# What are some uses of logistic regression at scale?

Many libraries that scale linear and logistic regression assume a tall-skinny design matrix (many samples, few features), but I don't understand why you would need billions of samples if your data has 250 features.

In what scenarios would more data help? It seems like, instead of using more computational resources, you could simply sub-sample the data and achieve comparable accuracy in scenarios where the feature count is relatively small.

When feature count is high, say 100k, would having samples on the order of billions help? How do we decide how many samples are needed for a given modeling problem?

Perhaps more data helps with imbalanced data? e.g. when performing binary logistic regression for outlier detection, where the occurrence of positive samples is very small.

Any help here would be greatly appreciated.

• Maybe it really matters if you can predict a probability of $0.5001$ instead of $0.5000$. To get that kind of resolution, you might need a lot of samples.
– Dave
Jul 30, 2021 at 19:24
• do you have a specific paper/model at mind? They usually include motivation for their research. Also, scale means different things for different people, you have papers that deal with situations with billions of samples for 250 features, but also for 100k features. Jul 30, 2021 at 20:08
• "250 features" really means only 250 features given to you. As soon as you consider nonlinear relations and interactions in your modeling, the number of potential features to include explodes. That design matrix might not look so skinny after all ;-).
– whuber
Jul 30, 2021 at 20:51
• Can you give examples of libraries, the classic example I know of is vowpal Wabbit that scales for large number of features ( basically sparse features from one hot encoding) and large number of samples ( to handle the disjoint sets of one hot encoding) eg estimating the click through rate of Amazons product catalog Jul 30, 2021 at 21:38