  Many modern statistical analysis and machine learning applications require
training models on sensitive user data. Differential privacy provides a formal
guarantee that individual-level information about users does not leak. In this
framework, randomized algorithms inject calibrated noise into the confidential
data, resulting in privacy-protected datasets or queries. However, restricting
access to only privatized data during statistical analysis makes it
computationally challenging to make valid inferences on the parameters
underlying the confidential data. In this work, we propose simulation-based
inference methods from privacy-protected datasets. In addition to sequential
Monte Carlo approximate Bayesian computation, we use neural conditional density
estimators as a flexible family of distributions to approximate the posterior
distribution of model parameters given the observed private query results. We
illustrate our methods on discrete time-series data under an infectious disease
model and with ordinary linear regression models. Illustrating the
privacy-utility trade-off, our experiments and analysis demonstrate the
necessity and feasibility of designing valid statistical inference procedures
to correct for biases introduced by the privacy-protection mechanisms.
