On fusers that perform better than best sensor

In a multiple sensor system, sensor S_i, i=1, 2..., N, outputs Y⁽ⁱ⁾ ∈ [0,1], according to an unknown probability distribution P(Y⁽ⁱ⁾|X), in response to input X ∈ [0,1]. We choose a fuser-that combines the outputs of sensors-from a function class F={f:[0,1]^N→[0,1]} by minimizing empirical error based on an i.i.d. sample. If F satisfies the isolation property, we show that the fuser performs at least as well as the best sensor in a probably approximately correct sense. Several well-known fusers, such as linear combinations, special potential functions, and certain feedforward networks, satisfy the isolation property