Machine learning (ML) has been used for various tasks in network operations in recent years. However, since the scale of networks has grown and the amount of data generated has increased, it has been increasingly difficult for network operators to conduct their tasks with a single server using ML. Thus, ML with edge-cloud cooperation has been attracting attention for efficiently processing and analyzing a large amount of data. In the edge-cloud cooperation setting, although transmission latency, bandwidth congestion, and accuracy of tasks using ML depend on the load balance of processing data with edge servers and a cloud server in edge-cloud cooperation, the relationship is too complex to estimate. In this paper, we focus on monitoring anomalous traffic as an example of ML tasks for network operations and formulate transmission latency, bandwidth congestion, and the accuracy of the task with edge-cloud cooperation considering the ratio of the amount of data preprocessed in edge servers to that in a cloud server. Moreover, we formulate an optimization problem under constraints for transmission latency and bandwidth congestion to select the proper ratio by using our formulation. By solving our optimization problem, the optimal load balance between edge servers and a cloud server can be selected, and the accuracy of anomalous traffic monitoring can be estimated. Our formulation and optimization framework can be used for other ML tasks by considering the generating distribution of data and the type of an ML model. In accordance with our formulation, we simulated the optimal load balance of edge-cloud cooperation in a topology that mimicked a Japanese network and conducted an anomalous traffic detection experiment by using real traffic data to compare the estimated accuracy based on our formulation and the actual accuracy based on the experiment.