  We analyze the measured optical conductivity spectra using the
density-functional-theory-based electronic structure calculation and
density-matrix renormalization group calculation of an effective model. We show
that, in contrast to a conventional description, the Bose-Einstein condensation
of preformed excitons occurs in Ta$_2$NiSe$_5$, despite the fact that a
noninteracting band structure is a band-overlap semimetal rather than a small
band-gap semiconductor. The system above the transition temperature is
therefore not a semimetal, but rather a state of preformed excitons with a
finite band gap. A novel insulator state caused by the strong electron-hole
attraction is thus established in a real material.
