The lecture begins by introducing choice models, focusing on discrete choice modeling as a foundational tool for understanding human preference learning in machine learning pipelines. Choice models aim to predict the choices individuals or groups make within specific contexts by observing their decisions and fitting models to this data. The instructor emphasizes the importance of engaging critically with the assumptions underlying these models, such as rationality, and highlights various real-world applications including marketing (e.g., car preferences), transportation route planning, logistics, and energy management. Features describing both the items and the decision-makers are crucial inputs to these models.
A brief historical overview traces the origins of choice modeling back to early 20th-century studies on food preferences, evolving through utility theory and discrete choice theory, with notable contributions recognized by a Nobel Prize in 2000. The lecture explains that choice models assume an underlying latent utility function that governs decision-making, though this utility is unobservable and can only be inferred from observed choices. The mathematical formulation involves modeling the probability that an individual prefers one item over another based on features of the items and the individual, often using linear models and logistic regression as a practical fitting method.
The discussion then delves into the technical details of modeling choices, including the use of noise distributions such as the independent and identically distributed (IID) extreme value noise, which leads to logistic regression models, or Gaussian noise, which leads to probit models. The instructor addresses common questions about assumptions like noise independence, the handling of multiple individuals with potentially different preferences, and the implications of monotonic transformations on the identifiability of utility functions. The lecture also covers extensions to multi-class and ordered choice models, such as the Plackett-Luce model for ranking multiple items.
A critical point raised is the assumption of rationality in choice models, meaning preferences are transitive and consistent, which excludes circular or intransitive preferences. The instructor acknowledges that this assumption may not always hold in real-world human behavior and that richer feature sets or alternative models may be needed to capture such complexities. The lecture also distinguishes between revealed preferences (actual observed choices) and stated preferences (hypothetical or survey-based choices), noting the trade-offs between control and realism in data collection, and how these impact model design and interpretation.
Finally, the lecture emphasizes that choice modeling is fundamentally a machine learning problem where standard techniques like maximum likelihood estimation, regularization, and model selection apply. The choice of model complexity must balance bias and variance, and practical considerations often lead to pooling data across individuals or incorporating individual-specific features. The instructor concludes by highlighting ongoing challenges and open questions in the field, such as modeling noise accurately, dealing with intransitive preferences, and integrating different types of preference data, encouraging further exploration and critical thinking about these foundational models.
