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Users frequently interact with software systems through data entry forms. However, form filling is time-consuming and error-prone. Although several techniques have been proposed to auto-complete or pre-fill fields in the forms, they provide limited support to help users fill categorical fields, i.e., fields that require users to choose the right value among a large set of options. In this paper, we propose LAFF, a learning-based automated approach for filling categorical fields in data entry forms. LAFF first builds Bayesian Network models by learning field dependencies from a set of historical input instances, representing the values of the fields that have been filled in the past. To improve its learning ability, LAFF uses local modeling to effectively mine the local dependencies of fields in a cluster of input instances. During the form filling phase, LAFF uses such models to predict possible values of a target field, based on the values in the already-filled fields of the form and their dependencies; the predicted values (endorsed based on field dependencies and prediction confidence) are then provided to the end-user as a list of suggestions. We evaluated LAFF by assessing its effectiveness and efficiency in form filling on two datasets, one of them proprietary from the banking domain. Experimental results show that LAFF is able to provide accurate suggestions with a Mean Reciprocal Rank value above 0.73. Furthermore, LAFF is efficient, requiring at most 317 ms per suggestion.