Finite Rank Deep Kernel Learning Linear Complexity
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Solution Overview
Problem
Deep kernel learning, a method for forecasting with uncertainty, is computationally expensive due to its O(n^3) complexity, making it inefficient for large and complex datasets, requiring significant resources and potentially raising security concerns with large-scale data processing.
Innovation Solution
Finite rank deep kernel learning reduces computational complexity by forming a composite kernel as a linear combination of simpler dot kernels, learned by a deep neural network, which captures local geometries and reduces processing requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If deep kernel learning is used to forecast values with uncertainty, then forecasting accuracy and uncertainty quantification are improved, but computational complexity increases to O(n^3)
Solution Approach 1:
The patent segments the single complex deep kernel learning computation into multiple simpler dot kernel computations. By decomposing the kernel into a sum of simpler kernels (K(x,x') = Σᵢ φᵢ(x)φᵢ(x')), each computed independently through separate deep neural networks, the computational burden is divided and reduced from cubic to linear complexity while preserving the ability to forecast with uncertainty.
2Quantity of substance
If deep kernel learning is applied to larger datasets, then forecasting capability is improved, but processing time and resource requirements increase significantly
Solution Approach 1:
The patent applies segmentation by breaking down the processing of large datasets into multiple parallel dot kernel computations. Each dot kernel is computed independently using separate deep neural networks, allowing for parallel processing that reduces overall computation time. This enables the system to handle larger datasets efficiently without the cubic time complexity penalty of traditional deep kernel learning.
Solution Approach 2:
The patent uses partial action by computing only the necessary dot kernels needed to achieve the desired forecasting accuracy. Rather than computing a single comprehensive deep kernel that would require processing all data points extensively, the system computes multiple simpler dot kernels that collectively provide the needed predictive power with reduced computational effort.
3Productivity
If more powerful computing resources are invested to handle larger datasets, then processing capability is improved, but cost and security concerns increase
Solution Approach 1:
The patent segments the computational workload into multiple independent dot kernel computations that can be distributed across fewer, less powerful computing resources. This segmentation allows the system to maintain high processing capability for large datasets without requiring a single powerful computing platform, thereby reducing costs and potential security risks associated with centralized high-power computing infrastructure.
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 dataset to a deep neural network; forming, from the set of embeddings, a plurality of dot kernels; linearly 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.