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We propose an inferential procedure that constructs a discrete confidence set for the true optimal assortment based upon the data collected by the dynamic policy, which can be applied to test any combinatorial properties of the optimal assortment, such as the number of product categories to include in the offer set.\r\n\r\nThe temporal dependency and combinatorial data structure due to adaptive sampling create challenges for convergence analysis. To address these, we develop new probabilistic results on anti-concentration bounds for the difference between the maxima of two Gaussian random vectors. Furthermore, we address the high dimensionality of the combinatorial inference problem by employing discretization via epsilon-covering and subspace projection techniques. We provide theoretical guarantees on both the validity and power of our inferential procedure, and establish information-theoretic lower bounds for the required signal strength, which match the upper bounds of our procedure up to logarithmic factors.\r\n\r\nhttps:\/\/judygiant.github.io\/", "occurrence_notes":null, "guid":"124598-21853250@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/124598", "building_id":"1000167", "building_name":"West Hall", "campus_maps_id":"163", "room":"411", "location_name":"West Hall", "has_livestream":0, "cost":"", "tags":["seminar"], "website":"https:\/\/lsa.umich.edu\/stats", "sponsors":[ { "group_name":"Department of Statistics", "group_id":"3473", "website":"" }, { "group_name":"Department of Statistics Seminar Series", "group_id":"3585", "website":"" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_thumb\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb_square\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "group_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_large\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_large_lightbox\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_large_crop\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_list":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_list\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_grid_2x\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_feature_large\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2024\/11\/event_124598_original-1.jpeg" }, "occurrence_count":1, "first_occurrence":21853250 } }