This paper investigates modeling nonlinear transformations based on deep neural networks (DNNs). Specifically, a DNN is used as a nonlinear mapping function for feature space transformation for HMM acoustic models. The nonlinear transformations are estimated under the sequence-based maximum likelihood criterion. The likelihood partition function is evaluated using the Monte Carlo method based on importance sampling. The DNN is first pre-trained approximately to a linear transformation then followed by fine-tuning using the gradient descent algorithm. In addition, a deep stacked architecture is proposed that builds a DNN as a series of sub-networks hierarchically with each representing a nonlinear transformation. A block-wise learning strategy is introduced. LVCSR speaker adaptation experiments on the proposed maximum likelihood nonlinear transformation have shown superior results than the widely-used CMLLR transformation.