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.
Code (0)
등록된 구현이 없습니다.
Tasks
Vocal Bursts Valence PredictionSimilar Papers 제목 키워드 기반
Learning an arbitrary mixture of two multinomial logits
In this paper, we consider mixtures of multinomial logistic models (MNL), which are known to $\epsilon$-approximate any random utility model. Despite its long history and broad use, rigorous results are only available fo…
Vocal Bursts Valence PredictionBetter Conditional Density Estimation for Neural Networks
The vast majority of the neural network literature focuses on predicting point values for a given set of response variables, conditioned on a feature vector. In many cases we need to model the full joint conditional dist…
Density EstimationAsymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models. In fact, the models are non-identifiable …
Learning large softmax mixtures with warm start EM
Mixed multinomial logits are discrete mixtures introduced several decades ago to model the probability of choosing an attribute from $p$ possible candidates, in heterogeneous populations. The model has recently attracted…
Attributeparameter estimationA Gamma-Poisson Mixture Topic Model for Short Text
Most topic models are constructed under the assumption that documents follow a multinomial distribution. The Poisson distribution is an alternative distribution to describe the probability of count data. For topic modell…
text-classificationText ClassificationTopic Models