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Bayesian Efficient Multiple Kernel Learning  [PDF]
Mehmet Gonen
Computer Science , 2012,
Abstract: Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is focused on the computational efficiency issue. However, it is still not feasible to combine many kernels using existing Bayesian approaches due to their high time complexity. We propose a fully conjugate Bayesian formulation and derive a deterministic variational approximation, which allows us to combine hundreds or thousands of kernels very efficiently. We briefly explain how the proposed method can be extended for multiclass learning and semi-supervised learning. Experiments with large numbers of kernels on benchmark data sets show that our inference method is quite fast, requiring less than a minute. On one bioinformatics and three image recognition data sets, our method outperforms previously reported results with better generalization performance.
Kernel-based Distance Metric Learning in the Output Space  [PDF]
Cong Li,Michael Georgiopoulos,Georgios C. Anagnostopoulos
Computer Science , 2013, DOI: 10.1109/IJCNN.2013.6706862
Abstract: In this paper we present two related, kernel-based Distance Metric Learning (DML) methods. Their respective models non-linearly map data from their original space to an output space, and subsequent distance measurements are performed in the output space via a Mahalanobis metric. The dimensionality of the output space can be directly controlled to facilitate the learning of a low-rank metric. Both methods allow for simultaneous inference of the associated metric and the mapping to the output space, which can be used to visualize the data, when the output space is 2- or 3-dimensional. Experimental results for a collection of classification tasks illustrate the advantages of the proposed methods over other traditional and kernel-based DML approaches.
Efficient Multi-Template Learning for Structured Prediction  [PDF]
Qi Mao,Ivor W. Tsang
Computer Science , 2011,
Abstract: Conditional random field (CRF) and Structural Support Vector Machine (Structural SVM) are two state-of-the-art methods for structured prediction which captures the interdependencies among output variables. The success of these methods is attributed to the fact that their discriminative models are able to account for overlapping features on the whole input observations. These features are usually generated by applying a given set of templates on labeled data, but improper templates may lead to degraded performance. To alleviate this issue, in this paper, we propose a novel multiple template learning paradigm to learn structured prediction and the importance of each template simultaneously, so that hundreds of arbitrary templates could be added into the learning model without caution. This paradigm can be formulated as a special multiple kernel learning problem with exponential number of constraints. Then we introduce an efficient cutting plane algorithm to solve this problem in the primal, and its convergence is presented. We also evaluate the proposed learning paradigm on two widely-studied structured prediction tasks, \emph{i.e.} sequence labeling and dependency parsing. Extensive experimental results show that the proposed method outperforms CRFs and Structural SVMs due to exploiting the importance of each template. Our complexity analysis and empirical results also show that our proposed method is more efficient than OnlineMKL on very sparse and high-dimensional data. We further extend this paradigm for structured prediction using generalized $p$-block norm regularization with $p>1$, and experiments show competitive performances when $p \in [1,2)$.
Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes  [PDF]
Mauricio A. álvarez,David Luengo,Michalis K. Titsias,Neil D. Lawrence
Statistics , 2009,
Abstract: Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function over correlated output functions. One way of constructing such kernels is based on convolution processes (CP). A key problem for this approach is efficient inference. Alvarez and Lawrence (2009) recently presented a sparse approximation for CPs that enabled efficient inference. In this paper, we extend this work in two directions: we introduce the concept of variational inducing functions to handle potential non-smooth functions involved in the kernel CP construction and we consider an alternative approach to approximate inference based on variational methods, extending the work by Titsias (2009) to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.
Online Multiple Kernel Learning for Structured Prediction  [PDF]
Andre F. T. Martins,Mario A. T. Figueiredo,Pedro M. Q. Aguiar,Noah A. Smith,Eric P. Xing
Statistics , 2010,
Abstract: Despite the recent progress towards efficient multiple kernel learning (MKL), the structured output case remains an open research front. Current approaches involve repeatedly solving a batch learning problem, which makes them inadequate for large scale scenarios. We propose a new family of online proximal algorithms for MKL (as well as for group-lasso and variants thereof), which overcomes that drawback. We show regret, convergence, and generalization bounds for the proposed method. Experiments on handwriting recognition and dependency parsing testify for the successfulness of the approach.
A simple yet efficient algorithm for multiple kernel learning under elastic-net constraints  [PDF]
Luca Citi
Computer Science , 2015,
Abstract: This report presents an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights.
Efficient Evaluation of Multiple-Output Boolean Functions in Embedded Software or Firmware  [cached]
Vaclav Dvorak
Journal of Software , 2007, DOI: 10.4304/jsw.2.5.52-63
Abstract: The paper addresses software and firmware implementation of multiple-output Boolean functions based on cascades of Look-Up Tables (LUTs). A LUT cascade is described as a means of compact representation of a large class of sparse Boolean functions, evaluation of which then reduces to multiple indirect memory accesses. The method is compared to a technique of direct PLA emulation and is illustrated on examples. A specialized micro-engine is proposed for even faster evaluation than is possible with universal microprocessors. The presented method is flexible in making trade-offs between performance and memory footprint and may be useful for embedded applications where the processing speed is not critical. Evaluation may run on various CPUs and DSP cores or slightly faster on FPGA-based micro-programmed controllers.
Kernel machines with two layers and multiple kernel learning  [PDF]
Francesco Dinuzzo
Computer Science , 2010,
Abstract: In this paper, the framework of kernel machines with two layers is introduced, generalizing classical kernel methods. The new learning methodology provide a formal connection between computational architectures with multiple layers and the theme of kernel learning in standard regularization methods. First, a representer theorem for two-layer networks is presented, showing that finite linear combinations of kernels on each layer are optimal architectures whenever the corresponding functions solve suitable variational problems in reproducing kernel Hilbert spaces (RKHS). The input-output map expressed by these architectures turns out to be equivalent to a suitable single-layer kernel machines in which the kernel function is also learned from the data. Recently, the so-called multiple kernel learning methods have attracted considerable attention in the machine learning literature. In this paper, multiple kernel learning methods are shown to be specific cases of kernel machines with two layers in which the second layer is linear. Finally, a simple and effective multiple kernel learning method called RLS2 (regularized least squares with two layers) is introduced, and his performances on several learning problems are extensively analyzed. An open source MATLAB toolbox to train and validate RLS2 models with a Graphic User Interface is available.
Learning Output Kernels for Multi-Task Problems  [PDF]
Francesco Dinuzzo
Computer Science , 2013, DOI: 10.1016/j.neucom.2013.02.024
Abstract: Simultaneously solving multiple related learning tasks is beneficial under a variety of circumstances, but the prior knowledge necessary to correctly model task relationships is rarely available in practice. In this paper, we develop a novel kernel-based multi-task learning technique that automatically reveals structural inter-task relationships. Building over the framework of output kernel learning (OKL), we introduce a method that jointly learns multiple functions and a low-rank multi-task kernel by solving a non-convex regularization problem. Optimization is carried out via a block coordinate descent strategy, where each subproblem is solved using suitable conjugate gradient (CG) type iterative methods for linear operator equations. The effectiveness of the proposed approach is demonstrated on pharmacological and collaborative filtering data.
Fast Bounded Online Gradient Descent Algorithms for Scalable Kernel-Based Online Learning  [PDF]
Peilin Zhao,Jialei Wang,Pengcheng Wu,Rong Jin,Steven C. H. Hoi
Computer Science , 2012,
Abstract: Kernel-based online learning has often shown state-of-the-art performance for many online learning tasks. It, however, suffers from a major shortcoming, that is, the unbounded number of support vectors, making it non-scalable and unsuitable for applications with large-scale datasets. In this work, we study the problem of bounded kernel-based online learning that aims to constrain the number of support vectors by a predefined budget. Although several algorithms have been proposed in literature, they are neither computationally efficient due to their intensive budget maintenance strategy nor effective due to the use of simple Perceptron algorithm. To overcome these limitations, we propose a framework for bounded kernel-based online learning based on an online gradient descent approach. We propose two efficient algorithms of bounded online gradient descent (BOGD) for scalable kernel-based online learning: (i) BOGD by maintaining support vectors using uniform sampling, and (ii) BOGD++ by maintaining support vectors using non-uniform sampling. We present theoretical analysis of regret bound for both algorithms, and found promising empirical performance in terms of both efficacy and efficiency by comparing them to several well-known algorithms for bounded kernel-based online learning on large-scale datasets.
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