Abstract: Described herein is a method and system for providing privacy guarantees with an improved privacy-accuracy trade-off. Dynamic data can be accessed from a database. A sum model is selected from window sum, exponential decay sum, and polynomial decay sum. An algorithm is initiated that produces polylogarithmic bounded error in the range of a sum function associated with the selected sum model and independent of time steps. The data can be assembled in a dyadic tree structure. A non-linearity component can be added to nodes of the dyadic tree structure. For example, this can be a noise components or a weight applied to the update. This can be done, for example, to different nodes differently. Differential private estimators can be constructed for fixed steps of time. The differential private estimators can be applied to a query means or filtering system to enhance privacy protection from potential adversaries.