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A Convex Feature Learning Formulation for Latent Task Structure Discovery
Machine Learning · Submitted 18 Jun 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Empirical results on benchmark datasets show that the proposed formulation achieves good generalization and outperforms state-of-the-art multi-task learning algorithms in some cases.
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The abstract, sentence by sentence
This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a common feature space to be known apriori. In real-world applications however, it is desirable to automatically discover the groups of related tasks that share a feature space. In this paper we aim at searching the exponentially large space of all possible groups of tasks that may share a feature space. The main contribution is a convex formulation that employs a graph-based regularizer and simultaneously discovers few groups of related tasks, having close-by task parameters, as well as the feature space shared within each group. The regularizer encodes an important structure among the groups of tasks leading to an efficient algorithm for solving it: if there is no feature space under which a group of tasks has close-by task parameters, then there does not exist such a feature space for any of its supersets. An efficient active set algorithm that exploits this simplification and performs a clever search in the exponentially large space is presented. The algorithm is guaranteed to solve the proposed formulation (within some precision) in a time polynomial in the number of groups of related tasks discovered. Empirical results on benchmark datasets show that the proposed formulation achieves good generalization and outperforms state-of-the-art multi-task learning algorithms in some cases.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. | background 1.00 | 0.21 | 0.02 | hedged possibility 0.70 |
| s1 | Most of the existing methods assume the extent to which the given tasks are related or share a common feature space to be known apriori. | background 0.51 | 0.03 | 0.02 | asserted 1.00 |
| s2 | In real-world applications however, it is desirable to automatically discover the groups of related tasks that share a feature space. | gap 0.53 | 0.05 | 0.03 | asserted 0.88 |
| s3 | In this paper we aim at searching the exponentially large space of all possible groups of tasks that may share a feature space. | contribution 0.75 | 0.58 | 0.05 | asserted 0.94 |
| s4 | The main contribution is a convex formulation that employs a graph-based regularizer and simultaneously discovers few groups of related tasks, having close-by task parameters, as well as the feature space shared within each group. | contribution 1.00 | 0.93 | 0.71 | asserted 1.00 |
| s5 | The regularizer encodes an important structure among the groups of tasks leading to an efficient algorithm for solving it: if there is no feature space under which a group of tasks has close-by task parameters, then there does not exist such a feature space for any of its supersets. | method 0.86 | 0.74 | 0.07 | asserted 1.00 |
| s6 | An efficient active set algorithm that exploits this simplification and performs a clever search in the exponentially large space is presented. | method 0.82 | 0.92 | 0.07 | asserted 1.00 |
| s7 | The algorithm is guaranteed to solve the proposed formulation (within some precision) in a time polynomial in the number of groups of related tasks discovered. | method 0.49 | 0.88 | 0.10 | asserted 1.00 |
| s8 | Empirical results on benchmark datasets show that the proposed formulation achieves good generalization and outperforms state-of-the-art multi-task learning algorithms in some cases. | result 1.00 | 0.96 | 0.26 | asserted 0.98 |
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The paper
Original abstract
This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a common feature space to be known apriori. In real-world applications however, it is desirable to automatically discover the groups of related tasks that share a feature space. In this paper we aim at searching the exponentially large space of all possible groups of tasks that may share a feature space. The main contribution is a convex formulation that employs a graph-based regularizer and simultaneously discovers few groups of related tasks, having close-by task parameters, as well as the feature space shared within each group. The regularizer encodes an important structure among the groups of tasks leading to an efficient algorithm for solving it: if there is no feature space under which a group of tasks has close-by task parameters, then there does not exist such a feature space for any of its supersets. An efficient active set algorithm that exploits this simplification and performs a clever search in the exponentially large space is presented. The algorithm is guaranteed to solve the proposed formulation (within some precision) in a time polynomial in the number of groups of related tasks discovered. Empirical results on benchmark datasets show that the proposed formulation achieves good generalization and outperforms state-of-the-art multi-task learning algorithms in some cases.
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How the literature uses it
2 arXiv papers cite this in 3 sentences
Papers citing it
Uses its method or tool 1 paper
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In the case of regression tasks, we report the variance explained (VE) and the normalized mean squared error (nMSE) following previous studies [ref] , whereas the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are employed as the classification performance measurements as used in previous studies [ref] .
Multi-Task Learning with Prior Information · Results · 0.85
Uses its data or values 1 paper
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Finally, we apply MT-HAL to the benchmark Parkinson's disease dataset, which predicts disease clinical symptom scores for each patient based on biomedical voice measurements [ref] .
Multi-task Highly Adaptive Lasso · Introduction · 0.95
Compares with it 1 paper
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FedEM [ref] , DMTL [ref] , MTFL [ref] , MMTFL [ref] , MTRL [ref] , RMTL [ref] , CLMT [ref] , MKMTL [ref] .
Multi-Task Learning with Prior Information · Experiment Setup · 0.81
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