I self-published and paid for several hundred copies of a book. Can I deduct the expense?

Your activity would be considered a hobby so there are no deductions allowed. 

To follow-up on the comments from @Bsch4477, if a taxpayer receives income for an activity that they don’t carry out to make a profit, the expenses they pay for the activity are miscellaneous itemized deductions and can no longer be deducted. The taxpayer must still report the income they receive on Schedule 1, Form 1040, line 21.

An activity that you engage in but not to make a profit would be fairly characterized as a hobby and expenses from that hobby would not be deductible. 

@joedunlap8648