CNN and the Los Angeles Times said West left the UCLA Medical Center. People magazine quoted an unidentified source as saying West was "home, getting some rest."
Representatives for West could not immediately be reached by Reuters for comment on West's health status or hospital release.
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A spokeswoman for West's wife, reality TV star Kim Kardashian, said in an email there were no updates and referred queries to West's representatives.
The Jesus Walks rapper, 39, was taken to the Resnick Neuropsychiatric Hospital at the University of California, Los Angeles, last week after police responded to a call for help, several media outlets reported.
Sources close to the rapper told People he was exhausted from a "spiritual crisis."
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West's hospitalization followed a series of public rants and the cancellation of the rest of his concert tour.
It came after a demanding couple of months for the rapper and his wife after she was robbed at gunpoint in Paris, forcing the family to reassess its security and public profile.
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Kardashian, according to reports, has been by West's bedside during his hospitalization. Her E! Network reality show, "Keeping Up with the Kardashians," is "currently in production and has not been halted," a network representative said in a statement.
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