In situ estimation of the individual absorption profiles of a room remains a challenging problem in building acoustics. This work is aimed at studying the feasibility of this estimation in a shoebox room of fixed and known geometry, using a room impulse response measured from a source and sensor at fixed and known positions. This problem is tackled using supervised learning. Three neural network architectures are compared. Simulated training and validation sets featuring various types of perturbations (surface diffusion, geometrical errors and additive white Gaussian noise) are generated. An extensive empirical simulated study is carried out to determine the influence of these perturbations on the performances of learned models, and to determine which components of the room impulse response are most useful for absorption coefficients prediction. Trained models are shown to yield errors significantly smaller than those of a naive mean estimator on every simulated datasets, including those featuring realistic perturbation levels. Our study outlines the benefit of using convolutional neural network layers, especially when geometrical errors exist. It also reveals that early acoustic echoes are the most salient feature of room impulse responses for absorption coefficient prediction under a fixed geometry.