Protein-ligand interactions are increasingly profiled at high throughput using affinity selection and massively parallel sequencing. However, these assays do not provide the biophysical parameters that most rigorously quantify molecular interactions. Here we describe a flexible machine learning method, called ProBound, that accurately defines sequence recognition in terms of equilibrium binding constants or kinetic rates. This is achieved using a multi-layered maximum-likelihood framework that models both the molecular interactions and the data generation process. We show that ProBound quantifies transcription factor (TF) behavior with models that predict binding affinity over a range exceeding that of previous resources; captures the impact of DNA modifications and conformational flexibility of multi-TF complexes; and infers specificity directly from in vivo data such as ChIP-seq without peak calling. When coupled with an assay called KD-seq, it determines the absolute affinity of protein-ligand interactions. We also apply ProBound to profile the kinetics of kinase-substrate interactions. ProBound opens new avenues for decoding biological networks and rationally engineering protein-ligand interactions.