Roberts grew up in Onondaga, New York and graduated from Westhill Senior High School in 1979. He obtained an undergraduate degree in physics at St. Lawrence University in 1983 and a master's degree in public health from Tulane University in 1986. He did post-graduate fellowship work with the Centers for Disease Control in Atlanta and obtained a Ph.D. in environmental engineering from Johns Hopkins University in 1992; he has been a regular lecturer there ever since. He is now an Associate Clinical Professor of Population and Family Health at Columbia University's Mailman School of Public Health.