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Directed laboratory evolution applies iterative rounds of mutation and selection to explore the protein fitness landscape and provides rich information regarding the underlying relationships between protein sequence, structure, and function. Laboratory evolution data consist of protein sequences sampled from evolving populations over multiple generations and this data type does not fit into established supervised and unsupervised machine learning approaches. We develop a statistical learning framework that models the evolutionary process and can infer the protein fitness landscape from multiple snapshots along an evolutionary trajectory. We apply our modeling approach to dihydrofolate reductase (DHFR) laboratory evolution data and the resulting landscape parameters capture important aspects of DHFR structure and function. We use the resulting model to understand the structure of the fitness landscape and find numerous examples of epistasis but an overall global peak that is evolutionarily accessible from most starting sequences. Finally, we use the model to perform an in silico extrapolation of the DHFR laboratory evolution trajectory and computationally design proteins from future evolutionary rounds. Author summary: Laboratory evolution has revolutionized our understanding of protein structure, function, and evolution, and has generated countless useful proteins broad applications in medicine, biocatalysis, and biotechnology. These experiments explore protein sequence space through iterative rounds of mutation and selection and can provide rich data of populations traversing the fitness landscape. In this paper, we present a statistical learning framework that models the evolutionary process and can infer the structure of the underlying protein fitness landscape from multiple snapshots along a laboratory evolution trajectory. We generate a dihydrofolate reductase (DHFR) laboratory evolution data set and apply our modeling approach to infer the landscape parameters. The estimated parameters pinpoint key residues that dictate DHFR structure and function. We use the resulting model to understand the local and global structure of the fitness landscape and to perform in silico directed evolution for protein engineering. [ABSTRACT FROM AUTHOR]