# Conditional Logit for recommender systems?

Are conditional multinomial logits used for recommendation engines? Although they are commonly used in econometrics, I've never heard it used or discussed in the context of recommender systems.

Economists use multinomial conditional logits to model which of several options a person would choose and how much they value each characteristic of the items being chosen. This is often referred to as the hedonic model.

The classic multinomial logit deals with discrete items (predict whether a commuter would "walk," "take the bus," or "take the subway."

The conditional multinomial logit uses data on ANY sets of observed choices and does not require that each person choose among the same set of things. It also puts values on various characteristics/variables. For example, you may see people decide which of several houses to buy. Each house is different -- square footage, number of rooms, price, etc. Based on observed choices, the model estimates the importance of various characteristics and you can derive a predicted "utility" score that each person has for each house. The model then predicts that the house with the highest score is chosen.

Here is a description: http://data.princeton.edu/wws509/notes/c6s3.html

• I'm a little confused about what you are looking for in an answer. A citation to a paper that uses a conditional multinomial logit in a recommender setting? Oct 20, 2013 at 6:30

Preface

I work with recommender systems on daily basis and have also never heard of the application of such a model as recommender system. I can only speculate about the reasons though.

The main overall reason might be that recommender systems are often applied in a domain where the price/cost of an item is too small to force the customer to invest time into making a nearly-optimal decision, maximizing his utility. This should be kept in mind in the following section. Such domains include e-commerce or news portals (where articles are recommended) or sites like tastekid.com, where the decision at this step costs only a click, i.e. virtually nothing.

Reasoning

The described conditional multinomial model requires (or works best) with ...

• characteristics of the customer
• characteristics of the items
• assumed rationality when it comes to the decision

Let's step through every point

Characteristics of the customers

Beside some basic demographic information like gender, address and (may be) age, little is known. The less the price of an item (see above), the harder it is to request a survey before the selection process starts. Activity data (bought items, ratings etc.) on the other hand can be collected without any work from the customer and can be used to describe the customer, following the motto "you are what you are interested in". The items the customer is interested in (the preferences) implicitly capture what is important to the customer.

Characteristics of the items

Building a model based on the characteristics of a item is already done, either via "content based collaborative filtering" or a model based approach. These are e.g. used to solve the cold-start-problem, i.e. the fresh new recommender system has not (enough) preferences yet.

The drawback here however is that is hard to automatically collect the properties of an item. Imagine the case of fashion: Some are easy (color, brand), some are very hard (how does the cloth feels like on skin, how does it look if my hip is broader than average). Sometime it is completely impossible because it entirely depends on the reception of the product, e.g. in case of movies. For certain items, such information can be collected by humans or by a very very sophisticated system understanding semantics and language. It is not clear that the resulting improvement will outweigh the costs.

So instead of saying: "Item A is similar to item B due to the properties p1,p2,...," it is easier to say "a lot of people have both bought item A and item B. I don't know why, but they are similar enough for the purpose of a recommender system". So the preferences implicitly capture how similar to items are.

Assumed rationality when it comes to the decision

We are humans and we pretend to be rational all the time. If e.g. the price or other circumstances forces us to think hard about it a decision, it might be the case that the rational part of a decision is higher than average. But when it comes to utilize advertising to sell people stuff (and yes, recommendations can be seen as advertising), marketing will tell that rationality plays a lesser role.

Additionally, people are often do not know beforehand which properties are most important to them in order to maximize their personal utility function. If this would be the case, all buying processes could be described via the usage of a search engine, where a) all relevant properties are listed b) the customer selects all properties relevant to him and name the product of interest and the search engine delivers exactly the right results.

Instead, people have a basic goal (e.g. buying a suit), but then are browsing around to see how products appeal to them and / or to get inspired. Making a buy decision is still partially rational (budget, invested time) but often comes down to "what feels right". Of course, every domain has its own distribution of rationality and emotionality. The more technical, the more facts do play an important role. But even than the customer might select a brand due to the curtain fire of advertising, which he would not have named as primary criterion beforehand.

So building a economic model here might be still be working and it surely correct, buth might be entirely over the top. Additionally, one might have to build a separate model for each type of item a shop is selling.

Summary

Building a recommender system entirely based on preferences is often done because ...

• it is simple (=> cheap)
• it can be done automatically, no extra work from the customer is required (=> cheap)
• it works (good enough), so that a more complicated model might not outweigh the additional costs.

But: There are domains, where such a economic model will be better. I do not doubt, that a good estate agent and hence a good expert system based on a economic model will easily outperform a recommender system based on preferences. I have regularly observed that recommendations made by human experts are often better than automatic ones. However, the automatics are still good and can produced en mass without too much costs, so that an expert can focus on more sophisticated tasks.

• Thanks for the thoughtful response! You raise a number of great points, especially about how decisions are made on a "what feels right" basis vs. a cost-benefit analysis. If the most important attributes of the item aren't observable (to us), associational rules are the way to go. It would be interesting to think of other domains and applications that lay somewhere between ecommerce recommender systems and real estate agents. Oct 23, 2013 at 6:47