Separating audio mixtures into individual tracks has been a long standing challenging task. We introduce a novel unsupervised audio source separation approach based on deep adversarial learning. Specifically, our loss function adopts the Wasserstein distance which directly measures the distribution distance between the separated sources and the real sources for each individual source. Moreover, a global regularization term is added to fulfill the spectrum energy preservation property regarding separation. Unlike state-of-the-art unsupervised models which often involve deliberately devised constraints or careful model selection, our approach need little prior model specification on the data, and can be straightforwardly learned in an end-to-end fashion. We show that the proposed method performs competitively on public benchmark against state-of-the-art unsupervised methods.
These unsupervised and weakly supervised methods are built on specific and adhoc assumptions, which limit their generalization capability. Besides, these methods require expensive computation and high processing time, making them difficult to use for real-world applications. Last but not least, state-of-the-art unsupervised models, which in essence are weakly supervised models, e.g. kernel additive model (KAM) @cite_8 and OZE @cite_17 all heavily rely on a precise and correct prior knowledge on the separated sources, the deliberate constraint design and kernel selection prevent them from user-friendly. More importantly, in many real-world applications, such prior knowledge is either hard to collect or difficult to be converted to a mathematical formula.
@cite_17 @cite_8
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We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces, a common practical limiting difficulty is the necessity of computing the kernel matrix, which most frequently leads to algorithms with running time at least quadratic in the number of observations n, i.e., O(n^2). Low-rank approximations of the kernel matrix are often considered as they allow the reduction of running time complexities to O(p^2 n), where p is the rank of the approximation. The practicality of such methods thus depends on the required rank p. In this paper, we show that in the context of kernel ridge regression, for approximations based on a random subset of columns of the original kernel matrix, the rank p may be chosen to be linear in the degrees of freedom associated with the problem, a quantity which is classically used in the statistical analysis of such methods, and is often seen as the implicit number of parameters of non-parametric estimators. This result enables simple algorithms that have sub-quadratic running time complexity, but provably exhibit the same predictive performance than existing algorithms, for any given problem instance, and not only for worst-case situations. We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces, a common practi cal limiting difficulty is the necessity of computing the kernel matrix, which most frequently leads to algorithms with running time at least quadratic in the number of observations n, i.e., O(n 2 ). Low-rank approximations of the kernel matrix are often considered as they allow the reduction of running time complexities to O(p 2 n), where p is the rank of the approximation. The practicality of such methods thus depends on the required rank p. In this paper, we show that in the context of kernel ridge regression, for approximations based on a random subset of columns of the original kernel matrix, the rank p may be chosen to be linear in the degrees of freedom associated with the problem, a quantity which is classically used in the statistical analysis of such method s, and is often seen as the implicit number of parameters of non-parametric estimators. This result enables simple algorithms that have sub-quadratic running time complexity, but provably exhibit the same predictive performancethan existing algorithms, for any given problem instance, and not only for worst-case situations. Weakly supervised learning with only coarse labels can obtain visual explanations of deep neural network such as attention maps by back-propagating gradients. These attention maps are then available as priors for tasks such as object localization and semantic segmentation. In one common framework we address three shortcomings of previous approaches in modeling such attention maps: We (1) first time make attention maps an explicit and natural component of the end-to-end training, (2) provide self-guidance directly on these maps by exploring supervision form the network itself to improve them, and (3) seamlessly bridge the gap between using weak and extra supervision if available. Despite its simplicity, experiments on the semantic segmentation task demonstrate the effectiveness of our methods. We clearly surpass the state-of-the-art on Pascal VOC 2012 val. and test set. Besides, the proposed framework provides a way not only explaining the focus of the learner but also feeding back with direct guidance towards specific tasks. Under mild assumptions our method can also be understood as a plug-in to existing weakly supervised learners to improve their generalization performance. Weakly supervised learning with only coarse labels can obtain visual explanations of deep neural network such as attention maps by back-propagating gradients. These attention maps are then available as priors for tasks such as object localization and semantic segmentation. In one common framework we address three shortcomings of previous approaches in modeling such attention maps: We (1) make attention maps an explicit and natural component of the end-to-end training for the first time, (2) provide self-guidance directly on these maps by exploring supervision from the network itself to improve them, and (3) seamlessly bridge the gap between using weak and extra supervision if available. Despite its simplicity, experiments on the semantic segmentation task demonstrate the effectiveness of our methods. We clearly surpass the state-of-the-art on PASCAL VOC 2012 test and val. sets. Besides, the proposed framework provides a way not only explaining the focus of the learner but also feeding back with direct guidance towards specific tasks. Under mild assumptions our method can also be understood as a plug-in to existing weakly supervised learners to improve their generalization performance.