Acoustic emission signals have been shown to accompany avalanche-like events in materials, such as dislocation avalanches in crystalline solids, collapse of voids in porous matter or domain wall movement in ferroics. The data provided by acoustic emission measurements is tremendously rich, but it is rather challenging to precisely connect it to the characteristics of the triggering avalanche. In our work we propose a machine learning based method with which one can infer microscopic details of dislocation avalanches in micropillar compression tests from merely acoustic emission data. As it is demonstrated in the paper, this approach is suitable for the prediction of the force-time response as it can provide outstanding prediction for the temporal location of avalanches and can also predict the magnitude of individual deformation events. Various descriptors (including frequency dependent and independent ones) are utilised in our machine learning approach and their importance in the prediction is analysed. The transferability of the method to other specimen sizes is also demonstrated and the possible application in more generic settings is discussed.