Knowledge of the underlying parameters of the spreading model is crucial for understanding the global properties of the dynamics and for development of effective control strategies for an optimal dissemination or mitigation of diffusion [ 1,2 ] . However , in many realistic settings effective transmission probabilities are not known a priori and need to be recovered from a limited number of realizations of the process . Examples of such situations include spreading of a disease [ 3 ] , propagation of information and opinions in a social network [ 4 ] , correlated infrastructure failures [ 5 ] , or activation cascades in biological and neural networks [ 6 ] : precise model and parameters , as well as propagation paths are often unknown , and one is left at most with several observed diffusion traces . It can be argued that for many interesting systems , even the functional form of the dynamic model is uncertain . Nevertheless , the reconstruction problem still makes sense in this case : the common approach is to assume some simple and reasonable form of the dynamics , and recover the parameters of the model which explain the data in the most accurate and minimalistic way ; this is crucial for understanding the basic mechanisms of the spreading process , as well as for making further predictions without overfitting . For example , if only a small number of samples is available , a few - parameter model should be used .