Parametric Model Causal Discovery Independence Invertibility
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Solution Overview
Problem
The existing PNL model-based causal discovery methods face challenges in precisely determining causality between data pieces due to the potential for improper function estimation and failure to satisfy the model's assumptions, especially when dealing with finite data, leading to difficulties in discerning correct causal directions.
Innovation Solution
The proposed method involves an information processing apparatus that performs parameter updates for parametric models to maximize independence between variables and includes an inverse converter to ensure the estimation of proper functions, thereby satisfying the assumptions of the PNL model and accurately determining causality by learning both independence and invertibility evaluation indices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If common model estimation methods are used for PNL model-based causal discovery, then the process is simple, but the accuracy of causal determination deteriorates due to improper function estimation and failure to satisfy model assumptions
Solution Approach 1:
The parameter update process is segmented into two distinct phases: first updating parameters to maximize independence between variables, then updating parameters to maximize invertibility of the estimated function. This segmentation allows each phase to focus on a specific assumption of the PNL model, thereby improving overall estimation accuracy without significantly increasing complexity.
Solution Approach 2:
The method performs preliminary parameter updates to maximize independence between variables before performing the final parameter updates to maximize invertibility. This preliminary action ensures that the independence assumption is satisfied first, providing a solid foundation for the subsequent invertibility optimization and improving the reliability of causal determination.
2Adaptability or versatility
If finite data is used for causal discovery, then the practical applicability is improved, but the reliability of causal determination deteriorates due to difficulty in satisfying PNL model assumptions
Solution Approach 1:
The method employs feedback mechanisms where the parameter updates are performed iteratively in two stages. The first stage updates parameters based on independence evaluation, and the second stage updates parameters based on invertibility evaluation. This feedback loop ensures that both assumptions of the PNL model are satisfied even with finite data, thereby improving reliability.
Solution Approach 2:
The method changes parameters in a specific sequence: first adjusting parameters to maximize independence between variables, then adjusting parameters to maximize invertibility of the estimated function. This parameter change strategy ensures that both independence and invertibility assumptions are satisfied, improving reliability of causal determination with finite data.
3Measurement precision
If two-stage parameter update is performed to maximize both independence and invertibility, then the accuracy of causal determination is improved, but the complexity of the estimation process increases
Solution Approach 1:
The complex parameter update process is segmented into two manageable stages: independence maximization and invertibility maximization. Each stage has a clear objective and can be implemented using standard optimization techniques, making the overall complex process more tractable and easier to implement.
Solution Approach 2:
The method merges two important requirements (independence and invertibility) into a single unified estimation framework. By combining both requirements in the parameter update process, the method achieves accurate causal determination without requiring separate independent analyses, thereby limiting the increase in complexity.
Data Source
AI summary
A non-transitory computer-readable recording medium has stored therein a program that causes a computer to execute a process, the process including: obtaining an estimation value of a third variable by subtracting a second output value of a second parametric model to which a second variable is input from a first output value of a first parametric model to which a first variable is input; performing first parameter update of updating first parameters of the first parametric model and second parameters of the second parametric model such that independence between the second variable and the estimation value of the third variable is maximized; and updating the first parameters and third parameters of a third parametric model in the first parameter update, such that a third output value of the third parametric model is approximated to the first variable, the third parametric model being input with the first output value.