Research map / Learning theory and algorithms / Matrix and tensor methods
Polynomial Networks and Factorization Machines: New Insights and Efficient Training Algorithms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| fit lambda jointly with P (instead of fixing lambda=1) in direct optimization (ablation) | polynomial ANOVA/homogeneous kernel, m=2 · diabetes | training objective | Helped |
| use the ANOVA kernel A^2 instead of homogeneous kernel H^2 for recommender systems (binary features) | FM/PN-style models · Last.fm and Movielens 1M | RMSE on test set | Helped |
| use H^3 instead of A^3 for low-budget non-linear regression | augmented-feature lifted model, m=3 · abalone, cadata, cpusmall | coefficient of determination on test set | Helped |
| augment features with a dummy feature (inhomogeneous model) instead of learning first-order weights w | A^2 models for recommender systems · Last.fm and Movielens 1M | RMSE on test set | No clear effect |
| lifted CD vs direct CD for A^2 objective (convergence speed) | A^2 model on E2006-tfidf · E2006-tfidf | convergence speed of objective | No clear effect |
| lifted CD instead of direct L-BFGS or SGD for H^2 model | H^2 model on E2006-tfidf · E2006-tfidf | objective value convergence | Helped |
Closest papers by meaning
- Multi-output Polynomial Networks and Factorization Machines (NeurIPS 2017 · similarity 0.94)
- Polynomial Optimization Methods for Matrix Factorization (AAAI 2017 · similarity 0.87)
- TMPNN: High-Order Polynomial Regression Based on Taylor Map Factorization (AAAI 2024 · similarity 0.86)
- Geometry-aware training of factorized layers in tensor Tucker format (NeurIPS 2024 · similarity 0.85)
- Implicit Regularization for Tubal Tensor Factorizations via Gradient Descent (ICML 2025 · similarity 0.85)
- Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetries (ICLR 2025 · similarity 0.84)
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