Random Projection Estimation of Discrete-Choice Models with Large Choice Sets
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclic monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semi-parametric and does not require explicit distributional assumptions to be made regarding the random utility errors. The random projection procedure is justified via the Johnson-Lindenstrauss Lemma -- the pairwise distances between data points are preserved during data compression, which we exploit to show convergence of our estimator. The estimator works well in simulations and in an application to a supermarket scanner dataset.
Code (0)
등록된 구현이 없습니다.
Tasks
Data CompressionDimensionality ReductionDiscrete Choice ModelsLEMMASimilar Papers 제목 키워드 기반
Network-based Representations and Dynamic Discrete Choice Models for Multiple Discrete Choice Analysis
In many choice modeling applications, people demand is frequently characterized as multiple discrete, which means that people choose multiple items simultaneously. The analysis and prediction of people behavior in multip…
Discrete Choice ModelsMultiple-choiceSparse principal component analysis via axis-aligned random projections
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most …
On the estimation of discrete choice models to capture irrational customer behaviors
The Random Utility Maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behavior, such as…
Discrete Choice ModelsTROLL: Trust Regions improve Reinforcement Learning for Large Language Models
Reinforcement Learning (RL) with PPO-like clip objectives has become the standard choice for reward-based fine-tuning of large language models (LLMs). Although recent work has explored improved estimators of advantages a…
Reinforcement LearningMathematical ReasoningCode GenerationLarge-scale optimal transport map estimation using projection pursuit
This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well-known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a ser…
Dimensionality Reduction