Example computing devices described herein enable computation of a machine learning model on distributed multi-party data that is vertically partitioned, in a privacy preserving fashion. The computing device computes at a party a sum of local data owned by the party, wherein the local data is vertically partitioned into a plurality of data segments, each data segment representing a non-overlapping subset of data features; transforms a cost function of a data analytics task to a gradient descent function, wherein the cost function comprises a summation of a plurality of cost function values; anonymizes aggregated data shards received from a mediator; updating local model parameters based on the aggregated data shards; and performs privacy-preserving multi-party analytics on the vertically partitioned local data based on a learned global analytic model. It leverages a secure-sum protocol that provides strong security guarantees against collusion and prior-knowledge attacks.