Measurements of various physical properties of oceanic sediment and crustal structures provide insight into a number of geological and geophysical processes. In particular, knowledge of the shear wave velocity (VS) structure of marine sediments and oceanic crust has wide ranging implications from geotechnical engineering projects to seismic mantle tomography studies. In this study, we propose a novel approach to nonlinearly invert compliance signals recorded by colocated ocean-bottom seismometers and high-sample-rate pressure gauges for shallow oceanic shear wave velocity structure. The inversion method is based on a type of machine learning neural network known as a mixture density neural network (MDN). We demonstrate the effectiveness of the MDN method on synthetic models with a fixed deployment depth of 2015 m and show that among 30 000 test models, the inverted shear wave velocity profiles achieve an average error of 0.025 km s−1. We then apply the method to observed data recorded by a broad-band ocean-bottom station in the Lau basin, for which a VS profile was estimated using Monte Carlo sampling methods. Using the mixture density network approach, we validate the method by showing that our VS profile is in excellent agreement with the previous result. Finally, we argue that the mixture density network approach to compliance inversion is advantageous over other compliance inversion methods because it is faster and allows for standardized measurements.