Sequential Binary Assignment Search for Quadratic-Time Biophysical Prediction
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Solution Overview
Problem
Evaluating all possible assignments of binary random variables in time series data, such as meal events based on blood glucose measurements, is computationally intractable due to an exponential number of possibilities, making it difficult to determine the most probable assignment efficiently.
Innovation Solution
An iterative method is employed to find the highest probability assignment by initializing a variable, generating assigned variables with different event values, and repeatedly evaluating them using a probability function until the highest probability variable is determined, utilizing parallel processing paths and machine learning models like ANNs to predict biophysical responses.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all possible assignments of binary random variables are evaluated to find the most probable assignment, then the accuracy of predicting biophysical responses is improved, but the computational complexity increases exponentially
Solution Approach 1:
The patent segments the exponential search space by organizing assignments into a systematic enumeration scheme where assignments are generated incrementally. Instead of evaluating all 2^T assignments simultaneously, the method divides the search into manageable iterations, evaluating assignments in a structured sequence that reduces computational burden while maintaining completeness.
Solution Approach 2:
The patent applies preliminary action by pre-computing and storing probabilities for individual time points and individual binary variable assignments before combining them. The probability function P(D|v1,v2,...,vT) is decomposed into components that can be calculated in advance, allowing efficient evaluation of complete assignments without recalculating from scratch each time.
2Manufacturing precision
If the number of time steps T increases in time series data, then the resolution of biophysical response prediction is improved, but the number of possible assignments increases exponentially to 2^T
Solution Approach 1:
The patent segments the exponential search space by organizing assignments into a systematic enumeration scheme where assignments are generated incrementally. Instead of evaluating all 2^T assignments simultaneously, the method divides the search into manageable iterations, evaluating assignments in a structured sequence that reduces computational burden while maintaining completeness.
Solution Approach 2:
The patent evaluates assignments in a systematic order, potentially evaluating more assignments than strictly necessary to find the maximum, but doing so in a computationally efficient manner. The method may evaluate all assignments in a reduced space or use heuristics to prune the search, accepting some redundant evaluations to achieve polynomial rather than exponential complexity.
Data Source
AI summary
A method may store time series data that includes a biophysical response over sequential time periods. An initial variable can be established having an event value corresponding to each time period. A plurality of assigned variables can be generated, each having an assigned event value corresponding to each time period with one assigned event value being different with respect those of the initial variable and the other assigned variables. The initial and assigned variables can be evaluated with a probability function to determine the variable having a highest probability of event occurrences with respect to the biophysical responses. Using the highest probability initial or assigned variable as the initial variable, generation of assigned variables and a highest probability determination can be repeated until a highest probability variable has been determined. The highest probability variable can be used to predict the biophysical response in a user. Corresponding systems are also disclosed.