are not combined into a single quality score."],"limits":["No user logs, learned retrieval model, MovieLens evaluation or A/B test. A higher diversity score does not establish better user satisfaction.","MMR is a greedy heuristic; topic coverage is not a fairness guarantee. Discrete slate changes can make curves non-monotonic. This does not benchmark Mamba4Rec or SASRec."],"references":[["Carbonell & Goldstein · MMR (1998)","https://doi.org/10.1145/290941.291025"]],"provenance":{"python":"3.13.0","numpy":"2.4.6","sourceSha256":{"showcase_benchmark.py":"7b4ba2f1364df061b886c91e908a1216d8c542477c495953e42fc3824ad670e9","recsys.py":"eb73af13c8419b2a46a485517cb7f51f2ae76f8ff219f95f47262f9a3aaf9e25"}}}