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Register a new userNested Barycentric Coordinate System as an Explicit Feature Map
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We propose a new embedding method which is particularly well-suited for settings where the sample size greatly exceeds the ambient dimension. Our technique consists of partitioning the space into simplices and then embedding the data points into features corresponding to the simplices barycentric coordinates. We then train a linear classifier in the rich feature space obtained from the simplices. The decision boundary may be highly non-linear, though it is linear within each simplex (and hence piecewise-linear overall). Further, our method can approximate any convex body. We give generalization bounds based on empirical margin and a novel hybrid sample compression technique. An extensive empirical evaluation shows that our method consistently outperforms a range of popular kernel embedding methods.
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We quantify conditions that ensure that a signed measure on a Riemannian manifold has a well defined centre of mass. We then use this result to quantify the extent of a neighbourhood on which the Riemannian barycentric coordinates of a set of $n+1$ points on an $n$-manifold provide a true coordinate chart, i.e., the barycentric coordinates provide a diffeomorphism between a neighbourhood of a Euclidean simplex, and a neighbourhood containing the points on the manifold.
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem is to identify promising (explicit) features leading to a satisfactory out-of-sample performance. In this work, we tackle this problem by efficiently choosing such features from multiple kernels in a greedy fashion. Our method sequentially selects these explicit features from a set of candidate features using a correlation metric. We establish an out-of-sample error bound capturing the trade-off between the error in terms of explicit features (approximation error) and the error due to spectral properties of the best model in the Hilbert space associated to the combined kernel (spectral error). The result verifies that when the (best) underlying data model is sparse enough, i.e., the spectral error is negligible, one can control the test error with a small number of explicit features, that can scale poly-logarithmically with data. Our empirical results show that given a fixed number of explicit features, the method can achieve a lower test error with a smaller time cost, compared to the state-of-the-art in data-dependent random features.
Feature maps contain rich information about image intensity and spatial correlation. However, previous online knowledge distillation methods only utilize the class probabilities. Thus in this paper, we propose an online knowledge distillation method that transfers not only the knowledge of the class probabilities but also that of the feature map using the adversarial training framework. We train multiple networks simultaneously by employing discriminators to distinguish the feature map distributions of different networks. Each network has its corresponding discriminator which discriminates the feature map from its own as fake while classifying that of the other network as real. By training a network to fool the corresponding discriminator, it can learn the other networks feature map distribution. We show that our method performs better than the conventional direct alignment method such as L1 and is more suitable for online distillation. Also, we propose a novel cyclic learning scheme for training more than two networks together. We have applied our method to various network architectures on the classification task and discovered a significant improvement of performance especially in the case of training a pair of a small network and a large one.
In digital advertising, Click-Through Rate (CTR) and Conversion Rate (CVR) are very important metrics for evaluating ad performance. As a result, ad event prediction systems are vital and widely used for sponsored search and display advertising as well as Real-Time Bidding (RTB). In this work, we introduce an enhanced method for ad event prediction (i.e. clicks,
Studies on acquiring appropriate continuous representations of discrete objects, such as graphs and knowledge base data, have been conducted by many researchers in the field of machine learning. In this study, we introduce Nested SubSpace (NSS) arrangement, a comprehensive framework for representation learning. We show that existing embedding techniques can be regarded as special cases of the NSS arrangement. Based on the concept of the NSS arrangement, we implement a Disk-ANChor ARrangement (DANCAR), a representation learning method specialized to reproducing general graphs. Numerical experiments have shown that DANCAR has successfully embedded WordNet in ${mathbb R}^{20}$ with an F1 score of 0.993 in the reconstruction task. DANCAR is also suitable for visualization in understanding the characteristics of graphs.
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