CTR prediction

Click-through rate (CTR) is the chance that a user clicks an item in a given context. A CTR model estimates P(click | user, item, context). Ads, feeds and many recommenders use it. Often the score is multiplied by a value, such as the money an ad earns when clicked, to get an expected value.

Four generations

The models you will hear about, in order:

1. Logistic regression on sparse one-hot or hashed features. It is interpretable and can be calibrated with care. You must build feature crosses by hand, such as user_id × item_category.
2. Gradient-boosted trees (XGBoost or LightGBM) on dense and sparse tabular features. They are strong at medium scale and work for ranking too.
3. Wide & Deep (Google, 2016). A linear "wide" part memorizes sparse crosses. A deep MLP generalizes over embeddings. The output is:

y = σ( w_wide · φ_cross(x) + MLP(embeddings(x)) + b )

4. DLRM-style models (Meta and successors). Embedding tables hold the categorical IDs. An MLP handles the dense features. Dot products between embeddings model interactions, and a top MLP produces the score. This is the common choice when the ID space is huge.

A feature sketch and an expected value

For one feed candidate, a model might use:

• User: click rate over the last 7 days, follow-graph size, topic preferences.
• Item: age in hours, the author's past CTR, and how similar its embedding is to the user's.
• Context: device, country, hour, and the surface (home feed or related items).
• Crosses: user cluster × author ID for the wide part, and an embedding dot product for the deep part.

The ranker scores each candidate independently, sorts them, and then re-ranking applies diversity rules.

For an ad, the expected value is the click probability times the value of a click. Suppose the model gives pCTR = 0.12 and a click is worth $0.40:

expected value = 0.12 × 0.40 = $0.048 per impression

That number is what an ads auction compares, which is why the probability has to be trustworthy. See calibration.

Common mistakes

• Using raw position as a feature. The model learns that the top slot causes clicks. See position bias.
• Using features that are not available at serving time. A feature computed from future data looks great in training and vanishes in production. See ML in production.
• Expecting a bigger model to fix bad labels. Architecture rarely fixes a label problem.

Check yourself

1. Why multiply the click probability by the click value? Answer: the expected value is what the platform gets per impression, so the ranking should use it.
2. What does the wide part of Wide & Deep memorize? Answer: sparse feature crosses, such as a specific user cluster paired with a specific author.

Key takeaways

• CTR models estimate the chance of a click for a user, item and context.
• The family grew from logistic regression to boosted trees, Wide & Deep, and DLRM-style embedding networks.
• Expected value is click probability times the value of a click.
• Keep features honest: no position leaks and nothing unavailable at serving time.

Further learning

Next, see why raw click logs are biased and how to correct them in position bias.