Yuan Qi, T. Minka, Rosalind W. Picard, Zoubin Ghahramani
{"title":"Predictive automatic relevance determination by expectation propagation","authors":"Yuan Qi, T. Minka, Rosalind W. Picard, Zoubin Ghahramani","doi":"10.1145/1015330.1015418","DOIUrl":"https://doi.org/10.1145/1015330.1015418","url":null,"abstract":"In many real-world classification problems the input contains a large number of potentially irrelevant features. This paper proposes a new Bayesian framework for determining the relevance of input features. This approach extends one of the most successful Bayesian methods for feature selection and sparse learning, known as Automatic Relevance Determination (ARD). ARD finds the relevance of features by optimizing the model marginal likelihood, also known as the evidence. We show that this can lead to overfitting. To address this problem, we propose Predictive ARD based on estimating the predictive performance of the classifier. While the actual leave-one-out predictive performance is generally very costly to compute, the expectation propagation (EP) algorithm proposed by Minka provides an estimate of this predictive performance as a side-effect of its iterations. We exploit this in our algorithm to do feature selection, and to select data points in a sparse Bayesian kernel classifier. Moreover, we provide two other improvements to previous algorithms, by replacing Laplace's approximation with the generally more accurate EP, and by incorporating the fast optimization algorithm proposed by Faul and Tipping. Our experiments show that our method based on the EP estimate of predictive performance is more accurate on test data than relevance determination by optimizing the evidence.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131772998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A kernel view of the dimensionality reduction of manifolds","authors":"Jihun Ham, Daniel D. Lee, S. Mika, B. Scholkopf","doi":"10.1145/1015330.1015417","DOIUrl":"https://doi.org/10.1145/1015330.1015417","url":null,"abstract":"We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127173103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generative modeling for continuous non-linearly embedded visual inference","authors":"C. Sminchisescu, A. Jepson","doi":"10.1145/1015330.1015371","DOIUrl":"https://doi.org/10.1145/1015330.1015371","url":null,"abstract":"Many difficult visual perception problems, like 3D human motion estimation, can be formulated in terms of inference using complex generative models, defined over high-dimensional state spaces. Despite progress, optimizing such models is difficult because prior knowledge cannot be flexibly integrated in order to reshape an initially designed representation space. Nonlinearities, inherent sparsity of high-dimensional training sets, and lack of global continuity makes dimensionality reduction challenging and low-dimensional search inefficient. To address these problems, we present a learning and inference algorithm that restricts visual tracking to automatically extracted, non-linearly embedded, low-dimensional spaces. This formulation produces a layered generative model with reduced state representation, that can be estimated using efficient continuous optimization methods. Our prior flattening method allows a simple analytic treatment of low-dimensional intrinsic curvature constraints, and allows consistent interpolation operations. We analyze reduced manifolds for human interaction activities, and demonstrate that the algorithm learns continuous generative models that are useful for tracking and for the reconstruction of 3D human motion in monocular video.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124543907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Margin based feature selection - theory and algorithms","authors":"Ran Gilad-Bachrach, A. Navot, Naftali Tishby","doi":"10.1145/1015330.1015352","DOIUrl":"https://doi.org/10.1145/1015330.1015352","url":null,"abstract":"Feature selection is the task of choosing a small set out of a given set of features that capture the relevant properties of the data. In the context of supervised classification problems the relevance is determined by the given labels on the training data. A good choice of features is a key for building compact and accurate classifiers. In this paper we introduce a margin based feature selection criterion and apply it to measure the quality of sets of features. Using margins we devise novel selection algorithms for multi-class classification problems and provide theoretical generalization bound. We also study the well known Relief algorithm and show that it resembles a gradient ascent over our margin criterion. We apply our new algorithm to various datasets and show that our new Simba algorithm, which directly optimizes the margin, outperforms Relief.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121460654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric classification with polynomial MPMC cascades","authors":"S. Bohté, M. Breitenbach, G. Grudic","doi":"10.1145/1015330.1015416","DOIUrl":"https://doi.org/10.1145/1015330.1015416","url":null,"abstract":"A new class of nonparametric algorithms for high-dimensional binary classification is proposed using cascades of low dimensional polynomial structures. Construction of polynomial cascades is based on Minimax Probability Machine Classification (MPMC), which results in direct estimates of classification accuracy, and provides a simple stopping criteria that does not require expensive cross-validation measures. This Polynomial MPMC Cascade (PMC) algorithm is constructed in linear time with respect to the input space dimensionality, and linear time in the number of examples, making it a potentially attractive alternative to algorithms like support vector machines and standard MPMC. Experimental evidence is given showing that, compared to state-of-the-art classifiers, PMCs are competitive; inherently fast to compute; not prone to overfitting; and generally yield accurate estimates of the maximum error rate on unseen data.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115286950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Links between perceptrons, MLPs and SVMs","authors":"Ronan Collobert, Samy Bengio","doi":"10.1145/1015330.1015415","DOIUrl":"https://doi.org/10.1145/1015330.1015415","url":null,"abstract":"We propose to study links between three important classification algorithms: Perceptrons, Multi-Layer Perceptrons (MLPs) and Support Vector Machines (SVMs). We first study ways to control the capacity of Perceptrons (mainly regularization parameters and early stopping), using the margin idea introduced with SVMs. After showing that under simple conditions a Perceptron is equivalent to an SVM, we show it can be computationally expensive in time to train an SVM (and thus a Perceptron) with stochastic gradient descent, mainly because of the margin maximization term in the cost function. We then show that if we remove this margin maximization term, the learning rate or the use of early stopping can still control the margin. These ideas are extended afterward to the case of MLPs. Moreover, under some assumptions it also appears that MLPs are a kind of mixture of SVMs, maximizing the margin in the hidden layer space. Finally, we present a very simple MLP based on the previous findings, which yields better performances in generalization and speed than the other models.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114773274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Appice, Michelangelo Ceci, S. Rawles, Peter A. Flach
{"title":"Redundant feature elimination for multi-class problems","authors":"A. Appice, Michelangelo Ceci, S. Rawles, Peter A. Flach","doi":"10.1145/1015330.1015397","DOIUrl":"https://doi.org/10.1145/1015330.1015397","url":null,"abstract":"We consider the problem of eliminating redundant Boolean features for a given data set, where a feature is redundant if it separates the classes less well than another feature or set of features. Lavrač et al. proposed the algorithm REDUCE that works by pairwise comparison of features, i.e., it eliminates a feature if it is redundant with respect to another feature. Their algorithm operates in an ILP setting and is restricted to two-class problems. In this paper we improve their method and extend it to multiple classes. Central to our approach is the notion of a neighbourhood of examples: a set of examples of the same class where the number of different features between examples is relatively small. Redundant features are eliminated by applying a revised version of the REDUCE method to each pair of neighbourhoods of different class. We analyse the performance of our method on a range of data sets.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"76 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125999586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linearized cluster assignment via spectral ordering","authors":"C. Ding, Xiaofeng He","doi":"10.1145/1015330.1015407","DOIUrl":"https://doi.org/10.1145/1015330.1015407","url":null,"abstract":"Spectral clustering uses eigenvectors of the Laplacian of the similarity matrix. They are most conveniently applied to 2-way clustering problems. When applying to multi-way clustering, either the 2-way spectral clustering is recursively applied or an embedding to spectral space is done and some other methods are used to cluster the points. Here we propose and study a K-way cluster assignment method. The method transforms the problem to find valleys and peaks of a 1-D quantity called cluster crossing, which measures the symmetric cluster overlap across a cut point along a linear ordering of the data points. The method can either determine K clusters in one shot or recursively split a current cluster into several smaller ones. We show that a linear ordering based on a distance sensitive objective has a continuous solution which is the eigenvector of the Laplacian, showing the close relationship between clustering and ordering. The method relies on the connectivity matrix constructed as the truncated spectral expansion of the similarity matrix, useful for revealing cluster structure. The method is applied to newsgroups to illustrate introduced concepts; experiments show it outperforms the recursive 2-way clustering and the standard K-means clustering.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131668477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Surrogate maximization/minimization algorithms for AdaBoost and the logistic regression model","authors":"Zhihua Zhang, J. Kwok, D. Yeung","doi":"10.1145/1015330.1015342","DOIUrl":"https://doi.org/10.1145/1015330.1015342","url":null,"abstract":"Surrogate maximization (or minimization) (SM) algorithms are a family of algorithm that can be regarded as a generalization of expectation-maximization (EM) algorithms. There are three major approaches to the construction of surrogate function, all relying on the convexity of some function. In this paper, we solve the boosting problem by proposing SM algorithms for the corresponding optimization problem. Specifically, for AdaBoost, we derive an SM algorithm that can be shown to be identical to the algorithm proposed by Collins et al. (2002) based on Bregman distance. More importantly, for LogitBoost (or logistic boosting), we use several methods to construct different surrogate functions which result in different SM algorithms. By combining multiple methods, we are able to derive an SM algorithm that is also the same as an algorithm derived by Collins et al. (2002). Our approach based on SM algorithms is much simpler and convergence results follow naturally.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130305031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Monte Carlo analysis of ensemble classification","authors":"Roberto Esposito, L. Saitta","doi":"10.1145/1015330.1015386","DOIUrl":"https://doi.org/10.1145/1015330.1015386","url":null,"abstract":"In this paper we extend previous results providing a theoretical analysis of a new Monte Carlo ensemble classifier. The framework allows us to characterize the conditions under which the ensemble approach can be expected to outperform the single hypothesis classifier. Moreover, we provide a closed form expression for the distribution of the true ensemble accuracy, as well as of its mean and variance. We then exploit this result in order to analyze the expected error behavior in a particularly interesting case.","PeriodicalId":159792,"journal":{"name":"Proceedings of the twenty-first international conference on Machine learning","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134067849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}