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Abstract Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas including materials design. In real world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are increasingly used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. Existing multi-fidelity BO (MFBO) methods operate under the following two assumptions: (1) Leveraging global (rather than local) correlation between HF and LF sources, and (2) Associating all the data sources with the same noise process. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. To dispense with these incorrect assumptions, we propose an MF emulation method that (1) learns a noise model for each data source, and (2) enables BO to leverage highly biased LF sources which are only locally correlated with the HF source. We illustrate the performance of our method through analytical examples and engineering problems on materials design.