For non-stationary distributions, it may be beneficial to learn (at least some) parameters for your models online. A common approach is to learn a logistic regression model for binary outcomes, and this technique appears as early as 2008 at Yahoo! News. There are several approaches to deriving the model weights distribution online, which additionally enables one to perform exploration via Thompson Sampling. Crucially, whatever method must estimate both the mean of the model parameters and their covariance.

In reading the YouTube Paper, I came across one technical section that seemed very subtle and was not readily apparent why it was true: the watch time estimation using weighted logistic regression. It’s easy to gloss over this detail, but as it turns out, many people before me were curious about this section as well. The previous links have already explored one view into the why behind this formula, but I would like to formalize the process and explain it end to end.

In this post, we explore two approaches for training a linear regression online and compare their behavior on non-stationary data. We begin by deriving online linear regression and the Kalman filter update from first principles. Then, we empirically show differences between the two methods by fitting models using each algorithm on non-stationary data and looking at the residuals.

In our previous posts, we walked through the sampled softmax and in-batch negatives as loss functions for training a retrieval model. In this post, we will explore the best of both worlds in the so-called mixed negative sampling. This method will prove the to be the most data efficient and yield the best performance of the previous two methods. The post contains a new implementation of all three methods which will allow all three to be trained from (approximately) the same data loader and compared.

Consider the retrieval problem in a recommendation system. One way to model the problem is to create a big classification model predicting the next item a user will click or watch. This basic approach could be extended to large catalogs via a sampled softmax loss, as discussed in our last post. Naturally, the resulting dataset will only contain positive examples (i.e., what was clicked). In this post, we explore a more optimized version of this approach for more complex models via in-batch negatives. We derive the LogQ Correction to improve the estimate of the gradient and present code in PyTorch to implement the method, building on the previous blog post.