In this paper, a new method of machine learning,viz., Modified Polynomial Networks (MPN) is proposed for the Dialect Recognition (DR) problem in an Indian language, viz., Marathi. The proposed algorithm for machine learning is interpreted as designing a neural network by viewing it as a curve-fitting (approximation) problem in a high-dimensional space with the help of Radial-Basis Functions (RBF)(polynomials expansion of feature vectors for the present problem). The experiments are shown for open set DR problem (training and testing of the machine done with the different sets of speakers of a particular dialectal zone) in Marathi for Mel Frequency Cepstral Coefficients (MFCC) and Subband Based Cepstral Coefficients (SBCC) (extracted usiing Daubechies wavelets of 8 vanishing moments, i.e., db8) as input cepstral feature vectors to the 2nd order modified polynomial networks.