Abstract With the precipitous decline in response rates, researchers and pollsters have been left with highly nonrepresentative samples, relying on constructed weights to make these samples representative of the desired target population. Though practitioners employ valuable expert knowledge to choose what variables X must be adjusted for, they rarely defend particular functional forms relating these variables to the response process or the outcome. Unfortunately, commonly used calibration weights—which make the weighted mean of X in the sample equal that of the population—only ensure correct adjustment when the portion of the outcome and the response process left unexplained by linear functions of X are independent. To alleviate this functional form dependency, we describe kernel balancing for population weighting (kpop). This approach replaces the design matrix X with a kernel matrix, K encoding high-order information about X. Weights are then found to make the weighted average row of K among sampled units approximately equal to that of the target population. This produces good calibration on a wide range of smooth functions of X, without relying on the user to decide which X or what functions of them to include. We describe the method and illustrate it by application to polling data from the 2016 US presidential election.