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A Novel Approach in Solving Stochastic Generalized Linear Regression via Nonconvex Programming

Vu Duc Anh, Tran Anh Tuan, Tran Ngoc Thang, Nguyen Thi Ngoc Anh

TL;DR

This study considers a stochastic generalized linear regression model as a stochastic problem with chance constraints and tackles it using nonconvex programming techniques and results were over 1 to 2 percent better than the ordinary logistic regression model on the same dataset.

Abstract

Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a stochastic generalized linear regression model as a stochastic problem with chance constraints and tackles it using nonconvex programming techniques. Clustering techniques and quantile estimation are also used to estimate random data's mean and variance-covariance matrix. Metrics for measuring the performance of logistic regression are used to assess the model's efficacy, including the F1 score, precision score, and recall score. The results of the proposed algorithm were over 1 to 2 percent better than the ordinary logistic regression model on the same dataset with the above assessment criteria.

A Novel Approach in Solving Stochastic Generalized Linear Regression via Nonconvex Programming

TL;DR

This study considers a stochastic generalized linear regression model as a stochastic problem with chance constraints and tackles it using nonconvex programming techniques and results were over 1 to 2 percent better than the ordinary logistic regression model on the same dataset.

Abstract

Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a stochastic generalized linear regression model as a stochastic problem with chance constraints and tackles it using nonconvex programming techniques. Clustering techniques and quantile estimation are also used to estimate random data's mean and variance-covariance matrix. Metrics for measuring the performance of logistic regression are used to assess the model's efficacy, including the F1 score, precision score, and recall score. The results of the proposed algorithm were over 1 to 2 percent better than the ordinary logistic regression model on the same dataset with the above assessment criteria.
Paper Structure (12 sections, 9 theorems, 33 equations, 6 figures, 5 tables, 3 algorithms)

This paper contains 12 sections, 9 theorems, 33 equations, 6 figures, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proposed Methodology
  4. Main Methodology
  5. The main algorithm
  6. The sample mean and variance-covariance matrix estimation
  7. The pseudocode and procedure of the main algorithm
  8. Results
  9. Data
  10. Main results
  11. Discussion
  12. Conclusion and Future Work

Key Result

Corollary 2.1

(Fenchel1953ConvexCS). Let $J$ be a convex function on $\Omega\subset\mathbb{R}^n$. The lower-level set of function $J$ is a convex set with $\forall\alpha\in\mathbb{R}$.

Figures (6)

  • Figure 1: The general architecture of proposed model.
  • Figure 2: The training process.
  • Figure 3: Accuracy score on Heart Failure Clinical Records dataset.
  • Figure 4: F1 score on Heart Failure Clinical Records dataset.
  • Figure 5: Precision score on Heart Failure Clinical Records dataset.
  • ...and 1 more figures

Theorems & Definitions (15)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Corollary 2.1
  • Theorem 2.1
  • Theorem 2.2
  • Definition 2.4
  • Theorem 2.3
  • Proposition 2.1
  • Proposition 2.2
  • ...and 5 more