Finite Rank Deep Kernel Learning for Long-Horizon 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
The implementation of finite rank deep kernel learning, which reduces computational complexity by forming a composite kernel from simpler dot kernels learned by deep neural networks, allowing for faster operation and lower resource usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If deep kernel learning is applied to large datasets, then forecasting accuracy and uncertainty quantification are improved, but computational complexity and resource requirements increase significantly
Solution Approach 1:
The patent segments the large training dataset into multiple smaller subsets, processes each subset independently to compute local kernel matrices, and then combines these local results to form the global solution. This segmentation reduces the computational complexity from O(n³) for the entire dataset to multiple O((n/k)³) operations on smaller subsets, where k is the number of subsets.
Solution Approach 2:
The patent uses low-rank approximations and Nyström methods to create simplified copies or representations of the full kernel matrix. Instead of computing and storing the complete n×n kernel matrix, it computes smaller rank-r approximations (where r << n) that capture the essential structure, reducing memory usage from O(n²) to O(nr) and computational complexity accordingly.
2Measurement precision
If deep kernel learning is applied to large datasets, then forecasting accuracy and uncertainty quantification are improved, but processing time increases significantly
Solution Approach 1:
The patent divides the training process into segments that can be processed in parallel. Multiple subsets of training data are processed simultaneously to compute their respective kernel contributions, and these computations can be distributed across multiple processors or computing nodes, significantly reducing wall-clock processing time while maintaining the ability to handle large datasets.
Solution Approach 2:
The patent performs preliminary dimensionality reduction and low-rank factorization of the kernel matrix before the main forecasting computations. By pre-computing the low-rank decomposition and storing only the essential factors, subsequent forecasting operations work with reduced-dimensional representations, dramatically speeding up prediction and uncertainty quantification tasks.
3Adaptability or versatility
If deep kernel learning is applied to large datasets, then representation power is improved, but memory usage increases significantly
Solution Approach 1:
The patent creates low-rank approximations of the kernel matrix that use significantly less memory. Instead of storing the full n×n kernel matrix requiring O(n²) memory, it stores factorized representations requiring O(nr) memory where r is the rank parameter (typically r << n). This allows the system to handle much larger datasets while maintaining the representational power needed for accurate forecasting.
Solution Approach 2:
The patent extracts and retains only the most important components of the kernel matrix through low-rank decomposition and subset-based sampling. By identifying and keeping only the dominant eigenvectors or singular vectors that capture the essential data structure, it discards redundant information that would consume memory without contributing significantly to forecasting accuracy.
Data Source
AI summary
In one embodiment a finite rank deep kernel learning method includes: receiving a training dataset; forming a plurality of training data subsets from the training dataset; for each respective training data subset of the plurality of training data subsets: calculating a subset-specific loss based on a loss function and the respective training data subset; and optimizing a model based on the subset-specific loss; determining a set of embeddings based on the optimized model; determining, based on 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.