In the era of digitalization, utilization of data-driven control approaches to minimize energy consumption of residential/commercial building is of far-reaching significance. Meanwhile, A number of recent approaches based on the application of Willems' fundamental lemma for data-driven controller design from input/output measurements are very promising for deterministic LTI systems. This paper addresses the key noise-free assumption, and extends these data-driven control schemes to adaptive building control with measured process noise and unknown measurement noise via a robust bilevel formulation, whose upper level ensures robustness and whose lower level guarantees prediction quality. Corresponding numerical improvements and an active excitation mechanism are proposed to enable a computationally efficient reliable operation. The efficacy of the proposed scheme is validated by a numerical example and a real-world experiment on a lecture hall on EPFL campus.