Finite Rank Deep Kernel Learning for Time Series Forecasting
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Solution Overview
Problem
Deep kernel learning methods are computationally expensive due to their O(n^3) complexity, making them inefficient for large and complex datasets, requiring significant resources and potentially raising security concerns for sensitive data.
Innovation Solution
Finite rank deep kernel learning reduces computational complexity to O(n^2) by decomposing the kernel into a linear combination of simpler dot kernels, which are easier to learn and combine into a composite kernel, allowing for faster operation and lower resource usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If deep kernel learning is applied to forecast values with uncertainty quantification, then forecasting accuracy and uncertainty estimation are improved, but computational complexity increases to O(n^3)
Solution Approach 1:
The patent segments the single complex kernel computation into multiple simpler dot kernels. By decomposing the kernel into a linear combination of dot kernels (K(x,x') = Σ_i w_i ⟨φ_i(x), φ_i(x')⟩), the method divides the O(n^3) computation into multiple O(n^2) operations, making the system more manageable and efficient while preserving uncertainty estimation capability.
Solution Approach 2:
The patent creates a composite kernel by combining multiple dot kernels with different weightings. This composite approach (combining multiple simple kernels into a complex kernel) allows the system to maintain high uncertainty estimation accuracy while reducing individual computational burdens, analogous to composite materials combining simple components for complex performance.
2Productivity
If deep kernel learning is used on larger datasets, then forecasting capability is improved, but processing time and resource requirements increase significantly
Solution Approach 1:
The patent segments the computational workload into multiple independent dot kernel computations that can be processed more efficiently. By breaking down the single complex kernel into multiple simpler kernels, the system can process larger datasets with reduced time complexity O(n^2) per kernel, enabling scaling to bigger datasets without linearly increasing processing time.
Solution Approach 2:
The patent uses a finite rank approximation of the kernel, computing only the necessary number of dot kernels (rank r) rather than the full complexity. This partial computation approach provides sufficient forecasting capability for large datasets while avoiding the excessive computational cost of full deep kernel learning, achieving a balance between accuracy and efficiency.
3Productivity
If deep kernel learning is deployed with additional computing resources, then processing efficiency is improved, but cost and security risks increase
Solution Approach 1:
The patent segments the computational task into multiple independent dot kernels that can be distributed across available resources more efficiently. This segmentation allows better utilization of existing computing infrastructure without requiring significant additional resources, reducing both cost and security risks associated with deploying powerful centralized computing systems.
Solution Approach 2:
The patent changes the computational parameters from O(n^3) to O(n^2) by using finite rank approximation and dot kernel decomposition. This parameter change enables the system to achieve high processing efficiency with moderate computing resources, avoiding the need for expensive, resource-intensive deep kernel learning deployments.
Data Source
AI summary
Certain aspects of the present disclosure provide techniques for performing finite rank deep kernel learning. In one example, a method for performing finite rank deep kernel learning includes receiving a training dataset; forming a set of embeddings by subjecting the training data set to a deep neural network; forming, from the set of embeddings, a plurality of dot kernels; combining the plurality of dot kernels to form a composite kernel for a Gaussian process; receiving live data from an application; and predicting a plurality of values and a plurality of uncertainties associated with the plurality of values simultaneously using the composite kernel.