Learning Structural Kernels for Natural Language Processing

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting default values for kernel hyperparameters or using grid search, which is slow and coarse-grained. In contrast, Bayesian methods allow efficient model selection by maximizing the evidence on the training data through gradient-based methods. In this paper we show how to perform this in the context of structural kernels by using Gaussian Processes. Experimental results on tree kernels show that this procedure results in better prediction performance compared to hyperparameter optimization via grid search. The framework proposed in this paper can be adapted to other structures besides trees, e.g., strings and graphs, thereby extending the utility of kernel-based methods

Extending local features with contextual information in graph kernels

Graph kernels are usually defined in terms of simpler kernels over local substructures of the original graphs. Different kernels consider different types of substructures. However, in some cases they have similar predictive performances, probably because the substructures can be interpreted as approximations of the subgraphs they induce. In this paper, we propose to associate to each feature a piece of information about the context in which the feature appears in the graph. A substructure appearing in two different graphs will match only if it appears with the same context in both graphs. We propose a kernel based on this idea that considers trees as substructures, and where the contexts are features too. The kernel is inspired from the framework in [6], even if it is not part of it. We give an efficient algorithm for computing the kernel and show promising results on real-world graph classification datasets.Comment: To appear in ICONIP 201

Graph kernels between point clouds

Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. In this paper, we present extensions of graph kernels for point clouds, which allow to use kernel methods for such ob jects as shapes, line drawings, or any three-dimensional point clouds. In order to design rich and numerically efficient kernels with as few free parameters as possible, we use kernels between covariance matrices and their factorizations on graphical models. We derive polynomial time dynamic programming recursions and present applications to recognition of handwritten digits and Chinese characters from few training examples

Kernelized Hashcode Representations for Relation Extraction

Kernel methods have produced state-of-the-art results for a number of NLP tasks such as relation extraction, but suffer from poor scalability due to the high cost of computing kernel similarities between natural language structures. A recently proposed technique, kernelized locality-sensitive hashing (KLSH), can significantly reduce the computational cost, but is only applicable to classifiers operating on kNN graphs. Here we propose to use random subspaces of KLSH codes for efficiently constructing an explicit representation of NLP structures suitable for general classification methods. Further, we propose an approach for optimizing the KLSH model for classification problems by maximizing an approximation of mutual information between the KLSH codes (feature vectors) and the class labels. We evaluate the proposed approach on biomedical relation extraction datasets, and observe significant and robust improvements in accuracy w.r.t. state-of-the-art classifiers, along with drastic (orders-of-magnitude) speedup compared to conventional kernel methods.Comment: To appear in the proceedings of conference, AAAI-1

Fast Supervised Hashing with Decision Trees for High-Dimensional Data

Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the Hamming space. Non-linear hash functions have demonstrated the advantage over linear ones due to their powerful generalization capability. In the literature, kernel functions are typically used to achieve non-linearity in hashing, which achieve encouraging retrieval performance at the price of slow evaluation and training time. Here we propose to use boosted decision trees for achieving non-linearity in hashing, which are fast to train and evaluate, hence more suitable for hashing with high dimensional data. In our approach, we first propose sub-modular formulations for the hashing binary code inference problem and an efficient GraphCut based block search method for solving large-scale inference. Then we learn hash functions by training boosted decision trees to fit the binary codes. Experiments demonstrate that our proposed method significantly outperforms most state-of-the-art methods in retrieval precision and training time. Especially for high-dimensional data, our method is orders of magnitude faster than many methods in terms of training time.Comment: Appearing in Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2014, Ohio, US

Maximum Inner-Product Search using Tree Data-structures

The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently finding the best match with respect to the inner product has never been explored in the general setting to the best of our knowledge. In this paper we consider this general problem and contrast it with the existing best-match algorithms. First, we propose a general branch-and-bound algorithm using a tree data structure. Subsequently, we present a dual-tree algorithm for the case where there are multiple queries. Finally we present a new data structure for increasing the efficiency of the dual-tree algorithm. These branch-and-bound algorithms involve novel bounds suited for the purpose of best-matching with inner products. We evaluate our proposed algorithms on a variety of data sets from various applications, and exhibit up to five orders of magnitude improvement in query time over the naive search technique.Comment: Under submission in KDD 201