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Computer-implemented systems and method train a generator and a discriminator, through machine learning, where the generator and discriminator are trained in an adversarial relationship using a simulated, multi-player game. The model parameters for the generator and the discriminator can be updated non-simultaneously. Also, the simulated, multi-player game may comprise a two-person, zero-sum game.

Computer-implemented systems and method train a generator and a discriminator, through machine learning, where the generator and discriminator are trained in an adversarial relationship using a simulated, multi-player game. The model parameters for the generator and the discriminator can be updated non-simultaneously. Also, the simulated, multi-player game may comprise a two-person, zero-sum game.

Computer-implemented systems and method train a generator and a discriminator, through machine learning, where the generator and discriminator are trained in an adversarial relationship using a simulated, multi-player game. The model parameters for the generator and the discriminator can be updated non-simultaneously. Also, the simulated, multi-player game may comprise a two-person, zero-sum game.

Computer systems and methods generate data examples by training, through machine learning, a data generator with a training objective to produce a data example for a specific value of R, where R is value related to S1(x) and S2(x), where, for a data example, x, generated by the data generator, S1(x) is a likelihood that the data example x is in a first class of a first selected data example and S2(x) is a likelihood that the data example x is in a second class of a second selected data example. S1(x) and S2(x) are determined by a discriminator that is trained through machine learning to discriminate between the first and second classes. After training the data generator, the data generator generates a synthetic data example for each of multiple specific values of R.

Computer systems and methods generate data examples by training, through machine learning, a data generator with a training objective to produce a data example for a specific value of R, where R is value related to S1(x) and S2(x), where, for a data example, x, generated by the data generator, S1(x) is a likelihood that the data example x is in a first class of a first selected data example and S2(x) is a likelihood that the data example x is in a second class of a second selected data example. S1(x) and S2(x) are determined by a discriminator that is trained through machine learning to discriminate between the first and second classes. After training the data generator, the data generator generates a synthetic data example for each of multiple specific values of R.

Computer systems and methods generate a stochastic categorical autoencoder learning network (SCAN). The SCAN is trained to have an encoder network that outputs, subject to one or more constraints, parameters for parametric probability distributions of sample random variables from input data. The parameters comprise measures of central tendency and measures of dispersion. The one or more constraints comprise a first constraint that constrains a measure of a magnitude of a vector of the measures of central tendency as compared to a measure of a magnitude of a vector of the measures of dispersion. Thereafter, the sample random variables are generated from the parameters and a decoder is trained to output the input data from the sample random variables.

Computer systems and computer-implemented methods train a machine-learning regression system. The method comprises the step of generating, with a machine-learning generator, output patterns; distorting the output patterns of the generator by a scale factor to generate distorted output patterns; and training the machine-learning regression system to predict the scaling factor, where the regression system receives the distorted output patterns as input and learns and the scaling factor is a target value for the regression system. The method may further comprise, after training the machine-learning regression system, training a second machine-learning generator by back propagating partial derivatives of an error cost function from the regression system to the second machine-learning generator and training the second machine-learning generator using stochastic gradient descent.

Machine-learning data generators use an additional objective to avoid generating data that is too similar to any previously known data example. This prevents plagiarism or simple copying of existing data examples, enhancing the ability of a generator to usefully generate novel data. A formulation of generative adversarial network (GAN) learning as the mixed strategy minimax solution of a zero-sum game solves the convergence and stability problem of GANs learning, without suffering mode collapse.