Asymmetric Hamiltonian Monte Carlo for Faster Bayesian Inference
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Solution Overview
Problem
Conventional Hamiltonian Monte Carlo (HMC) methods, which use symmetric Gaussian auxiliary distributions, face limitations in convergence speed and may not apply to asymmetric momentum distributions, leading to inefficient and slow computations in Bayesian Variational Inference.
Innovation Solution
Implementing asymmetric Hamiltonian Monte Carlo (HMC) methods with adaptive auxiliary distributions that are dynamically updated to match the target distribution, using alternating direction HMC (AD-HMC) to ensure faster and guaranteed convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If symmetric Gaussian auxiliary distributions are used in conventional HMC methods, then the computation is simpler to implement, but the convergence speed is slow and the method cannot handle asymmetric momentum distributions
Solution Approach 1:
The patent applies asymmetry by replacing the symmetric Gaussian auxiliary distribution with an asymmetric auxiliary distribution that can model asymmetric momentum distributions. This allows the HMC method to converge faster by better matching the target distribution's characteristics, directly resolving the contradiction between implementation simplicity and convergence speed.
Solution Approach 2:
The patent implements dynamics by making the auxiliary distribution adaptive through iterative updates. The auxiliary distribution is dynamically adjusted to match the target distribution's characteristics during the sampling process, enabling faster convergence while maintaining computational feasibility through automated adaptation.
2Device complexity
If conventional HMC methods are used, then the computational process is simpler, but the convergence is slow and may not guarantee convergence for complex models
Solution Approach 1:
The patent applies feedback by implementing an iterative process where the auxiliary distribution is continuously updated based on the sampling outcomes. This feedback mechanism allows the method to adapt to complex models and guarantee convergence by adjusting the auxiliary distribution to better match the target distribution's properties.
Solution Approach 2:
The patent changes parameters by iteratively updating the auxiliary distribution's parameters to match the target distribution. This parameter adaptation enables the method to handle complex models reliably by adjusting the auxiliary distribution's characteristics to converge toward the true posterior.
3Productivity
If asymmetric auxiliary distributions are used, then the convergence speed improves significantly, but the computational process becomes more complex
Solution Approach 1:
The patent applies self-service by implementing an automated adaptive process where the auxiliary distribution updates itself based on the sampling results. This self-adjusting mechanism handles the complexity internally, allowing the user to benefit from fast convergence with asymmetric distributions without manually managing the computational complexity.
Data Source
AI summary
A method of Bayesian Variational Inference using Asymmetric Hamiltonian Monte Carlo includes gathering a number of data samples for a Hamiltonian Monte Carlo computation and instantiating an auxiliary distribution on the data samples, the auxiliary distribution being asymmetric. A Hamiltonian Monte Carlo computation is performed with the auxiliary distribution and the plurality of data samples. Upon determining that a metric of the computation outcome does not meet a target metric criterion that is based on a target distribution, the auxiliary distribution is adapted to an output of the computation and the Hamiltonian Monte Carlo computation is re-executed with the adapted auxiliary distribution. A report is generated in response to determining that the target metric is well estimated.