Research map / Learning theory and algorithms / Sample complexity
On the Theory of Transfer Learning: The Importance of Task Diversity
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use diverse tasks with a normalized task matrix | Multilinear representation learning · New task in the multilinear model | excess prediction error: O \left(\sqrt{\frac{dr^2}{t}} + \sqrt{\frac{r}{n}} \right) -> \tilde{O} \left(\frac{1}{\nu} \cdot \frac{dr}{n \cdot t} + | Helped |
| Recover features with the method-of-moments estimator under Gaussian design | Multilinear feature learning · Multilinear feature learning | subspace angle: \tilde{O} \left(\sqrt{\frac{1}{\nu} \frac{d r}{n t}} \right) | Helped |
| Require task diversity and common sub-Gaussian design | ERM feature learning · Multilinear feature learning | subspace angle: \tilde{O}(\frac{1}{\sqrt{\nu}} \sqrt{\frac{\max(t,d) r}{nt})} | Helped |
| Use task diversity in the general shared-representation framework | ERM for transfer learning · General transfer learning with shared representation | excess LTL risk: 1/\sqrt{\text{div}{\mathcal{F}_t}} | Helped |
| Increase diversity of the task coefficient matrix | Linear or nonlinear shared-feature regression · Squared-loss multi-task regression | task diversity: \text{div}(\mathcal{F}_t) \geq \nu | Helped |
| Use diverse task coefficients in the linear logistic model | Multi-task logistic regression · Logistic loss | task diversity: \text{div}(\mathcal{F}_t) \geq \Omega(\nu) | Helped |
| Assume the new task lies in the convex hull of training tasks | Multi-task regression with convex losses · Convex-loss regression | task diversity: \text{div}(\mathcal{F}_t) \geq \frac{1}{t} | Helped |
| Increase the number of meta-training tasks | Representation learning for transfer · Multilinear transfer learning | feature recovery error: \tilde{O} \left(\sqrt{\frac{1}{\nu} \frac{d r}{n t}} \right) | Helped |
| Use an estimated representation with subspace error δ in loaded regression | New-task linear regression · New task in the multilinear model | squared parameter prediction error: \tilde{O} \left( \delta^2 + \frac{r}{n} \right) | Hurt |
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