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Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been difficult for these to compete with modern classification algorithms in performance and even in feature extraction. In this work, we propose a novel approach explicitly designed to address a number of subtle yet important issues which have stymied earlier DML algorithms. It maintains an explicit model of the distributions of the different classes in representation space. It then employs this knowledge to adaptively assess similarity, and achieve local discrimination by penalizing class distribution overlap. We demonstrate the effectiveness of this idea on several tasks. Our approach achieves state-of-the-art classification results on a number of fine-grained visual recognition datasets, surpassing the standard softmax classifier and outperforming triplet loss by a relative margin of 30-40%. In terms of computational performance, it alleviates training inefficiencies in the traditional triplet loss, reaching the same error in 5-30 times fewer iterations. Beyond classification, we further validate the saliency of the learnt representations via their attribute concentration and hierarchy recovery properties, achieving 10-25% relative gains on the softmax classifier and 25-50% on triplet loss in these tasks.
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In transfer learning, we wish to make inference about a target population when we have access to data both from the distribution itself, and from a different but related source distribution. We introduce a flexible framework for transfer learning in the context of binary classification, allowing for covariate-dependent relationships between the source and target distributions that are not required to preserve the Bayes decision boundary. Our main contributions are to derive the minimax optimal rates of convergence (up to poly-logarithmic factors) in this problem, and show that the optimal rate can be achieved by an algorithm that adapts to key aspects of the unknown transfer relationship, as well as the smoothness and tail parameters of our distributional classes. This optimal rate turns out to have several regimes, depending on the interplay between the relative sample sizes and the strength of the transfer relationship, and our algorithm achieves optimality by careful, decision tree-based calibration of local nearest-neighbour procedures.
Deep semi-supervised learning has been widely implemented in the real-world due to the rapid development of deep learning. Recently, attention has shifted to the approaches such as Mean-Teacher to penalize the inconsistency between two perturbed input sets. Although these methods may achieve positive results, they ignore the relationship information between data instances. To solve this problem, we propose a novel method named Metric Learning by Similarity Network (MLSN), which aims to learn a distance metric adaptively on different domains. By co-training with the classification network, similarity network can learn more information about pairwise relationships and performs better on some empirical tasks than state-of-art methods.
In this paper we present a novel adaptive deep density approximation strategy based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck equation. It is known that this equation typically has high-dimensional spatial variables posed on unbounded domains, which limit the application of traditional grid based numerical methods. With the Knothe-Rosenblatt rearrangement, our newly proposed flow-based generative model, called KRnet, provides a family of probability density functions to serve as effective solution candidates of the Fokker-Planck equation, which have weaker dependence on dimensionality than traditional computational approaches. To result in effective stochastic collocation points for training KRnet, we develop an adaptive sampling procedure, where samples are generated iteratively using KRnet at each iteration. In addition, we give a detailed discussion of KRnet and show that it can efficiently estimate general high-dimensional density functions. We present a general mathematical framework of ADDA-KR, validate its accuracy and demonstrate its efficiency with numerical experiments.
We present the Variational Adaptive Newton (VAN) method which is a black-box optimization method especially suitable for explorative-learning tasks such as active learning and reinforcement learning. Similar to Bayesian methods, VAN estimates a distribution that can be used for exploration, but requires computations that are similar to continuous optimization methods. Our theoretical contribution reveals that VAN is a second-order method that unifies existing methods in distinct fields of continuous optimization, variational inference, and evolution strategies. Our experimental results show that VAN performs well on a wide-variety of learning tasks. This work presents a general-purpose explorative-learning method that has the potential to improve learning in areas such as active learning and reinforcement learning.
Metric elicitation is a recent framework for eliciting performance metrics that best reflect implicit user preferences. This framework enables a practitioner to adjust the performance metrics based on the application, context, and population at hand. However, available elicitation strategies have been limited to linear (or fractional-linear) functions of predictive rates. In this paper, we develop an approach to elicit from a wider range of complex multiclass metrics defined by quadratic functions of rates by exploiting their local linear structure. We apply this strategy to elicit quadratic metrics for group-based fairness, and also discuss how it can be generalized to higher-order polynomials. Our elicitation strategies require only relative preference feedback and are robust to both feedback and finite sample noise.
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