Our goal is to synthesize realistic underwater scenes with various fish species in different fish cages, which can be utilized to train computer vision models to automate fish counting task.

Our second, which attains a slightly worse approximation factor, runs in nearly-linear time and sample complexity under a mild spectral gap assumption.

Let Assumptions 1 and 2 hold. By substituting (A.5) into (A.3) and using Assumption 2, we derive Hence by (A.7), we obtain (A.2). Jensen's inequality for conditional expectations, we obtain that Enull nulle Suppose Assumptions 1, and 2, hold. By combing (2) with (A.14) and (A.8), there holds x Note by the Jensen's inequality that Then from (A.13) it follows that E null Then the theorem is proved. This combined with (A.19) proves the theorem.

Our approach instead builds a powerful Gaussian process surrogate model based on string kernels, naturally supporting variable length inputs, and performs efficient acquisition function maximization for spaces with syntactical constraints.