I ended up making spamassassin manually learn some ham in order to initialise the database.
sa-learn --progress --no-sync --ham /firstname.lastname@example.org_/Maildir/_somehamfolder_/cur/ --dbpath /var/spool/amavisd/.spamassassin/
First I did that on the INBOX folder. It took a long time, and then I noticed that there were timeouts in maillog when mail were received by postfix.
Therefore I simply took the last 200 mails from my INBOX, copied them into a HAM folder and made spamassassin make its thing on this folder. It works perfectly.
The results are immediately noticeable, the filtering looks much more effective.
I believe that there should be a “Bayesian filter” section in the mail filter tab in the GUI, that help a user to do this without too much hassle.