Research map / Probabilistic and scientific modeling / Variational and generative sampling
One-vs-Each Approximation to Softmax for Scalable Estimation of Probabilities
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace exact softmax training with the one-vs-each lower bound | linear multiclass model · MNIST, 20news, and Bibtex | parameter norm: MNIST: 0.64 -> 0.50; 20news: 0.65 -> 0.05; Bibtex: 0.25 -> 0.09 | Helped |
| Optimize OVE using stochastic minibatches and subsampled classes | OVE linear multiclass model · MNIST, 20news, and Bibtex | parameter norm: MNIST: 0.50 -> 0.53; 20news: 0.05 -> 0.14; Bibtex: 0.09 -> 0.10 | Mixed |
| Replace exact softmax training with OVE | linear multiclass model · MNIST, 20news, and Bibtex | nlpd: MNIST: 0.271 -> 0.287; 20news: 1.263 -> 1.297; Bibtex: 2.793 -> 2.888 | Hurt |
| Replace exact softmax training with OVE-SGD | linear multiclass model · MNIST, 20news, and Bibtex | nlpd: MNIST: 0.271 -> 0.278; 20news: 1.263 -> 1.312; Bibtex: 2.793 -> 2.875 | Hurt |
| Use Bouchard's bound instead of exact softmax training | linear multiclass model · MNIST, 20news, and Bibtex | classification error: MNIST: 0.074 -> 0.073; 20news: 0.272 -> 0.249; Bibtex: 0.622 -> 0.621 | Mixed |
| Use Bouchard's bound instead of exact softmax training | linear multiclass model · MNIST, 20news, and Bibtex | nlpd: MNIST: 0.271 -> 0.333; 20news: 1.263 -> 1.337; Bibtex: 2.793 -> 2.955 | Hurt |
| Apply OVE-SGD with five sampled competing classes per update | linear multiclass model · AmazonCat-13K | classification error: 53.11% (most-populated-class error around 79%) | Helped |
| Replace OVE with Bouchard's bound | softmax likelihood lower-bound training · classification experiments | lower-bound tightness | Hurt |
| Subsample class labels as well as training instances during OVE optimization | OVE stochastic optimization · large-scale classification | scalability: 26 minutes | Helped |
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