No, improvise can only help pay for the generic mana costs of spells.
702.125a Improvise is a static ability that functions while the spell with improvise is on the stack. “Improvise” means “For each generic
mana in this spell’s total cost, you may tap an untapped artifact you
control rather than pay that mana.”
While Hostage Taker enables you to "spend mana as though it were mana of any type to cast the spell" to pay for the non-generic portion of the mana cost, that does not make it a generic mana cost. The mana in your pool is transmutable, while the mana in the cost retains its mana type. It is a case of all thumbs are fingers but not all fingers are thumbs.
Also from the gatherer entries on Improvise: Improvise can’t pay for White, Blue, Black, Red, Green, or Colorless mana symbols in a spell’s total cost.
Do remember that the statue only gives non-artifacts improvise. This includes ones from zones you would not be able to cast them normally from (Like what is the case from the Hostage Taker.)