Shootings like Newtown, Chris Kyle, Columbine and others throughout the world are so rare and random they're essentially unpredictable.
Prediction of violence by the average psychiatrist and Ph.D. level psychologist is no better than chance.
Psychiatrists and psychologists who specialize in prediction of violence based on interviews and psychological testing have a prediction rate of only 70%.
The best predictor is a past history of violence. Many perpetrators of mass killings have little or no history. Some suffer from closed head injuries or other brain abnormalities (Charles Whitman 1966 University of Texas tower sniper had a brain tumor).
Emotional and mental illnesses that have agitation and aggression as diagnostic criteria range from regular depression and anxiety to PTSD, dementia, schizophrenia and severe personality disorders. Legally and ethically, mental health providers are prohibited to report patients as violent unless they're a clear threat to themselves or someone else.
These facts aren't meant to paint a hopeless picture, just putting things into perspective without any political or cultural bias.