Multiclass learning with margin: exponential rates with no bias-variance trade-off
Authors: Stefano Vigogna, Giacomo Meanti, Ernesto De Vito, Lorenzo Rosasco
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This section is concerned with empircally verifying the theoretical analysis presented in Section 3. We will first consider a classification problem in which the true function satisfies the hard-margin condition (defined in (9)), and show how under optimization of a surrogate loss by gradient descent the misclassification loss decreases faster than the surrogate loss. Then we will take into account a different synthetic dataset, where the weaker soft-margin or low noise condition (see (8)) is satisfied. We will verify how the rate of change of the misclassification error with the number of data-points adheres to the theoretical rates. |
| Researcher Affiliation | Academia | 1RoMaDS, University of Rome Tor Vergata, Rome, Italy 2MLG@DIBRIS, University of Genova, Italy 3MLG@DIMA, University of Genova, Italy 4Istituto Italiano di Tecnologia, Genova, Italy 5CBMM MIT, Cambridge, MA, USA. |
| Pseudocode | No | No pseudocode or algorithm blocks (e.g., labeled 'Algorithm' or 'Pseudocode') were found in the paper. |
| Open Source Code | No | The paper does not provide any explicit statement about releasing open-source code or a link to a code repository for the described methodology. |
| Open Datasets | No | The paper uses 'synthetic, two-dimensional dataset[s]' which are generated for the experiments. While the generation process is described, no specific link, DOI, repository name, formal citation, or reference to established benchmark datasets is provided for public access to these datasets. |
| Dataset Splits | No | The paper mentions 'training points' and 'unseen data' for evaluation, but does not provide specific details on dataset splits (e.g., exact percentages, sample counts for training, validation, or test sets), nor does it reference predefined splits with citations. |
| Hardware Specification | No | No specific hardware details (e.g., exact GPU/CPU models, processor types, memory amounts, or detailed computer specifications) used for running experiments were mentioned in the paper. |
| Software Dependencies | No | The paper describes algorithms and models (e.g., 'gradient descent', 'Random Fourier features models', 'logistic loss') but does not specify any software dependencies with version numbers (e.g., 'Python 3.8', 'PyTorch 1.9'). |
| Experiment Setup | No | The paper mentions that experiments were 'repeated 20 times to obtain error bands' and 'repeated 100 times using different values of α... and an increasing number of training points'. It also notes that 'A linear model was trained on this dataset by minimizing the regularized logistic loss with gradient descent until convergence.' However, it does not provide concrete hyperparameter values such as learning rate, batch size, or specific optimizer settings. |