{"id":1190664,"date":"2026-10-21T10:26:09","date_gmt":"2026-10-21T17:26:09","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/learning-from-a-mixture-of-information-sources\/"},"modified":"2026-10-26T16:07:01","modified_gmt":"2026-10-26T23:07:01","slug":"learning-from-a-mixture-of-information-sources","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/learning-from-a-mixture-of-information-sources\/","title":{"rendered":"Learning from a Mixture of Information Sources"},"content":{"rendered":"\n\n\n<p class=\"wp-block-paragraph\">We often learn from multiple sources that convey information in different ways. How informative is it to know the source of a signal, and how is this informativeness shaped by the distribution of sources? We extend the standard (binary-state, binary-signal) Blackwell experiment model by introducing a commonly known distribution over signaling schemes, representing the distribution of information sources. We compare learning under two information models: source-aware, where decision makers observe a signaling scheme and its realization (e.g., raw reviews, search results), and source-blind, where only the signal realization is observed (e.g., aggregate ratings, LLM-generated summaries). We show that a mean-preserving spread in the distribution of signaling schemes translates into Blackwell dominance for source-aware decision makers, implying they are &#8220;risk-loving&#8221; in information sources. In contrast, it has no impact on source-blind decision makers. When learning from repeated draws of signaling schemes, source-blind decision makers learn more slowly. However, as long as the average signaling scheme is <math><mi>\u03b5<\/mi><\/math> away from being completely uninformative, source-blind learning can match source-aware learning by using at most <math><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\/<\/mo><mi>\u03b5<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/math> times more data.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We often learn from multiple sources that convey information in different ways. How informative is it to know the source of a signal, and how is this informativeness shaped by the distribution of sources? We extend the standard (binary-state, binary-signal) Blackwell experiment model by introducing a commonly known distribution over signaling schemes, representing the distribution [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"user_nicename","value":"Nicole Immorlica","user_id":"33086"},{"type":"user_nicename","value":"Brendan Lucier","user_id":"31303"},{"type":"text","value":"Yaroslav Mukhin","user_id":0},{"type":"user_nicename","value":"Clayton Thomas","user_id":"42840"},{"type":"text","value":"Ruqing 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