Abstract: A system for computational estimation sampling from non-trivial probability distributions. The system comprises a processor, operating in conjunction with computer memory. The processor is configured to conduct importance sampling using normalizing flows where a base distribution has a set of parameters that can be adjusted to account for heavy-tailed distributions.

Abstract: Generative and inference machine learning models with discrete-variable latent spaces are provided. Discrete variables may be transformed by a smoothing transformation with overlapping conditional distributions or made natively reparametrizable by definition over a GUMBEL distribution. Models may be trained by sampling from different models in the positive and negative phase and/or sample with different frequency in the positive and negative phase. Machine learning models may be defined over high-dimensional quantum statistical systems near a phase transition to take advantage of long-range correlations. Machine learning models may be defined over graph-representable input spaces and use multiple spanning trees to form latent representations. Machine learning models may be relaxed via continuous proxies to support a greater range of training techniques, such as importance weighting. Example architectures for (discrete) variational autoencoders using such techniques are also provided.