How can I train/teach GMail which "category" email should be filed under?

Question

I use GMail's inbox categories to group some of the messages I receive. For the most part, it does manage to keep annoying offers out of my primary inbox, filing them away in the "Promotions" category.

However, I find that it miscategorizes many messages that should be in the primary inbox. For example, email alerts from systems I maintain sometimes are put into "Updates". Alerts from GitHub always get put into "Social".

How does GMail determine which category messages belong in and how can I influence that determination?

A few years ago, I remember GMail's web UI had a button to indicate that some messages were miscategorized, but that's no longer available. I think that used to allow picking a new category as well.

Note:

• My question is similar to this other question. The difference is that I do not want to create more filters as suggested by the top answer there. I've used filters to specify categories for messages when necessary, like I wanted to specify which label to add to messages from a sender, so I set the category as well. To correct this miscategorization would require dozens of new filters.
• I know how to enable and disable categories, but that's not what I'm trying to do here. I like the concept of categories, but I would like to train GMail which categories some messages belong in or that some messages shouldn't be categorized at all.

Answer 1

This Making Gmail’s tabbed inbox work better for you blog post provides some detail from Google.

On how it determines which categories messages belong in:

Gmail tabs use a classification system that applies machine learning to determine where to put email based on a variety of signals. Signals include (but aren’t limited to) who the email comes from, what type of content is in the message and how Gmail users have interacted with similar content.

On influencing how messages are categorised the article points out:

Your actions teach Gmail how best to sort your email based on your preferences. Here are four things you can do to teach Gmail to sort email from certain senders into specific tabs, so you stay in control of where your email goes.

• Move a message from one tab to another: Just drag and drop it, or use the right click menu. Gmail will prompt you to remember this preference in the future from email from this sender.
• Create a filter: Use this option to create a filter that marks email from specific senders as important and/or directs it to a category of your choice.
• Add senders to your contact list: This option tells Gmail you’re getting mail from a person you know.
• Reply to the email: This is another way to indicate you and the sender are familiar with each other.

Based on that it looks like moving a message from one tab to another is as close as you're going to get to training.