Summary of Optimizing Cox Models with Stochastic Gradient Descent: Theoretical Foundations and Practical Guidances, by Lang Zeng et al.
Optimizing Cox Models with Stochastic Gradient Descent: Theoretical Foundations and Practical Guidances
by Lang Zeng, Weijing Tang, Zhao Ren, Ying Ding
First submitted to arxiv on: 5 Aug 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The authors of this paper investigate the computational challenges posed by optimizing Cox regression models, specifically variants that employ neural networks (Cox-NN). They focus on stochastic gradient descent (SGD), a popular optimization algorithm known for its scalability. The authors analyze the theoretical foundations of SGD in optimizing Cox partial likelihood and demonstrate that the estimator targets an objective function dependent on batch size. They establish consistency and optimal minimax convergence rate for Cox-NN, as well as consistency and asymptotic normality for Cox regression. Additionally, they quantify the impact of batch size on training and asymptotic efficiency. The authors validate their findings through numerical experiments and demonstrate the effectiveness of SGD in a real-world application where gradient descent is computationally unfeasible. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at ways to make Cox regression models work better with large amounts of data. It focuses on an algorithm called stochastic gradient descent (SGD) that helps optimize these models. The authors want to understand how well SGD works for these types of models and what factors affect its performance. They found out that the way SGD works depends on the size of the group of data it’s working with, which affects how well it optimizes the model. This is important because sometimes you need to use large groups of data to make accurate predictions. The authors tested their findings using real-world data and showed that SGD can be a useful tool for solving big-data problems. |
Keywords
» Artificial intelligence » Gradient descent » Likelihood » Objective function » Optimization » Regression » Stochastic gradient descent
