Adaptive Low-Complexity Sequential Inference for Dirichlet Process Mixture Models

We develop a sequential low-complexity inference procedure for the Infinite Gaussian Mixture Model (IGMM) for the general case of an unknown mean and covariance. The observations are sequentially allocated to classes based on a sequential maximum a-posterior (MAP) criterion. We present an easily computed, closed form for the conditional likelihood, in which the parameters can be recursively updated as a function of the streaming data. We propose a novel adaptive design for the Dirichlet process concentration parameter at each iteration, and prove, under a simplified model, that the sequence of concentration parameters is asymptotically well-behaved. We sketch an equivalence between the steady-state performance of the algorithm and Gaussian classification. The methodology is applied to the problem of adaptive modulation recognition and obviates the need for storing a large modulation library required for traditional modulation recognition. We also numerically evaluate the bit error rate performance (BER) of the DPMM-trained classifier when used as a demodulator and show that there is critical signal-to-noise ratio (SNR) that characterizes whether successful decoding is possible. This work is sponsored by the Assistant Secretary of Defense for Research & Engineering under Air Force Contract #FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the United States Government. 1 ar X iv :1 40 9. 81 85 v1 [ st at .M L ] 2 9 Se p 20 14