The focus of this dissertation is the application of statistical learning and computational thinking to stubborn problems in development economics and welfare dynamics including the problems of poverty targeting, the identification of heterogeneous welfare dynamics, and the assessment of the risks and returns of diverse asset portfolios. Approaching such problems with statistical learning has allowed me to overcome some of the commonly imposed constraints and weaken some of the commonly made assumptions that prevent us from learning more about the empirical problem. By using out-of-sample validation and algorithmic model building, the first chapter presents an important step forward in making poverty targeting more accurate and efficient. The second chapter considers the theory and empirics of poverty and welfare dynamics more generally; the findings include several important implications for the study of welfare dynamics in diverse asset environments. The final chapter finds evidence consistent with a pattern in which households with greater initial asset holdings also hold a riskier portfolios and enjoy greater returns to their assets; however the analysis is limited by a poor accounting of human capital assets. The chapter concludes that allowing for the heterogeneity of assets, including non-physical assets, that may play a role in the livelihoods of households in developing countries is important. This dissertation demonstrates some of the ways in which algorithmic approaches can assist us in learning from the data.