A method for transforms input signals, by first defining a model for transforming the input signals, wherein the model is specified by constraints and a set of model parameters. An iterative inference procedure is derived from the model and the set of model parameters and unfolded into a set of layers, wherein there is one layer for each iteration of the procedure, and wherein a same set of network parameters is used by all layers. A neural network is formed by untying the set of network parameters such that there is one set of network parameters for each layer and each set of network parameters is separately maintainable and separately applicable to the corresponding layer. The neural network is trained to obtain a trained neural network, and then input signals are transformed using the trained neural network to obtain output signals.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for transforming input signals, comprising the steps of: defining a model for transforming the input signals, wherein the model is specified by constraints and a set of model parameters; defining an iterative inference procedure derived from the model and the set of model parameters; unfolding the iterative inference procedure into a set of layers, wherein there is one layer for each iteration of the procedure, and wherein a same set of network parameters is used by all layers; forming a neural network by untying the set of network parameters such that there is one set of network parameters for each layer and each set of network parameters is separately maintainable and separately applicable to the corresponding layer; training the neural network to obtain a trained neural network; and transforming the input signals using the trained neural network to obtain output signals, wherein the steps are performed in a processor. 2. The method of claim 1, further comprising: adjusting one or more sets of network parameters independently during the training. 3. The method of claim 1, wherein the model is a probabilistic generative model and the inference procedure is variational inference, and further comprising optimizing a lower bound on a likelihood of the input signals to obtain approximate posterior probabilities. 4. The method of claim 1, wherein the model is a Markov random field and the inference procedure is loopy belief propagation (BP) that enforces local consistency constraints on marginal posterior probabilities. 5. The method of claim 1, wherein the model is a non-negative basis function expansion model and the inference procedure is based on multiplicative updates. 6. The method of claim 1, wherein the sets of parameters specify relationships between the output signals and the input signals. 7. The method of claim 6, further comprising: obtaining the output signals by optimizing an inference objective function involving intermediate variables from which the output signals can be determined. 8. The method of claim 7, wherein the inference objective function is an approximation to a log likelihood. 9. The method of claim 7, wherein the intermediate variables are variational parameters of a variational inference procedure. 10. The method of claim 7, wherein the intermediate variables are posterior marginal probabilities of a loopy belief propagation procedure. 11. The method of claim 7, wherein the intermediate variables are activation coefficients of basis functions. 12. The method of claim 2, wherein the sets of network parameters specify relationships between the input signals and the output signals, and the adjusting optimizes the sets of network parameters using a discriminative objective function involving a loss function that takes as argument a reference value and estimated output signals. 13. The method of claim 1, wherein the input signals are noisy speech and the output signals are clean speech. 14. The method of claim 1, wherein the input signals are a mixture of signals and the output signals are one or more source signals. 15. The method of claim 1, wherein the neural network is extended by using one neural network for each element of a set of data instances and adding connections between one or more layers of one or more neural networks. 16. The method of claim 15, wherein the set of data instances is a sequence, and the resulting neural network is a recurrent neural network. 17. The method of claim 16, wherein the set of data instances is an array. 18. The method of claim 12, wherein the optimizing is based on a gradient-descent implemented by back-propagation of gradients from higher layers to lower layers. 19. The method of claim 12, wherein one or more of the network parameters are non-negative, and the optimizing is based on multiplicative updates. 20. The method of claim 19, wherein the multiplicative updates are based on a ratio of a negative part to a positive part of a decomposition of the gradient in a difference of two non-negative terms, and the decomposition is obtained by back-propagation of the positive and negative parts of the decomposition of the gradient of a higher layer.