Online selection of dynamic features has attracted intensive interest in recent years. However, existing online feature selection methods evaluate features individually and ignore the underlying structure of a feature stream. For instance, in image analysis, features are generated in groups which represent color, texture, and other visual information. Simply breaking the group structure in feature selection may degrade performance. Motivated by this observation, we formulate the problem as an online group feature selection. The problem assumes that features are generated individually but there are group structures in the feature stream. To the best of our knowledge, this is the first time that the correlation among streaming features has been considered in the online feature selection process. To solve this problem, we develop a novel online group feature selection method named OGFS. Our proposed approach consists of two stages: online intra-group selection and online inter-group selection. In the intra-group selection, we design a criterion based on spectral analysis to select discriminative features in each group. In the inter-group selection, we utilize a linear regression model to select an optimal subset. This two-stage procedure continues until there are no more features arriving or some predefined stopping conditions are met. Finally, we apply our method to multiple tasks including image classification and face verification. Extensive empirical studies performed on real-world and benchmark data sets demonstrate that our method outperforms other state-of-the-art online feature selection methods.
@cite_6 proposed an online algorithm for the group Lasso. The weight vector @math is updated by the arrival of a new sample. Important features corresponding to large values in @math are selected in a group manner. Thus, the algorithm is suitable for sequential samples, especially for the applications with large scale data.
@cite_6
179182636 2561368111 2739284222 2123202508
We develop a novel online learning algorithm for the group lasso in order to efficiently find the important explanatory factors in a grouped manner. Different from traditional batch-mode group lasso algorithms, which suffer from the inefficiency and poor scalability, our proposed algorithm performs in an online mode and scales well: at each iteration one can update the weight vector according to a closed-form solution based on the average of previous subgradients. Therefore, the proposed online algorithm can be very efficient and scalable. This is guaranteed by its low worst-case time complexity and memory cost both in the order of O(d), where d is the number of dimensions. Moreover, in order to achieve more sparsity in both the group level and the individual feature level, we successively extend our online system to efficiently solve a number of variants of sparse group lasso models. We also show that the online system is applicable to other group lasso models, such as the group lasso with overlap and graph lasso. Finally, we demonstrate the merits of our algorithm by experimenting with both synthetic and real-world datasets. For the AI community, the lasso proposed by Tibshirani is an important regression approach in finding explanatory predictors in high dimensional data. The coordinate descent algorithm is a standard approach to solve the lasso which iteratively updates weights of predictors in a round-robin style until convergence. However, it has high computation cost. This paper proposes Sling, a fast approach to the lasso. It achieves high efficiency by skipping unnecessary updates for the predictors whose weight is zero in the iterations. Sling can obtain high prediction accuracy with fewer predictors than the standard approach. Experiments show that Sling can enhance the efficiency and the effectiveness of the lasso. The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the l1,2 and the l1,∞ version have been studied in detail and efficient algorithms exist, there are still open questions regarding other l1,p variants. We characterize conditions for solutions of the l1,p Group-Lasso for all p-norms with 1 ≤ p ≤ ∞, and we present a unified active set algorithm. For all p-norms, a highly efficient projected gradient algorithm is presented. This new algorithm enables us to compare the prediction performance of many variants of the Group-Lasso in a multi-task learning setting, where the aim is to solve many learning problems in parallel which are coupled via the Group-Lasso constraint. We conduct large-scale experiments on synthetic data and on two real-world data sets. In accordance with theoretical characterizations of the different norms we observe that the weak-coupling norms with p between 1.5 and 2 consistently outperform the strong-coupling norms with p ≫ 2. We consider the problem of learning a coefficient vector xο ∈ RN from noisy linear observation y = Axo + ∈ Rn. In many contexts (ranging from model selection to image processing), it is desirable to construct a sparse estimator x. In this case, a popular approach consists in solving an l1-penalized least-squares problem known as the LASSO or basis pursuit denoising. For sequences of matrices A of increasing dimensions, with independent Gaussian entries, we prove that the normalized risk of the LASSO converges to a limit, and we obtain an explicit expression for this limit. Our result is the first rigorous derivation of an explicit formula for the asymptotic mean square error of the LASSO for random instances. The proof technique is based on the analysis of AMP, a recently developed efficient algorithm, that is inspired from graphical model ideas. Simulations on real data matrices suggest that our results can be relevant in a broad array of practical applications.