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108
Sparse multinomial logistic regression: fast algorithms and generalization bounds
 IEEE Trans. on Pattern Analysis and Machine Intelligence
"... Abstract—Recently developed methods for learning sparse classifiers are among the stateoftheart in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsitypromoting priors encouraging the weight estimates to be either significantly larg ..."
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Cited by 190 (1 self)
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Abstract—Recently developed methods for learning sparse classifiers are among the stateoftheart in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsitypromoting priors encouraging the weight estimates to be either significantly large or exactly zero. From a learningtheoretic perspective, these methods control the capacity of the learned classifier by minimizing the number of basis functions used, resulting in better generalization. This paper presents three contributions related to learning sparse classifiers. First, we introduce a true multiclass formulation based on multinomial logistic regression. Second, by combining a bound optimization approach with a componentwise update procedure, we derive fast exact algorithms for learning sparse multiclass classifiers that scale favorably in both the number of training samples and the feature dimensionality, making them applicable even to large data sets in highdimensional feature spaces. To the best of our knowledge, these are the first algorithms to perform exact multinomial logistic regression with a sparsitypromoting prior. Third, we show how nontrivial generalization bounds can be derived for our classifier in the binary case. Experimental results on standard benchmark data sets attest to the accuracy, sparsity, and efficiency of the proposed methods.
Machine learning classifiers and fmri: A tutorial overview
 NeuroImage
, 2009
"... Interpreting brain image experiments requires analysis of complex, multivariate data. In recent years, one analysis approach that has grown in popularity is the use of machine learning algorithms to train classifiers to decode stimuli, mental states, behaviors and other variables of interest from fM ..."
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Cited by 145 (5 self)
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Interpreting brain image experiments requires analysis of complex, multivariate data. In recent years, one analysis approach that has grown in popularity is the use of machine learning algorithms to train classifiers to decode stimuli, mental states, behaviors and other variables of interest from fMRI data and thereby show the data contain enough information about them. In this tutorial overview we review some of the key choices faced in using this approach as well as how to derive statistically significant results, illustrating each point from a case study. Furthermore, we show how, in addition to answering the question of ‘is there information about a variable of interest ’ (pattern discrimination), classifiers can be used to tackle other classes of question, namely ‘where is the information ’ (pattern localization) and ‘how is that information encoded ’ (pattern characterization). 1
Importance Weighted Active Learning
"... We present a practical and statistically consistent scheme for actively learning binary classifiers under general loss functions. Our algorithm uses importance weighting to correct sampling bias, and by controlling the variance, we are able to give rigorous label complexity bounds for the learning p ..."
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Cited by 94 (9 self)
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We present a practical and statistically consistent scheme for actively learning binary classifiers under general loss functions. Our algorithm uses importance weighting to correct sampling bias, and by controlling the variance, we are able to give rigorous label complexity bounds for the learning process. 1.
An Empirical Evaluation of Thompson Sampling
"... Thompson sampling is one of oldest heuristic to address the exploration / exploitation tradeoff, but it is surprisingly unpopular in the literature. We present here some empirical results using Thompson sampling on simulated and real data, and show that it is highly competitive. And since this heur ..."
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Cited by 70 (6 self)
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Thompson sampling is one of oldest heuristic to address the exploration / exploitation tradeoff, but it is surprisingly unpopular in the literature. We present here some empirical results using Thompson sampling on simulated and real data, and show that it is highly competitive. And since this heuristic is very easy to implement, we argue that it should be part of the standard baselines to compare against. 1
PACBayesian Learning of Linear Classifiers
"... We present a general PACBayes theorem from which all known PACBayes risk bounds are obtained as particular cases. We also propose different learning algorithms for finding linear classifiers that minimize these bounds. These learning algorithms are generally competitive with both AdaBoost and the ..."
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Cited by 59 (8 self)
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We present a general PACBayes theorem from which all known PACBayes risk bounds are obtained as particular cases. We also propose different learning algorithms for finding linear classifiers that minimize these bounds. These learning algorithms are generally competitive with both AdaBoost and the SVM. 1. Intoduction For the classification problem, we are given a training set of examples—each generated according to the same (but unknown) distribution D, and the goal is to find a classifier that minimizes the true risk (i.e., the generalization error or the expected loss). Since the true risk is defined only with respect to the unknown distribution D, we are automatically confronted with the problem of specifying exactly what we should optimize on the training data to find a classifier having the smallest possible true risk. Many different specifications (of what should be optimized on the training data) have been provided by using different inductive principles but the final guarantee on the true risk, however, always comes with a socalled risk bound that holds uniformly over a set of classifiers. Hence, the formal justification of a learning strategy has always come a posteriori via a risk bound. Since a risk bound can be computed from what a classifier achieves on the training data, it automatically suggests the following optimization problem for learning algorithms: given a risk (upper) bound, find a classifier that minimizes it. Despite the enormous impact they had on our understanding of learning, the VC bounds are generally very loose. These bounds are characterized by the fact that
Learning minimum volume sets
 J. Machine Learning Res
, 2006
"... Given a probability measure P and a reference measure µ, one is often interested in the minimum µmeasure set with Pmeasure at least α. Minimum volume sets of this type summarize the regions of greatest probability mass of P, and are useful for detecting anomalies and constructing confidence region ..."
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Cited by 41 (9 self)
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Given a probability measure P and a reference measure µ, one is often interested in the minimum µmeasure set with Pmeasure at least α. Minimum volume sets of this type summarize the regions of greatest probability mass of P, and are useful for detecting anomalies and constructing confidence regions. This paper addresses the problem of estimating minimum volume sets based on independent samples distributed according to P. Other than these samples, no other information is available regarding P, but the reference measure µ is assumed to be known. We introduce rules for estimating minimum volume sets that parallel the empirical risk minimization and structural risk minimization principles in classification. As in classification, we show that the performances of our estimators are controlled by the rate of uniform convergence of empirical to true probabilities over the class from which the estimator is drawn. Thus we obtain finite sample size performance bounds in terms of VC dimension and related quantities. We also demonstrate strong universal consistency and an oracle inequality. Estimators based on histograms and dyadic partitions illustrate the proposed rules. 1
The balanced accuracy and its posterior distribution
 Pattern Recognition (ICPR), 2010 20th International Conference on
, 2010
"... Abstract—Evaluating the performance of a classification algorithm critically requires a measure of the degree to which unseen examples have been identified with their correct class labels. In practice, generalizability is frequently estimated by averaging the accuracies obtained on individual cross ..."
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Cited by 24 (4 self)
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Abstract—Evaluating the performance of a classification algorithm critically requires a measure of the degree to which unseen examples have been identified with their correct class labels. In practice, generalizability is frequently estimated by averaging the accuracies obtained on individual crossvalidation folds. This procedure, however, is problematic in two ways. First, it does not allow for the derivation of meaningful confidence intervals. Second, it leads to an optimistic estimate when a biased classifier is tested on an imbalanced dataset. We show that both problems can be overcome by replacing the conventional point estimate of accuracy by an estimate of the posterior distribution of the balanced accuracy. Keywordsclassification performance; generalizability; bias; class imbalance I.
Outlier Detection with the Kernelized Spatial Depth Function
, 2008
"... Statistical depth functions provide from the “deepest ” point a “centeroutward ordering” of multidimensional data. In this sense, depth functions can measure the “extremeness” or “outlyingness” of a data point with respect to a given data set. Hence they can detect outliers – observations that appe ..."
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Cited by 22 (4 self)
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Statistical depth functions provide from the “deepest ” point a “centeroutward ordering” of multidimensional data. In this sense, depth functions can measure the “extremeness” or “outlyingness” of a data point with respect to a given data set. Hence they can detect outliers – observations that appear extreme relative to the rest of the observations. Of the various statistical depths, the spatial depth is especially appealing because of its computational efficiency and mathematical tractability. In this article, we propose a novel statistical depth, the kernelized spatial depth (KSD), which generalizes the spatial depth via positive definite kernels. By choosing a proper kernel, the KSD can capture the local structure of a data set while the spatial depth fails. We demonstrate this by the halfmoon data and the ringshaped data. Based on the KSD, we propose a novel outlier detection algorithm, by which an observation with a depth value less than a threshold is declared as an outlier. The proposed algorithm is simple in structure: the threshold is the only one parameter for a given kernel. It applies to a oneclass learning setting, in which “normal ” observations are given as the training data, as well as to a missing label scenario where the training set consists of a mixture of normal observations and outliers with unknown labels. We give upper bounds on the false alarm probability of a depthbased detector. These upper bounds can be used to determine the threshold. We perform extensive experiments on synthetic data and data sets from real applications. The proposed outlier detector is compared with existing methods. The KSD outlier detector demonstrates competitive performance.
On Bayesian bounds
 In Proceedings of the 23rd International Conference on Machine Learning
, 2006
"... We show that several important Bayesian bounds studied in machine learning, both in the batch as well as the online setting, arise by an application of a simple compression lemma. In particular, we derive (i) PACBayesian bounds in the batch setting, (ii) Bayesian logloss bounds and (iii) Bayesian ..."
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Cited by 20 (2 self)
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We show that several important Bayesian bounds studied in machine learning, both in the batch as well as the online setting, arise by an application of a simple compression lemma. In particular, we derive (i) PACBayesian bounds in the batch setting, (ii) Bayesian logloss bounds and (iii) Bayesian boundedloss bounds in the online setting using the compression lemma. Although every setting has different semantics for prior, posterior and loss, we show that the core bound argument is the same. The paper simplifies our understanding of several important and apparently disparate results, as well as brings to light a powerful tool for developing similar arguments for other methods. 1.