Sparse Variational Gaussian Process Inference on Unit Hypersphere
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Solution Overview
Problem
Current Gaussian process (GP) models face computational bottlenecks due to the need to invert dense covariance matrices, limiting their scalability and efficiency, especially in high-dimensional data scenarios, which prevents their widespread adoption in machine learning applications.
Innovation Solution
Performing sparse variational inference on a unit hypersphere using a zonal kernel with inducing variables distributed according to a multi-dimensional Gaussian distribution and spherical harmonics, allowing for parallelized computation and reduced numerical precision, thereby overcoming the inversion bottleneck and enhancing efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exact Gaussian process regression is used to achieve accurate inference, then prediction accuracy is improved, but computational complexity increases to O(N³) due to dense matrix inversion
Solution Approach 1:
The patent segments the single dense N×N covariance matrix inversion into multiple smaller M×M matrix inversions where M << N. By introducing inducing points and factorizing the covariance matrix into low-rank components, the computational complexity is reduced from O(N³) to O(M³) while maintaining prediction accuracy through the variational inference framework.
Solution Approach 2:
The patent introduces inducing points as intermediary variables that mediate between the training data and predictions. These inducing points serve as a bridge, allowing the model to capture global patterns through a smaller set of representative points, thereby reducing the dimensionality of the covariance matrix that needs to be inverted.
2Adaptability or versatility
If the number of input dimensions increases to handle high-dimensional data, then model versatility is improved, but computational cost increases due to larger covariance matrices
Solution Approach 1:
The patent transforms the high-dimensional input space into a lower-dimensional latent space defined by the inducing points. Instead of directly processing the high-dimensional covariance matrix, the model operates in the reduced dimensionality of the inducing point space, effectively changing the dimensionality of the computational problem from N input dimensions to M inducing point dimensions where M << N.
3Reliability
If standard floating-point precision is used to maintain numerical accuracy, then inference reliability is improved, but processing speed decreases on specialized hardware
Solution Approach 1:
The patent changes the numerical precision parameter from standard floating-point (32-bit or 64-bit) to low-precision formats (8-bit or 16-bit). This parameter change enables the model to run efficiently on specialized hardware such as FPGAs and ASICs that are optimized for low-precision arithmetic, while the variational inference framework maintains sufficient numerical accuracy for practical applications.
Data Source
AI summary
A system configured to determine candidate sets of values for enforceable parameters for a physical system, and for each candidate set of values, determine a performance measurement for the physical system and generate a data point having an input portion indicative of the candidate set of values and an output portion indicative of the determined performance measurement. The system is further arranged to augment each data point to include an additional dimension comprising a bias value; project each augmented data point onto a surface of a unit hypersphere of the first number of dimensions; determine, using the projected augmented data points, a set of parameter values for a sparse variational Gaussian process, GP, on said unit hypersphere; and determine, using the sparse variational GP with the determined set of parameter values, a further set of values for the set of enforceable parameters.