Physical Unclonable Functions (PUFs) are promising security primitives for device authentication and key generation. This paper proposes a two-step methodology to improve the reliability of PUF under noisy conditions. The first step involves acquiring the parameters of PUF models by using machine learning algorithms. The second step then utilizes these obtained parameters to improve the reliability of PUFs by selectively choosing challenge-response pairs (CRPs) for authentication. Two distinct algorithms for improving the reliability of multiplexer (MUX) PUF, i.e., total delay difference thresholding and sensitive hits grouping, are presented. It is important to note that the methodology can be easily applied to other types of PUFs as well. Our experimental results show that the reliability of PUF-based authentication can be significantly improved by the proposed approaches. For example, in one experimental setting, the reliability of an MUX PUF is improved from 89.75% to 94.07% usmg total delay difference thresholding, while 89.30% of generated challenges are stored. As opposed to total delay difference thresholding, sensitive bits grouping possesses higher efficiency, as it can produce reliable CRPs directly. Our experimental results show that the reliability can be improved to 96.91% under the same setting, when we group 12 bits in the challenge vector of a 128-stage MUX PUF.