Terminal Event Likelihood Estimation via Mixture Model Segmentation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Computing devices face inaccuracies in processing high-dimensional input data due to the 'curse of dimensionality,' which limits their ability to accurately compute causal effects for individual values of a treatment metric when the number of values exceeds a threshold, forcing them to cluster values into bins and compute effects only for each bin, rather than for each individual value.
Innovation Solution
Implementing a termination system that groups treatment metric values using a mixture model represented as a mixture of distributions, estimating distribution parameters and mixing proportions via an expectation-maximization algorithm, and forming a directed acyclic graph to compute accurate likelihoods of terminal events for each value by considering probabilities across all groups, rather than just the group containing the value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If computing devices cluster treatment metric values into bins to overcome the curse of dimensionality, then processing accuracy for high-dimensional data is improved, but the ability to compute causal effects for individual values is lost
Solution Approach 1:
The patent segments the treatment metric values into multiple clusters or bins, where each cluster represents a group of similar values. By computing causal effects for each cluster separately and then aggregating the results, the system maintains individual value information while managing the curse of dimensionality through structured segmentation of the high-dimensional space.
Solution Approach 2:
The patent introduces additional dimensions or layers to the computation process, such as computing causal effects at multiple levels (individual values, clusters, and aggregated levels) and combining results across these dimensions. This multi-dimensional approach allows recovery of individual value information that would be lost in simple binning.
2Measurement precision
If computing devices process all individual values of treatment metric, then accuracy for individual values is maintained, but computational complexity increases due to curse of dimensionality
Solution Approach 1:
The patent divides the computation task into segments by grouping similar treatment metric values into clusters. This segmentation reduces the number of computations required while maintaining the ability to derive individual value estimates through cluster-based inference, thereby reducing computational complexity without sacrificing individual value accuracy.
Solution Approach 2:
The patent combines computational results from multiple clusters to estimate causal effects for individual values. By merging information across clusters and using aggregation techniques, the system achieves individual value accuracy with reduced computational burden compared to processing all values individually.
3Productivity
If computing devices cluster values into bins, then computational load is reduced, but causal effect accuracy for values within bins deteriorates
Solution Approach 1:
The patent applies local quality by computing causal effects with high precision within each cluster locally, then aggregating these local results to obtain accurate estimates for individual values. Each cluster is processed with appropriate detail, and the local computations are combined to restore individual value accuracy while maintaining computational efficiency.
Solution Approach 2:
The patent performs preliminary computation of causal effects for clusters before combining results to estimate individual value effects. This preliminary action at the cluster level reduces computational load, while subsequent aggregation steps recover individual value accuracy, achieving both efficiency and precision.
Data Source
AI summary
In implementations of systems for estimating terminal event likelihood, a computing device implements a termination system to receive observed data describing values of a treatment metric and indications of a terminal event. Values of the treatment metric are grouped into groups using a mixture model that represents the treatment metric as a mixture of distributions. Parameters of a distribution are estimated for each of the groups and mixing proportions are also estimated for each of the groups. In response to receiving a user input requesting an estimate of a likelihood of the terminal event for a particular value of the treatment metric, the termination system generates an indication of the estimate of the likelihood of the terminal event for the particular value based on a distribution density at the particular value for each of the groups and a probability of including the particular value in each of the groups.