Gaussian Process State-Space Inference Without Sequential Sampling
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Solution Overview
Problem
Existing Gaussian process state-space models face inefficiencies in processing time-series data due to sequential sampling of temporal states during inference, which hinders effective optimization and calibrated uncertainty in prediction tasks.
Innovation Solution
A method that distinguishes between two types of latent variables in Gaussian process state-space models, applying variational inference to the Gaussian process part and Laplace approximation to the temporal states, allowing joint optimization without sequential sampling and assuming locally linear dynamics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If sequential sampling of temporal states is used during inference in Gaussian process state-space models, then the model can process latent variables, but the computational efficiency deteriorates and optimization becomes hindered
Solution Approach 1:
The patent segments the inference process by distinguishing between two types of latent variables (inducing outputs and temporal states) and applying different inference methods to each. Variational inference is applied to inducing outputs while Laplace approximation is applied to temporal states, avoiding the need for sequential sampling and improving computational efficiency
Solution Approach 2:
The patent changes the inference approach by transitioning from sequential sampling methods to Laplace approximation with joint optimization. This parameter change in the inference methodology eliminates the sequential dependency and improves computational productivity while maintaining model processing capability
2Measurement precision
If sequential sampling is performed during inference, then temporal states can be processed, but the optimization capability and calibrated uncertainty deteriorate
Solution Approach 1:
The patent segments the latent variables into two distinct types and applies specialized inference methods to each type. This segmentation allows for better uncertainty calibration through Laplace approximation while managing inference complexity through structured differentiation of variable types
Solution Approach 2:
The patent introduces a variational distribution as an intermediary for the inducing outputs, which mediates between the Gaussian process prior and the temporal states. This intermediary structure enables better uncertainty calibration while simplifying the overall inference process compared to direct sequential sampling
Data Source
AI summary
A device and computer-implemented method for machine learning with time-series data representing observations related to a technical system. The comprising includes: providing (the time-series data, and model parameters of a distribution over the time-series data and over a first latent variable and over a second latent variable, and variational parameters of an approximate distribution over a second latent variable, sampling a value of the second latent variable from the approximate distribution over the second latent variable, finding a value of the first latent variable depending on a density of the distribution over the time-series data and over the first latent variable and over the value of the second latent variable, determining a Hessian depending on a second order Taylor approximation of the distribution over the time-series data and the first latent variable and the value of the second latent variable evaluated at the value of the first latent variable.