There is an exciting fertile relationship between statistics/machine learning  and combinatorial geometry. My talk shows how variations of Tverberg’s theorem (to be  explained, don’t worry!) can answer several basic questions from machine learning and statistical inference. In particular, touches on the question: When do I have sufficient data in my sample to conclude learning was properly done?

I will not assume any prior knowledge. All new theorems are joint work with subsets of the following wonderful researchers: T. Hogan, D. Oliveros, E. Jaramillo-Rodriguez, and A. Torres-Hernandez.

We will have a talk and open reflexions by all the MMD participants.

"Multi-Channel Autobidding with Budget and ROI Constraints" -  Nicki Golrezaei

Drafts are sequential allocation procedures for distributing heterogeneous and indivisible objects among agents subject to some priority order (e.g., allocating players’ contract rights to teams in professional sports leagues). Agents report ordinal preferences over objects and bundles are partially ordered by pairwise comparison. We provide a simple characterization of draft rules: they are the only allocation rules which are respectful of a priority (RP), envy-free up to one object (EF1), non-wasteful (NW) and resource-monotonic (RM). RP and EF1 are crucial for competitive balance in sports leagues. We also prove three related impossibility theorems: (i) weak strategy-proofness (WSP) is incompatible with RP, EF1, and NW; (ii) WSP is incompatible with EF1 and (Pareto) efficiency (EFF); and (iii) when there are two agents, strategy-proofness (SP) is incompatible with EF1 and NW. However, draft rules satisfy the competitive-balance properties, RP and EF1, together with EFF and maxmin strategy-proofness. If agents may declare some objects unacceptable, then draft rules are characterized by RP, EF1, NW, and RM, in conjunction with individual rationality and truncation-invariance. In a model with variable populations, draft rules are characterized by EF1, EFF, and RM, together with (population) consistency, top-object consistency, and neutrality; in this setting, the priority emerges endogenously from the properties.