Noise-Contrastive Estimation for Marked Temporal Point Process Training
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Solution Overview
Problem
Existing marked temporal point process (MTPP) models face challenges in training due to the intractable likelihood function, leading to suboptimal parameterization and mode dropping issues, particularly when using Maximum Likelihood Estimation (MLE) with neural networks.
Innovation Solution
A noise-contrastive estimation (NCE) based training framework is introduced, which learns model parameters by solving a binary classification problem between true and noise samples, allowing for adaptive noise generation and sidestepping the normalizer computation, thereby alleviating the issues with MLE.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Maximum Likelihood Estimation (MLE) is used to train MTPP models, then the training process can be simplified, but the likelihood function becomes intractable to compute due to the definite integral of CIF
Solution Approach 1:
The patent extracts and removes the intractable normalizer term from the likelihood function computation. By using noise-contrastive estimation, the method only requires computing the unnormalized CIF for observed events and noise samples, eliminating the need to compute the definite integral of CIF over the entire time domain. This extraction of the problematic normalization term resolves the computational intractability while maintaining training simplicity.
Solution Approach 2:
The patent introduces noise samples as an intermediary element to approximate the likelihood computation. Instead of directly computing the intractable likelihood function, the method uses noise-contrastive estimation where noise samples serve as a mediator to approximate the normalization constant. This intermediary approach allows the training process to proceed without directly computing the difficult integral.
2Measurement precision
If MLE is used for training MTPP models, then parameter estimation can be performed, but mode dropping occurs due to asymmetric KL divergence minimization
Solution Approach 1:
The patent inverts the traditional MLE approach by using noise-contrastive estimation. Instead of directly maximizing the likelihood of observed data (which leads to asymmetric KL divergence and mode dropping), the method frames the problem as distinguishing observed events from noise samples. This inversion of the estimation paradigm transforms the asymmetric optimization into a more balanced discriminative task, reducing mode dropping and improving prediction reliability.
Solution Approach 2:
The patent changes the optimization objective from direct likelihood maximization to noise-contrastive loss minimization. By parameterizing the CIF with neural networks and training via NCE, the method alters the loss landscape from asymmetric KL divergence to a more symmetric contrastive objective. This parameter change in the optimization criterion prevents mode dropping while maintaining parameter estimation accuracy.
3Ease of manufacture
If CIF is limited to integrable functions to enable MLE training, then training becomes feasible, but the specification of CIF becomes suboptimal
Solution Approach 1:
The patent extracts the integrability constraint from the CIF specification by using noise-contrastive estimation. The method removes the requirement for CIF to be analytically integrable by approximating the likelihood through contrastive sampling. This extraction allows neural networks to parameterize CIF with arbitrary functional forms without needing to satisfy integrability conditions, greatly enhancing specification flexibility while maintaining training feasibility.
Solution Approach 2:
The patent changes the training paradigm from direct likelihood maximization requiring integrable functions to noise-contrastive estimation that works with unnormalized functions. By parameterizing CIF with neural networks and using NCE, the method transforms the problem from requiring closed-form integrable specifications to allowing flexible functional approximations. This parameter change enables sophisticated CIF specifications that would be intractable under traditional MLE.
4Device complexity
If Monte Carlo sampling is used to approximate the likelihood function, then the intractable integral can be estimated, but the marginal distribution of event time must be taken as a priori
Solution Approach 1:
The patent extracts and eliminates the need to specify the marginal distribution of event times by using noise-contrastive estimation. The method removes this a priori requirement by framing the problem as distinguishing observed events from noise samples, where the noise distribution can be chosen flexibly without constraining the data distribution. This extraction of the marginal distribution requirement enhances adaptability while maintaining computability.
Solution Approach 2:
The patent introduces noise samples as an intermediary that replaces the need for marginal distribution specification. Instead of requiring the marginal distribution of event times as a fixed a priori, the method uses noise samples drawn from a flexible distribution as a mediator to approximate the likelihood. This intermediary approach allows the marginal distribution to be learned or chosen adaptively rather than fixed beforehand.
Data Source
AI summary
Embodiments for systems and methods of sequential event prediction with noise-contrastive estimation for marked temporal point process are disclosed.