Learning a mixture of two multinomial logits

The classical Multinomial Logit (MNL) is a behavioral model for user choice. In this model, a user is offered a slate of choices (a subset of a finite universe of n items), and selects exactly one item from the slate, each with probability proportional to its (positive) weight. Given a set of observed slates and choices, the likelihood-maximizing item weights are easy to learn at scale, and easy to interpret. However, the model fails to represent common real-world behavior. As a result, researchers in user choice often turn to mixtures of MNLs, which are known to approximate a large class of models of rational user behavior. Unfortunately, the only known algorithms for this problem have been heuristic in nature. In this paper we give the first polynomial-time algorithms for exact learning of uniform mixtures of two MNLs. Interestingly, the parameters of the model can be learned for any n by sampling the behavior of random users only on slates of sizes 2 and 3; in contrast, we show that slates of size 2 are insufficient by themselves

Discrete choice, permutations, and reconstruction

In this paper we study the well-known family of Random Utility Models, developed over 50 years ago to codify rational user behavior in choosing one item from a finite set of options. In this setting each user draws i.i.d. from some distribution a utility function mapping each item in the universe to a real-valued utility. The user is then offered a subset of the items, and selects theone of maximum utility. A Max-Dist oracle for this choice model takes any subset of items and returns the probability (over the distribution of utility functions) that each will be selected. A discrete choice algorithm, given access to a Max-Dist oracle, must return a function that approximates the oracle. We show three primary results. First, we show that any algorithm exactly reproducing the oracle must make exponentially many queries. Second, we show an equivalent representation of the distribution over utility functions, based on permutations, and show that if this distribution has support size k, then it is possible to approximate the oracle using O(nk) queries. Finally, we consider settings in which the subset of items is always small. We give an algorithm that makes less than n(1=2)K queries, each to sets of size at most (1/2)K, in order to approximate the Max-Dist oracle on every set of size |T| K with statistical error at most. In contrast, we show that any algorithm that queries for subsets of size 2O( p log n) must make maximal statistical error on some large sets

Espacios florecientes: por unos asentamientos de refugiados más ecológicos

Al incorporar iniciativas de agricultura urbana en los entornos de los campos de refugiados se puede ampliar el concepto de alojamiento para incluir la protección contra el clima, abordar las deficiencias nutricionales y aumentar los niveles de dignidad humana, creación de espacios y autosuficiencia

Poster 153: Walking Assessment in People With Lumbar Spinal Stenosis: Capacity, Performance, and Self‐report Measures

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146939/1/pmr2s71a.pd

Microscopic evolution of social networks

We present a detailed study of network evolution by analyzing four large online social networks with full temporal information about node and edge arrivals. For the first time at such a large scale, we study individual node arrival and edge creation processes that collectively lead to macroscopic properties of networks. Using a methodology based on the maximum-likelihood principle, we investigate a wide variety of network formation strategies, and show that edge locality plays a critical role in evolution of networks. Our findings supplement earlier network models based on the inherently non-local preferential attachment. Based on our observations, we develop a complete model of network evolution, where nodes arrive at a prespecified rate and select their lifetimes. Each node then independently initiates edges according to a “gap” process, selecting a destination for each edge according to a simple triangle-closing model free of any parameters. We show analytically that the combination of the gap distribution with the node lifetime leads to a power law out-degree distribution that accurately reflects the true network in all four cases. Finally, we give model parameter settings that allow automatic evolution and generation of realistic synthetic networks of arbitrary scale