Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for online training of machine learning models predicting time-series data. In one aspect, a method comprises training a machine learning model having a plurality of weights by maintaining weight data, specifying a plurality of sub-weights for each of the plurality of weights and covariance data that estimates the joint uncertainty between the sub-weights, and, at each of a plurality of time steps, receiving model inputs, processing the model inputs using the weight data to generate corresponding model outputs, receiving corresponding ground truth outputs, and updating the weight data using the corresponding ground truth outputs.