Latent-Space Sampling of Complex Probability Distributions
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Solution Overview
Problem
Existing methods face challenges in efficiently extracting sample data pieces that conform to complex probability distributions, particularly in high-dimensional spaces, leading to increased rejection rates and prolonged processing times.
Innovation Solution
A method utilizing a machine learning model that maps a data space to a latent space with a simpler probability distribution, employing a variational autoencoder to perform local transitions in the latent space, adjusting the proposal method based on the sampling target, and calculating adoption probabilities to improve sampling efficiency and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the pure Monte Carlo method is used to extract sample data pieces from a complex probability distribution, then the sampling process is simple, but the extraction efficiency is low and rejection rate is high
Solution Approach 1:
The patent introduces a machine learning model as an intermediary between the complex probability distribution and the sampling process. The model learns the complex distribution and uses it to generate proposals, thereby improving both sampling efficiency and accuracy without directly modifying the underlying complex distribution.
Solution Approach 2:
The patent performs preliminary training of the machine learning model on the complex probability distribution before actual sampling. This preliminary action allows the model to internalize the distribution characteristics, enabling more efficient and accurate sampling during the subsequent sampling phase.
2Productivity
If a machine learning model is introduced to improve sampling efficiency, then the sampling accuracy improves, but the device complexity increases
Solution Approach 1:
The patent transforms the complex probability distribution into a simpler form through the machine learning model's learned representation. By changing the parameterization of the distribution, the model can generate samples more efficiently while maintaining accuracy, effectively reducing the computational complexity of the sampling process.
3Adaptability or versatility
If random sampling is performed from the entire latent space, then the coverage is comprehensive, but the rejection rate increases due to poor proposal quality
Solution Approach 1:
The patent transitions from uniform random sampling across the entire latent space to local sampling around the current point. This local quality approach generates higher-quality proposals that are more likely to be accepted, thereby improving the acceptance rate while maintaining adequate coverage through sequential sampling.
Data Source
AI summary
A computer acquires first sample data included in a data space which conforms to a first probability distribution. The computer selects, by use of a machine learning model that maps the data space and a latent space which conforms to a second probability distribution to each other, a second latent representation in the latent space based on a first latent representation in the latent space. The first latent representation corresponds to the first sample data. The computer outputs, by use of the machine learning model, second sample data corresponding to the second latent representation from among sample data included in the data space.