Nonparametric Regression Convex Envelope for Server Fault Detection
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Solution Overview
Problem
Conventional nonparametric functional relationship approximation techniques for fault detection in server systems are computationally intensive, require large training datasets, produce inconsistent estimates, and are numerically unstable, especially in multidimensional cases.
Innovation Solution
A method that constructs a functional relationship approximation using regression primitives in n-dimensional space, combining them to form a convex envelope through R-function operations, allowing for efficient classification of data points and anomaly detection in telemetry signals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional nonparametric techniques (artificial neural networks, kernel regression, support vector machines) are used for functional relationship approximation, then prediction accuracy can be achieved, but computational intensity increases significantly due to iterative learning algorithms
Solution Approach 1:
The patent segments the functional relationship approximation into two distinct phases: an offline training phase where the convex envelope is constructed from training data, and an online inference phase where predictions are made by evaluating the pre-computed convex envelope. This segmentation moves the computationally intensive work to the offline phase, making the online phase computationally efficient.
Solution Approach 2:
The patent performs preliminary action by pre-computing the convex envelope during the offline training phase using the training dataset. The convex envelope serves as a pre-processed structure that captures the functional relationship, eliminating the need for iterative computations during online predictions.
2Measurement precision
If conventional nonparametric techniques are used to achieve accurate predictions, then large training data sets are required, especially for multidimensional cases
Solution Approach 1:
The patent changes the parameter representation by using a convex envelope formulation with a small number of parameters (the vertices and coefficients of the envelope) instead of requiring large datasets. The convex envelope approach transforms the problem into finding a compact parametric representation that captures the essential functional relationship with fewer parameters.
3Measurement precision
If conventional nonparametric techniques are used for functional relationship approximation, then inconsistent estimates are produced due to stochastic optimization of weights
Solution Approach 1:
The patent replaces the mechanical iterative optimization process (stochastic gradient descent, weight adjustments) with a direct geometric construction of the convex envelope. This substitution eliminates the stochastic elements and iterative adjustments, providing deterministic and consistent estimates.
4Measurement precision
If conventional nonparametric techniques are used for functional relationship approximation, then careful tuning of bandwidth parameter or preprocessing of training data is required
Solution Approach 1:
The patent implements self-service by allowing the convex envelope to automatically adapt to the data characteristics without requiring manual bandwidth parameter tuning or extensive preprocessing. The convex envelope construction process inherently handles scale and distribution variations, making the method robust and easy to apply.
Data Source
AI summary
One embodiment of the present invention provides a system that constructs a functional relationship approximation from a set of data points through nonparametric regression. During operation, the system receives a training data set in an n-dimensional space. Next, the system defines a set of regression primitives in the n-dimensional space, wherein a regression primitive in the set passes through N data points in the training data set, wherein N≧n. The system then logically combines the set of regression primitives to produce a convex envelope F, such that for each point p in the n-dimensional space: (1) F(p)=0, if p is on the convex envelope; (2) F(p)<0, if p is inside the convex envelope; and (3) F(p)>0, if p is outside the convex envelope. The system next obtains the functional relationship approximation by computing an argument of the minimum of F in the n-dimensional space. The system subsequently uses the functional relationship approximation to classify data.