The large number of parameters in deep neural networks (DNNs) often makes them prohibitive for low-power devices, such as field-programmable gate arrays (FPGA). In this paper, we propose a method to determine the relative importance of all network parameters by measuring the amount of information that the network output carries about each of the parameters -the Fisher Information. Based on the importance ranking, we design a complexity reduction scheme that discards unimportant parameters and assigns more quantization bits to more important parameters. For evaluation, we construct a deep autoencoder and learn a non-linear dimensionality reduction scheme for accelerometer data measuring the gait of individuals with Parkinson's disease. Experimental results confirm that the proposed ranking method can help reduce the complexity of the network with minimal impact on performance.