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Associative Classifier is a novel technique which is the integration of Association Rule Mining and Classification. The difficult task in building Associative Classifier model is the selection of relevant rules from a large number of class association rules (CARs). A very popular method of ordering rules for selection is based on confidence, support and antecedent size (CSA). Other methods are based on hybrid orderings in which CSA method is combined with other measures. In the present work, we study the effect of using different interestingness measures of Association rules in CAR rule ordering and selection for associative classifier. | Role of Interestingness Measures in CAR Rule Ordering for Associative
Classifier: An Empirical Approach | 2,100 |
This paper presents a framework aimed at monitoring the behavior of aircraft in a given airspace. Nominal trajectories are determined and learned using data driven methods. Standard procedures are used by air traffic controllers (ATC) to guide aircraft, ensure the safety of the airspace, and to maximize the runway occupancy. Even though standard procedures are used by ATC, the control of the aircraft remains with the pilots, leading to a large variability in the flight patterns observed. Two methods to identify typical operations and their variability from recorded radar tracks are presented. This knowledge base is then used to monitor the conformance of current operations against operations previously identified as standard. A tool called AirTrajectoryMiner is presented, aiming at monitoring the instantaneous health of the airspace, in real time. The airspace is "healthy" when all aircraft are flying according to the nominal procedures. A measure of complexity is introduced, measuring the conformance of current flight to nominal flight patterns. When an aircraft does not conform, the complexity increases as more attention from ATC is required to ensure a safe separation between aircraft. | Trajectory Clustering and an Application to Airspace Monitoring | 2,101 |
The paper deals with on-line regression settings with signals belonging to a Banach lattice. Our algorithms work in a semi-online setting where all the inputs are known in advance and outcomes are unknown and given step by step. We apply the Aggregating Algorithm to construct a prediction method whose cumulative loss over all the input vectors is comparable with the cumulative loss of any linear functional on the Banach lattice. As a by-product we get an algorithm that takes signals from an arbitrary domain. Its cumulative loss is comparable with the cumulative loss of any predictor function from Besov and Triebel-Lizorkin spaces. We describe several applications of our setting. | Aggregating Algorithm competing with Banach lattices | 2,102 |
The performance in higher secondary school education in India is a turning point in the academic lives of all students. As this academic performance is influenced by many factors, it is essential to develop predictive data mining model for students' performance so as to identify the slow learners and study the influence of the dominant factors on their academic performance. In the present investigation, a survey cum experimental methodology was adopted to generate a database and it was constructed from a primary and a secondary source. While the primary data was collected from the regular students, the secondary data was gathered from the school and office of the Chief Educational Officer (CEO). A total of 1000 datasets of the year 2006 from five different schools in three different districts of Tamilnadu were collected. The raw data was preprocessed in terms of filling up missing values, transforming values in one form into another and relevant attribute/ variable selection. As a result, we had 772 student records, which were used for CHAID prediction model construction. A set of prediction rules were extracted from CHIAD prediction model and the efficiency of the generated CHIAD prediction model was found. The accuracy of the present model was compared with other model and it has been found to be satisfactory. | A CHAID Based Performance Prediction Model in Educational Data Mining | 2,103 |
The recent increase in dimensionality of data has thrown a great challenge to the existing dimensionality reduction methods in terms of their effectiveness. Dimensionality reduction has emerged as one of the significant preprocessing steps in machine learning applications and has been effective in removing inappropriate data, increasing learning accuracy, and improving comprehensibility. Feature redundancy exercises great influence on the performance of classification process. Towards the better classification performance, this paper addresses the usefulness of truncating the highly correlated and redundant attributes. Here, an effort has been made to verify the utility of dimensionality reduction by applying LVQ (Learning Vector Quantization) method on two Benchmark datasets of 'Pima Indian Diabetic patients' and 'Lung cancer patients'. | Dimensionality Reduction: An Empirical Study on the Usability of IFE-CF
(Independent Feature Elimination- by C-Correlation and F-Correlation)
Measures | 2,104 |
A key problem in sensor networks is to decide which sensors to query when, in order to obtain the most useful information (e.g., for performing accurate prediction), subject to constraints (e.g., on power and bandwidth). In many applications the utility function is not known a priori, must be learned from data, and can even change over time. Furthermore for large sensor networks solving a centralized optimization problem to select sensors is not feasible, and thus we seek a fully distributed solution. In this paper, we present Distributed Online Greedy (DOG), an efficient, distributed algorithm for repeatedly selecting sensors online, only receiving feedback about the utility of the selected sensors. We prove very strong theoretical no-regret guarantees that apply whenever the (unknown) utility function satisfies a natural diminishing returns property called submodularity. Our algorithm has extremely low communication requirements, and scales well to large sensor deployments. We extend DOG to allow observation-dependent sensor selection. We empirically demonstrate the effectiveness of our algorithm on several real-world sensing tasks. | Online Distributed Sensor Selection | 2,105 |
Recently Kutin and Niyogi investigated several notions of algorithmic stability--a property of a learning map conceptually similar to continuity--showing that training-stability is sufficient for consistency of Empirical Risk Minimization while distribution-free CV-stability is necessary and sufficient for having finite VC-dimension. This paper concerns a phase transition in the training stability of ERM, conjectured by the same authors. Kutin and Niyogi proved that ERM on finite hypothesis spaces containing a unique risk minimizer has training stability that scales exponentially with sample size, and conjectured that the existence of multiple risk minimizers prevents even super-quadratic convergence. We prove this result for the strictly weaker notion of CV-stability, positively resolving the conjecture. | On the Stability of Empirical Risk Minimization in the Presence of
Multiple Risk Minimizers | 2,106 |
We show that matrix completion with trace-norm regularization can be significantly hurt when entries of the matrix are sampled non-uniformly. We introduce a weighted version of the trace-norm regularizer that works well also with non-uniform sampling. Our experimental results demonstrate that the weighted trace-norm regularization indeed yields significant gains on the (highly non-uniformly sampled) Netflix dataset. | Collaborative Filtering in a Non-Uniform World: Learning with the
Weighted Trace Norm | 2,107 |
We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social networks with hidden information. We give an approximation guarantee for a novel greedy algorithm and give a hardness of approximation result which matches up to constant factors. We also discuss negative results for simpler approaches and present encouraging early experimental results. | Interactive Submodular Set Cover | 2,108 |
India is a multi-lingual country where Roman script is often used alongside different Indic scripts in a text document. To develop a script specific handwritten Optical Character Recognition (OCR) system, it is therefore necessary to identify the scripts of handwritten text correctly. In this paper, we present a system, which automatically separates the scripts of handwritten words from a document, written in Bangla or Devanagri mixed with Roman scripts. In this script separation technique, we first, extract the text lines and words from document pages using a script independent Neighboring Component Analysis technique. Then we have designed a Multi Layer Perceptron (MLP) based classifier for script separation, trained with 8 different wordlevel holistic features. Two equal sized datasets, one with Bangla and Roman scripts and the other with Devanagri and Roman scripts, are prepared for the system evaluation. On respective independent text samples, word-level script identification accuracies of 99.29% and 98.43% are achieved. | Word level Script Identification from Bangla and Devanagri Handwritten
Texts mixed with Roman Script | 2,109 |
We address the problem of learning in an online, bandit setting where the learner must repeatedly select among $K$ actions, but only receives partial feedback based on its choices. We establish two new facts: First, using a new algorithm called Exp4.P, we show that it is possible to compete with the best in a set of $N$ experts with probability $1-\delta$ while incurring regret at most $O(\sqrt{KT\ln(N/\delta)})$ over $T$ time steps. The new algorithm is tested empirically in a large-scale, real-world dataset. Second, we give a new algorithm called VE that competes with a possibly infinite set of policies of VC-dimension $d$ while incurring regret at most $O(\sqrt{T(d\ln(T) + \ln (1/\delta))})$ with probability $1-\delta$. These guarantees improve on those of all previous algorithms, whether in a stochastic or adversarial environment, and bring us closer to providing supervised learning type guarantees for the contextual bandit setting. | Contextual Bandit Algorithms with Supervised Learning Guarantees | 2,110 |
We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function such as L2-squared, and modify it only via a single time-dependent parameter. Our algorithm's regret bounds are worst-case optimal, and for certain realistic classes of loss functions they are much better than existing bounds. These bounds are problem-dependent, which means they can exploit the structure of the actual problem instance. Critically, however, our algorithm does not need to know this structure in advance. Rather, we prove competitive guarantees that show the algorithm provides a bound within a constant factor of the best possible bound (of a certain functional form) in hindsight. | Adaptive Bound Optimization for Online Convex Optimization | 2,111 |
Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative semi-supervised learning. In doing so, we complement distribution-free analysis by providing an alternative framework to measure the value associated with different labeling policies and resolve the fundamental question of how much data to label and in what manner. We demonstrate our approach with both simulation studies and real world experiments using naive Bayes for text classification and MRFs and CRFs for structured prediction in NLP. | Asymptotic Analysis of Generative Semi-Supervised Learning | 2,112 |
Many popular linear classifiers, such as logistic regression, boosting, or SVM, are trained by optimizing a margin-based risk function. Traditionally, these risk functions are computed based on a labeled dataset. We develop a novel technique for estimating such risks using only unlabeled data and the marginal label distribution. We prove that the proposed risk estimator is consistent on high-dimensional datasets and demonstrate it on synthetic and real-world data. In particular, we show how the estimate is used for evaluating classifiers in transfer learning, and for training classifiers with no labeled data whatsoever. | Unsupervised Supervised Learning II: Training Margin Based Classifiers
without Labels | 2,113 |
A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polynomials. We suggest a novel principle - the Loss Rank Principle (LoRP) - for model selection in regression and classification. It is based on the loss rank, which counts how many other (fictitious) data would be fitted better. LoRP selects the model that has minimal loss rank. Unlike most penalized maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the regression functions and the loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like kNN. | Model Selection with the Loss Rank Principle | 2,114 |
Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of the estimators resolve the computation-accuracy tradeoff differently, and taken together they span a continuous spectrum of computation-accuracy tradeoff resolutions. We prove the consistency of the estimators, provide formulas for their asymptotic variance, statistical robustness, and computational complexity. We discuss experimental results in the context of Boltzmann machines and conditional random fields. The theoretical and experimental studies demonstrate the effectiveness of the estimators when the computational resources are insufficient. They also demonstrate that in some cases reduced computational complexity is associated with robustness thereby increasing statistical accuracy. | Statistical and Computational Tradeoffs in Stochastic Composite
Likelihood | 2,115 |
We present an approach to semi-supervised learning based on an exponential family characterization. Our approach generalizes previous work on coupled priors for hybrid generative/discriminative models. Our model is more flexible and natural than previous approaches. Experimental results on several data sets show that our approach also performs better in practice. | Exponential Family Hybrid Semi-Supervised Learning | 2,116 |
In recent years, predicting the user's next request in web navigation has received much attention. An information source to be used for dealing with such problem is the left information by the previous web users stored at the web access log on the web servers. Purposed systems for this problem work based on this idea that if a large number of web users request specific pages of a website on a given session, it can be concluded that these pages are satisfying similar information needs, and therefore they are conceptually related. In this study, a new clustering approach is introduced that employs logical path storing of a website pages as another parameter which is regarded as a similarity parameter and conceptual relation between web pages. The results of simulation have shown that the proposed approach is more than others precise in determining the clusters. | A New Clustering Approach based on Page's Path Similarity for Navigation
Patterns Mining | 2,117 |
Most Web page classification models typically apply the bag of words (BOW) model to represent the feature space. The original BOW representation, however, is unable to recognize semantic relationships between terms. One possible solution is to apply the topic model approach based on the Latent Dirichlet Allocation algorithm to cluster the term features into a set of latent topics. Terms assigned into the same topic are semantically related. In this paper, we propose a novel hierarchical classification method based on a topic model and by integrating additional term features from neighboring pages. Our hierarchical classification method consists of two phases: (1) feature representation by using a topic model and integrating neighboring pages, and (2) hierarchical Support Vector Machines (SVM) classification model constructed from a confusion matrix. From the experimental results, the approach of using the proposed hierarchical SVM model by integrating current page with neighboring pages via the topic model yielded the best performance with the accuracy equal to 90.33% and the F1 measure of 90.14%; an improvement of 5.12% and 5.13% over the original SVM model, respectively. | Hierarchical Web Page Classification Based on a Topic Model and
Neighboring Pages Integration | 2,118 |
We apply the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice. In the traditional setting of a countable number of experts and a finite number of outcomes, the Defensive Forecasting Algorithm is very close to the well-known Aggregating Algorithm. Not only the performance guarantees but also the predictions are the same for these two methods of fundamentally different nature. We discuss also a new setting where the experts can give advice conditional on the learner's future decision. Both the algorithms can be adapted to the new setting and give the same performance guarantees as in the traditional setting. Finally, we outline an application of defensive forecasting to a setting with several loss functions. | Supermartingales in Prediction with Expert Advice | 2,119 |
This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state-space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset. Then, distances are obtained attending to the transition matrices induced by each sequence in that state-space. This approach solves some of the usual overfitting and scalability issues of the existing semi-parametric techniques, that rely on training a model for each sequence. Empirical studies on both synthetic and real-world datasets illustrate the advantages of the proposed similarity measure for clustering sequences. | State-Space Dynamics Distance for Clustering Sequential Data | 2,120 |
In regular statistical models, the leave-one-out cross-validation is asymptotically equivalent to the Akaike information criterion. However, since many learning machines are singular statistical models, the asymptotic behavior of the cross-validation remains unknown. In previous studies, we established the singular learning theory and proposed a widely applicable information criterion, the expectation value of which is asymptotically equal to the average Bayes generalization loss. In the present paper, we theoretically compare the Bayes cross-validation loss and the widely applicable information criterion and prove two theorems. First, the Bayes cross-validation loss is asymptotically equivalent to the widely applicable information criterion as a random variable. Therefore, model selection and hyperparameter optimization using these two values are asymptotically equivalent. Second, the sum of the Bayes generalization error and the Bayes cross-validation error is asymptotically equal to $2\lambda/n$, where $\lambda$ is the real log canonical threshold and $n$ is the number of training samples. Therefore the relation between the cross-validation error and the generalization error is determined by the algebraic geometrical structure of a learning machine. We also clarify that the deviance information criteria are different from the Bayes cross-validation and the widely applicable information criterion. | Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable
Information Criterion in Singular Learning Theory | 2,121 |
We present a solution to the problem of understanding a system that produces a sequence of temporally ordered observations. Our solution is based on generating and interpreting a set of temporal decision rules. A temporal decision rule is a decision rule that can be used to predict or retrodict the value of a decision attribute, using condition attributes that are observed at times other than the decision attribute's time of observation. A rule set, consisting of a set of temporal decision rules with the same decision attribute, can be interpreted by our Temporal Investigation Method for Enregistered Record Sequences (TIMERS) to signify an instantaneous, an acausal or a possibly causal relationship between the condition attributes and the decision attribute. We show the effectiveness of our method, by describing a number of experiments with both synthetic and real temporal data. | Generation and Interpretation of Temporal Decision Rules | 2,122 |
In this work we investigate the relationship between Bregman distances and regularized Logistic Regression model. We present a detailed study of Bregman Distance minimization, a family of generalized entropy measures associated with convex functions. We convert the L1-regularized logistic regression into this more general framework and propose a primal-dual method based algorithm for learning the parameters. We pose L1-regularized logistic regression into Bregman distance minimization and then apply non-linear constrained optimization techniques to estimate the parameters of the logistic model. | Bregman Distance to L1 Regularized Logistic Regression | 2,123 |
We describe and analyze efficient algorithms for learning a linear predictor from examples when the learner can only view a few attributes of each training example. This is the case, for instance, in medical research, where each patient participating in the experiment is only willing to go through a small number of tests. Our analysis bounds the number of additional examples sufficient to compensate for the lack of full information on each training example. We demonstrate the efficiency of our algorithms by showing that when running on digit recognition data, they obtain a high prediction accuracy even when the learner gets to see only four pixels of each image. | Efficient Learning with Partially Observed Attributes | 2,124 |
We propose a novel problem formulation of learning a single task when the data are provided in different feature spaces. Each such space is called an outlook, and is assumed to contain both labeled and unlabeled data. The objective is to take advantage of the data from all the outlooks to better classify each of the outlooks. We devise an algorithm that computes optimal affine mappings from different outlooks to a target outlook by matching moments of the empirical distributions. We further derive a probabilistic interpretation of the resulting algorithm and a sample complexity bound indicating how many samples are needed to adequately find the mapping. We report the results of extensive experiments on activity recognition tasks that show the value of the proposed approach in boosting performance. | Learning from Multiple Outlooks | 2,125 |
In Bayesian machine learning, conjugate priors are popular, mostly due to mathematical convenience. In this paper, we show that there are deeper reasons for choosing a conjugate prior. Specifically, we formulate the conjugate prior in the form of Bregman divergence and show that it is the inherent geometry of conjugate priors that makes them appropriate and intuitive. This geometric interpretation allows one to view the hyperparameters of conjugate priors as the {\it effective} sample points, thus providing additional intuition. We use this geometric understanding of conjugate priors to derive the hyperparameters and expression of the prior used to couple the generative and discriminative components of a hybrid model for semi-supervised learning. | A Geometric View of Conjugate Priors | 2,126 |
In this paper, we consider the distributive queue-aware power and subband allocation design for a delay-optimal OFDMA uplink system with one base station, $K$ users and $N_F$ independent subbands. Each mobile has an uplink queue with heterogeneous packet arrivals and delay requirements. We model the problem as an infinite horizon average reward Markov Decision Problem (MDP) where the control actions are functions of the instantaneous Channel State Information (CSI) as well as the joint Queue State Information (QSI). To address the distributive requirement and the issue of exponential memory requirement and computational complexity, we approximate the subband allocation Q-factor by the sum of the per-user subband allocation Q-factor and derive a distributive online stochastic learning algorithm to estimate the per-user Q-factor and the Lagrange multipliers (LM) simultaneously and determine the control actions using an auction mechanism. We show that under the proposed auction mechanism, the distributive online learning converges almost surely (with probability 1). For illustration, we apply the proposed distributive stochastic learning framework to an application example with exponential packet size distribution. We show that the delay-optimal power control has the {\em multi-level water-filling} structure where the CSI determines the instantaneous power allocation and the QSI determines the water-level. The proposed algorithm has linear signaling overhead and computational complexity $\mathcal O(KN)$, which is desirable from an implementation perspective. | Distributive Stochastic Learning for Delay-Optimal OFDMA Power and
Subband Allocation | 2,127 |
This paper presents a method for automated healing as part of off-line automated troubleshooting. The method combines statistical learning with constraint optimization. The automated healing aims at locally optimizing radio resource management (RRM) or system parameters of cells with poor performance in an iterative manner. The statistical learning processes the data using Logistic Regression (LR) to extract closed form (functional) relations between Key Performance Indicators (KPIs) and Radio Resource Management (RRM) parameters. These functional relations are then processed by an optimization engine which proposes new parameter values. The advantage of the proposed formulation is the small number of iterations required by the automated healing method to converge, making it suitable for off-line implementation. The proposed method is applied to heal an Inter-Cell Interference Coordination (ICIC) process in a 3G Long Term Evolution (LTE) network which is based on soft-frequency reuse scheme. Numerical simulations illustrate the benefits of the proposed approach. | Statistical Learning in Automated Troubleshooting: Application to LTE
Interference Mitigation | 2,128 |
Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we focus our attention on the complex gaussian kernel and its possible application in the complex Kernel LMS algorithm. In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), we employ the powerful tool of Wirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, the notion of Writinger's calculus is extended to include complex RKHSs. Experiments verify that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities. | The Complex Gaussian Kernel LMS algorithm | 2,129 |
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. However, so far, the emphasis has been on batch techniques. It is only recently, that online adaptive techniques have been considered in the context of signal processing tasks. To the best of our knowledge, no kernel-based strategy has been developed, so far, that is able to deal with complex valued signals. In this paper, we take advantage of a technique called complexification of real RKHSs to attack this problem. In order to derive gradients and subgradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool ofWirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, in this paper, the notion of Writinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS can be used to derive nonlinear stable algorithms, which offer significant performance improvements over the traditional complex LMS orWidely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities. | Extension of Wirtinger Calculus in RKH Spaces and the Complex Kernel LMS | 2,130 |
Semi-supervised support vector machines (S3VMs) are a kind of popular approaches which try to improve learning performance by exploiting unlabeled data. Though S3VMs have been found helpful in many situations, they may degenerate performance and the resultant generalization ability may be even worse than using the labeled data only. In this paper, we try to reduce the chance of performance degeneration of S3VMs. Our basic idea is that, rather than exploiting all unlabeled data, the unlabeled instances should be selected such that only the ones which are very likely to be helpful are exploited, while some highly risky unlabeled instances are avoided. We propose the S3VM-\emph{us} method by using hierarchical clustering to select the unlabeled instances. Experiments on a broad range of data sets over eighty-eight different settings show that the chance of performance degeneration of S3VM-\emph{us} is much smaller than that of existing S3VMs. | Improving Semi-Supervised Support Vector Machines Through Unlabeled
Instances Selection | 2,131 |
We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds. | Prediction with Expert Advice under Discounted Loss | 2,132 |
In this paper, we formulate a novel problem for finding blackhole and volcano patterns in a large directed graph. Specifically, a blackhole pattern is a group which is made of a set of nodes in a way such that there are only inlinks to this group from the rest nodes in the graph. In contrast, a volcano pattern is a group which only has outlinks to the rest nodes in the graph. Both patterns can be observed in real world. For instance, in a trading network, a blackhole pattern may represent a group of traders who are manipulating the market. In the paper, we first prove that the blackhole mining problem is a dual problem of finding volcanoes. Therefore, we focus on finding the blackhole patterns. Along this line, we design two pruning schemes to guide the blackhole finding process. In the first pruning scheme, we strategically prune the search space based on a set of pattern-size-independent pruning rules and develop an iBlackhole algorithm. The second pruning scheme follows a divide-and-conquer strategy to further exploit the pruning results from the first pruning scheme. Indeed, a target directed graphs can be divided into several disconnected subgraphs by the first pruning scheme, and thus the blackhole finding can be conducted in each disconnected subgraph rather than in a large graph. Based on these two pruning schemes, we also develop an iBlackhole-DC algorithm. Finally, experimental results on real-world data show that the iBlackhole-DC algorithm can be several orders of magnitude faster than the iBlackhole algorithm, which has a huge computational advantage over a brute-force method. | Detecting Blackholes and Volcanoes in Directed Networks | 2,133 |
We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work. | Robustness and Generalization | 2,134 |
We study online learning when individual instances are corrupted by adversarially chosen random noise. We assume the noise distribution is unknown, and may change over time with no restriction other than having zero mean and bounded variance. Our technique relies on a family of unbiased estimators for non-linear functions, which may be of independent interest. We show that a variant of online gradient descent can learn functions in any dot-product (e.g., polynomial) or Gaussian kernel space with any analytic convex loss function. Our variant uses randomized estimates that need to query a random number of noisy copies of each instance, where with high probability this number is upper bounded by a constant. Allowing such multiple queries cannot be avoided: Indeed, we show that online learning is in general impossible when only one noisy copy of each instance can be accessed. | Online Learning of Noisy Data with Kernels | 2,135 |
We consider the question of the stability of evolutionary algorithms to gradual changes, or drift, in the target concept. We define an algorithm to be resistant to drift if, for some inverse polynomial drift rate in the target function, it converges to accuracy 1 -- \epsilon , with polynomial resources, and then stays within that accuracy indefinitely, except with probability \epsilon , at any one time. We show that every evolution algorithm, in the sense of Valiant (2007; 2009), can be converted using the Correlational Query technique of Feldman (2008), into such a drift resistant algorithm. For certain evolutionary algorithms, such as for Boolean conjunctions, we give bounds on the rates of drift that they can resist. We develop some new evolution algorithms that are resistant to significant drift. In particular, we give an algorithm for evolving linear separators over the spherically symmetric distribution that is resistant to a drift rate of O(\epsilon /n), and another algorithm over the more general product normal distributions that resists a smaller drift rate. The above translation result can be also interpreted as one on the robustness of the notion of evolvability itself under changes of definition. As a second result in that direction we show that every evolution algorithm can be converted to a quasi-monotonic one that can evolve from any starting point without the performance ever dipping significantly below that of the starting point. This permits the somewhat unnatural feature of arbitrary performance degradations to be removed from several known robustness translations. | Evolution with Drifting Targets | 2,136 |
We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the \emph{zero-one} loss function. Unlike most previous formulations which rely on surrogate convex loss functions (e.g. hinge-loss in SVM and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural zero-one loss function. The proposed algorithm can learn kernel-based halfspaces in worst-case time $\poly(\exp(L\log(L/\epsilon)))$, for $\emph{any}$ distribution, where $L$ is a Lipschitz constant (which can be thought of as the reciprocal of the margin), and the learned classifier is worse than the optimal halfspace by at most $\epsilon$. We also prove a hardness result, showing that under a certain cryptographic assumption, no algorithm can learn kernel-based halfspaces in time polynomial in $L$. | Learning Kernel-Based Halfspaces with the Zero-One Loss | 2,137 |
This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still can give clustering results, thus providing a theoretical support for many works, e.g., Xu et al. [1] and Kim et al. [2], that show the superiority of the standard NMF as a clustering method. | On the clustering aspect of nonnegative matrix factorization | 2,138 |
The sample complexity of active learning under the realizability assumption has been well-studied. The realizability assumption, however, rarely holds in practice. In this paper, we theoretically characterize the sample complexity of active learning in the non-realizable case under multi-view setting. We prove that, with unbounded Tsybakov noise, the sample complexity of multi-view active learning can be $\widetilde{O}(\log\frac{1}{\epsilon})$, contrasting to single-view setting where the polynomial improvement is the best possible achievement. We also prove that in general multi-view setting the sample complexity of active learning with unbounded Tsybakov noise is $\widetilde{O}(\frac{1}{\epsilon})$, where the order of $1/\epsilon$ is independent of the parameter in Tsybakov noise, contrasting to previous polynomial bounds where the order of $1/\epsilon$ is related to the parameter in Tsybakov noise. | Multi-View Active Learning in the Non-Realizable Case | 2,139 |
In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the NormalHedge bound, which mainly depends on the effective number of experts and also weakly depends on the nominal one, we obtain a bound that does not contain the nominal number of experts at all. We use the defensive forecasting method and introduce an application of defensive forecasting to multivalued supermartingales. | Prediction with Advice of Unknown Number of Experts | 2,140 |
Exchangeable random variables form an important and well-studied generalization of i.i.d. variables, however simple examples show that no nontrivial concept or function classes are PAC learnable under general exchangeable data inputs $X_1,X_2,\ldots$. Inspired by the work of Berti and Rigo on a Glivenko--Cantelli theorem for exchangeable inputs, we propose a new paradigm, adequate for learning from exchangeable data: predictive PAC learnability. A learning rule $\mathcal L$ for a function class $\mathscr F$ is predictive PAC if for every $\e,\delta>0$ and each function $f\in {\mathscr F}$, whenever $\abs{\sigma}\geq s(\delta,\e)$, we have with confidence $1-\delta$ that the expected difference between $f(X_{n+1})$ and the image of $f\vert\sigma$ under $\mathcal L$ does not exceed $\e$ conditionally on $X_1,X_2,\ldots,X_n$. Thus, instead of learning the function $f$ as such, we are learning to a given accuracy $\e$ the predictive behaviour of $f$ at the future points $X_i(\omega)$, $i>n$ of the sample path. Using de Finetti's theorem, we show that if a universally separable function class $\mathscr F$ is distribution-free PAC learnable under i.i.d. inputs, then it is distribution-free predictive PAC learnable under exchangeable inputs, with a slightly worse sample complexity. | Predictive PAC learnability: a paradigm for learning from exchangeable
input data | 2,141 |
The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. | Regression on fixed-rank positive semidefinite matrices: a Riemannian
approach | 2,142 |
In dyadic prediction, labels must be predicted for pairs (dyads) whose members possess unique identifiers and, sometimes, additional features called side-information. Special cases of this problem include collaborative filtering and link prediction. We present the first model for dyadic prediction that satisfies several important desiderata: (i) labels may be ordinal or nominal, (ii) side-information can be easily exploited if present, (iii) with or without side-information, latent features are inferred for dyad members, (iv) it is resistant to sample-selection bias, (v) it can learn well-calibrated probabilities, and (vi) it can scale to very large datasets. To our knowledge, no existing method satisfies all the above criteria. In particular, many methods assume that the labels are ordinal and ignore side-information when it is present. Experimental results show that the new method is competitive with state-of-the-art methods for the special cases of collaborative filtering and link prediction, and that it makes accurate predictions on nominal data. | Dyadic Prediction Using a Latent Feature Log-Linear Model | 2,143 |
We present and analyze an agnostic active learning algorithm that works without keeping a version space. This is unlike all previous approaches where a restricted set of candidate hypotheses is maintained throughout learning, and only hypotheses from this set are ever returned. By avoiding this version space approach, our algorithm sheds the computational burden and brittleness associated with maintaining version spaces, yet still allows for substantial improvements over supervised learning for classification. | Agnostic Active Learning Without Constraints | 2,144 |
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space. However, so far, the emphasis has been on batch techniques. It is only recently, that online techniques have been considered in the context of adaptive signal processing tasks. Moreover, these efforts have only been focussed on real valued data sequences. To the best of our knowledge, no adaptive kernel-based strategy has been developed, so far, for complex valued signals. Furthermore, although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications that deal with complex signals, with Communications being a typical example. In this paper, we present a general framework to attack the problem of adaptive filtering of complex signals, using either real reproducing kernels, taking advantage of a technique called \textit{complexification} of real RKHSs, or complex reproducing kernels, highlighting the use of the complex gaussian kernel. In order to derive gradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool of Wirtinger's Calculus, which has recently attracted attention in the signal processing community. To this end, in this paper, the notion of Wirtinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS offers significant performance improvements over several linear and nonlinear algorithms, when dealing with nonlinearities. | Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces
and the Complex Kernel LMS | 2,145 |
This paper studies the MINLIP estimator for the identification of Wiener systems consisting of a sequence of a linear FIR dynamical model, and a monotonically increasing (or decreasing) static function. Given $T$ observations, this algorithm boils down to solving a convex quadratic program with $O(T)$ variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control. The resulting estimates of the linear submodel are found to be almost consistent when no noise is present in the data, under a condition of smoothness of the true nonlinearity and local Persistency of Excitation (local PE) of the data. This result is novel as it does not rely on classical tools as a 'linearization' using a Taylor decomposition, nor exploits stochastic properties of the data. It is indicated how to extend the method to cope with noisy data, and empirical evidence contrasts performance of the estimator against other recently proposed techniques. | MINLIP for the Identification of Monotone Wiener Systems | 2,146 |
In response to a 1997 problem of M. Vidyasagar, we state a necessary and sufficient condition for distribution-free PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain $\Omega$. Clearly, finiteness of the classical Vapnik-Chervonenkis dimension of $\mathscr C$ is a sufficient, but no longer necessary, condition. Besides, learnability of $\mathscr C$ under non-atomic measures does not imply the uniform Glivenko-Cantelli property with regard to non-atomic measures. Our learnability criterion is stated in terms of a combinatorial parameter $\VC({\mathscr C}\,{\mathrm{mod}}\,\omega_1)$ which we call the VC dimension of $\mathscr C$ modulo countable sets. The new parameter is obtained by ``thickening up'' single points in the definition of VC dimension to uncountable ``clusters''. Equivalently, $\VC(\mathscr C\modd\omega_1)\leq d$ if and only if every countable subclass of $\mathscr C$ has VC dimension $\leq d$ outside a countable subset of $\Omega$. The new parameter can be also expressed as the classical VC dimension of $\mathscr C$ calculated on a suitable subset of a compactification of $\Omega$. We do not make any measurability assumptions on $\mathscr C$, assuming instead the validity of Martin's Axiom (MA). | PAC learnability of a concept class under non-atomic measures: a problem
by Vidyasagar | 2,147 |
We present a new latent-variable model employing a Gaussian mixture integrated with a feature selection procedure (the Bernoulli part of the model) which together form a "Latent Bernoulli-Gauss" distribution. The model is applied to MAP estimation, clustering, feature selection and collaborative filtering and fares favorably with the state-of-the-art latent-variable models. | The Latent Bernoulli-Gauss Model for Data Analysis | 2,148 |
We address in this paper the problem of multi-channel signal sequence labeling. In particular, we consider the problem where the signals are contaminated by noise or may present some dephasing with respect to their labels. For that, we propose to jointly learn a SVM sample classifier with a temporal filtering of the channels. This will lead to a large margin filtering that is adapted to the specificity of each channel (noise and time-lag). We derive algorithms to solve the optimization problem and we discuss different filter regularizations for automated scaling or selection of channels. Our approach is tested on a non-linear toy example and on a BCI dataset. Results show that the classification performance on these problems can be improved by learning a large margin filtering. | Filtrage vaste marge pour l'étiquetage séquentiel à noyaux de
signaux | 2,149 |
We show that the learning sample complexity of a sigmoidal neural network constructed by Sontag (1992) required to achieve a given misclassification error under a fixed purely atomic distribution can grow arbitrarily fast: for any prescribed rate of growth there is an input distribution having this rate as the sample complexity, and the bound is asymptotically tight. The rate can be superexponential, a non-recursive function, etc. We further observe that Sontag's ANN is not Glivenko-Cantelli under any input distribution having a non-atomic part. | A note on sample complexity of learning binary output neural networks
under fixed input distributions | 2,150 |
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains. | Reinforcement Learning via AIXI Approximation | 2,151 |
Search engines today present results that are often oblivious to abrupt shifts in intent. For example, the query `independence day' usually refers to a US holiday, but the intent of this query abruptly changed during the release of a major film by that name. While no studies exactly quantify the magnitude of intent-shifting traffic, studies suggest that news events, seasonal topics, pop culture, etc account for 50% of all search queries. This paper shows that the signals a search engine receives can be used to both determine that a shift in intent has happened, as well as find a result that is now more relevant. We present a meta-algorithm that marries a classifier with a bandit algorithm to achieve regret that depends logarithmically on the number of query impressions, under certain assumptions. We provide strong evidence that this regret is close to the best achievable. Finally, via a series of experiments, we demonstrate that our algorithm outperforms prior approaches, particularly as the amount of intent-shifting traffic increases. | Adapting to the Shifting Intent of Search Queries | 2,152 |
Recently, applying the novel data mining techniques for evaluating enterprise financial distress has received much research alternation. Support Vector Machine (SVM) and back propagation neural (BPN) network has been applied successfully in many areas with excellent generalization results, such as rule extraction, classification and evaluation. In this paper, a model based on SVM with Gaussian RBF kernel is proposed here for enterprise financial distress evaluation. BPN network is considered one of the simplest and are most general methods used for supervised training of multilayered neural network. The comparative results show that through the difference between the performance measures is marginal; SVM gives higher precision and lower error rates. | Comparison of Support Vector Machine and Back Propagation Neural Network
in Evaluating the Enterprise Financial Distress | 2,153 |
Most image-search approaches today are based on the text based tags associated with the images which are mostly human generated and are subject to various kinds of errors. The results of a query to the image database thus can often be misleading and may not satisfy the requirements of the user. In this work we propose our approach to automate this tagging process of images, where image results generated can be fine filtered based on a probabilistic tagging mechanism. We implement a tool which helps to automate the tagging process by maintaining a training database, wherein the system is trained to identify certain set of input images, the results generated from which are used to create a probabilistic tagging mechanism. Given a certain set of segments in an image it calculates the probability of presence of particular keywords. This probability table is further used to generate the candidate tags for input images. | Close Clustering Based Automated Color Image Annotation | 2,154 |
We present a framework for discriminative sequence classification where the learner works directly in the high dimensional predictor space of all subsequences in the training set. This is possible by employing a new coordinate-descent algorithm coupled with bounding the magnitude of the gradient for selecting discriminative subsequences fast. We characterize the loss functions for which our generic learning algorithm can be applied and present concrete implementations for logistic regression (binomial log-likelihood loss) and support vector machines (squared hinge loss). Application of our algorithm to protein remote homology detection and remote fold recognition results in performance comparable to that of state-of-the-art methods (e.g., kernel support vector machines). Unlike state-of-the-art classifiers, the resulting classification models are simply lists of weighted discriminative subsequences and can thus be interpreted and related to the biological problem. | Bounded Coordinate-Descent for Biological Sequence Classification in
High Dimensional Predictor Space | 2,155 |
We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher discriminant analysis. The second, LSKPCA is a hybrid of least squares regression and kernel PCA. The final LR-KPCA is an iteratively reweighted version of the previous which achieves a sigmoid loss function on the labeled points. We provide a theoretical risk bound as well as illustrative experiments on real and toy data sets. | Semi-Supervised Kernel PCA | 2,156 |
In this paper the sequential prediction problem with expert advice is considered for the case where losses of experts suffered at each step cannot be bounded in advance. We present some modification of Kalai and Vempala algorithm of following the perturbed leader where weights depend on past losses of the experts. New notions of a volume and a scaled fluctuation of a game are introduced. We present a probabilistic algorithm protected from unrestrictedly large one-step losses. This algorithm has the optimal performance in the case when the scaled fluctuations of one-step losses of experts of the pool tend to zero. | Online Learning in Case of Unbounded Losses Using the Follow Perturbed
Leader Algorithm | 2,157 |
In prediction with expert advice the goal is to design online prediction algorithms that achieve small regret (additional loss on the whole data) compared to a reference scheme. In the simplest such scheme one compares to the loss of the best expert in hindsight. A more ambitious goal is to split the data into segments and compare to the best expert on each segment. This is appropriate if the nature of the data changes between segments. The standard fixed-share algorithm is fast and achieves small regret compared to this scheme. Fixed share treats the experts as black boxes: there are no assumptions about how they generate their predictions. But if the experts are learning, the following question arises: should the experts learn from all data or only from data in their own segment? The original algorithm naturally addresses the first case. Here we consider the second option, which is more appropriate exactly when the nature of the data changes between segments. In general extending fixed share to this second case will slow it down by a factor of T on T outcomes. We show, however, that no such slowdown is necessary if the experts are hidden Markov models. | Switching between Hidden Markov Models using Fixed Share | 2,158 |
A problem posed by Freund is how to efficiently track a small pool of experts out of a much larger set. This problem was solved when Bousquet and Warmuth introduced their mixing past posteriors (MPP) algorithm in 2001. In Freund's problem the experts would normally be considered black boxes. However, in this paper we re-examine Freund's problem in case the experts have internal structure that enables them to learn. In this case the problem has two possible interpretations: should the experts learn from all data or only from the subsequence on which they are being tracked? The MPP algorithm solves the first case. Our contribution is to generalise MPP to address the second option. The results we obtain apply to any expert structure that can be formalised using (expert) hidden Markov models. Curiously enough, for our interpretation there are \emph{two} natural reference schemes: freezing and sleeping. For each scheme, we provide an efficient prediction strategy and prove the relevant loss bound. | Freezing and Sleeping: Tracking Experts that Learn by Evolving Past
Posteriors | 2,159 |
We propose a novel feature selection strategy to discover language-independent acoustic features that tend to be responsible for emotions regardless of languages, linguistics and other factors. Experimental results suggest that the language-independent feature subset discovered yields the performance comparable to the full feature set on various emotional speech corpora. | Exploring Language-Independent Emotional Acoustic Features via Feature
Selection | 2,160 |
The group Lasso is an extension of the Lasso for feature selection on (predefined) non-overlapping groups of features. The non-overlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation, where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. We have performed empirical evaluations using the breast cancer gene expression data set, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results demonstrate the efficiency and effectiveness of the proposed algorithm. | Fast Overlapping Group Lasso | 2,161 |
This paper introduces an approach to Reinforcement Learning Algorithm by comparing their immediate rewards using a variation of Q-Learning algorithm. Unlike the conventional Q-Learning, the proposed algorithm compares current reward with immediate reward of past move and work accordingly. Relative reward based Q-learning is an approach towards interactive learning. Q-Learning is a model free reinforcement learning method that used to learn the agents. It is observed that under normal circumstances algorithm take more episodes to reach optimal Q-value due to its normal reward or sometime negative reward. In this new form of algorithm agents select only those actions which have a higher immediate reward signal in comparison to previous one. The contribution of this article is the presentation of new Q-Learning Algorithm in order to maximize the performance of algorithm and reduce the number of episode required to reach optimal Q-value. Effectiveness of proposed algorithm is simulated in a 20 x20 Grid world deterministic environment and the result for the two forms of Q-Learning Algorithms is given. | Reinforcement Learning by Comparing Immediate Reward | 2,162 |
We study three families of online convex optimization algorithms: follow-the-proximally-regularized-leader (FTRL-Proximal), regularized dual averaging (RDA), and composite-objective mirror descent. We first prove equivalence theorems that show all of these algorithms are instantiations of a general FTRL update. This provides theoretical insight on previous experimental observations. In particular, even though the FOBOS composite mirror descent algorithm handles L1 regularization explicitly, it has been observed that RDA is even more effective at producing sparsity. Our results demonstrate that FOBOS uses subgradient approximations to the L1 penalty from previous rounds, leading to less sparsity than RDA, which handles the cumulative penalty in closed form. The FTRL-Proximal algorithm can be seen as a hybrid of these two, and outperforms both on a large, real-world dataset. Our second contribution is a unified analysis which produces regret bounds that match (up to logarithmic terms) or improve the best previously known bounds. This analysis also extends these algorithms in two important ways: we support a more general type of composite objective and we analyze implicit updates, which replace the subgradient approximation of the current loss function with an exact optimization. | A Unified View of Regularized Dual Averaging and Mirror Descent with
Implicit Updates | 2,163 |
We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a sufficient condition for when the hybrid loss is Fisher consistent for classification. This condition depends on a measure of dominance between labels - specifically, the gap in per observation probabilities between the most likely labels. We also prove Fisher consistency is necessary for parametric consistency when learning models such as CRFs. We demonstrate empirically that the hybrid loss typically performs as least as well as - and often better than - both of its constituent losses on variety of tasks. In doing so we also provide an empirical comparison of the efficacy of probabilistic and margin based approaches to multiclass and structured prediction and the effects of label dominance on these results. | Conditional Random Fields and Support Vector Machines: A Hybrid Approach | 2,164 |
In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy to assess the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node, are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree. | Geometric Decision Tree | 2,165 |
Margin theory provides one of the most popular explanations to the success of \texttt{AdaBoost}, where the central point lies in the recognition that \textit{margin} is the key for characterizing the performance of \texttt{AdaBoost}. This theory has been very influential, e.g., it has been used to argue that \texttt{AdaBoost} usually does not overfit since it tends to enlarge the margin even after the training error reaches zero. Previously the \textit{minimum margin bound} was established for \texttt{AdaBoost}, however, \cite{Breiman1999} pointed out that maximizing the minimum margin does not necessarily lead to a better generalization. Later, \cite{Reyzin:Schapire2006} emphasized that the margin distribution rather than minimum margin is crucial to the performance of \texttt{AdaBoost}. In this paper, we first present the \textit{$k$th margin bound} and further study on its relationship to previous work such as the minimum margin bound and Emargin bound. Then, we improve the previous empirical Bernstein bounds \citep{Maurer:Pontil2009,Audibert:Munos:Szepesvari2009}, and based on such findings, we defend the margin-based explanation against Breiman's doubts by proving a new generalization error bound that considers exactly the same factors as \cite{Schapire:Freund:Bartlett:Lee1998} but is sharper than \cite{Breiman1999}'s minimum margin bound. By incorporating factors such as average margin and variance, we present a generalization error bound that is heavily related to the whole margin distribution. We also provide margin distribution bounds for generalization error of voting classifiers in finite VC-dimension space. | On the Doubt about Margin Explanation of Boosting | 2,166 |
In this work, we propose a new optimization framework for multiclass boosting learning. In the literature, AdaBoost.MO and AdaBoost.ECC are the two successful multiclass boosting algorithms, which can use binary weak learners. We explicitly derive these two algorithms' Lagrange dual problems based on their regularized loss functions. We show that the Lagrange dual formulations enable us to design totally-corrective multiclass algorithms by using the primal-dual optimization technique. Experiments on benchmark data sets suggest that our multiclass boosting can achieve a comparable generalization capability with state-of-the-art, but the convergence speed is much faster than stage-wise gradient descent boosting. In other words, the new totally corrective algorithms can maximize the margin more aggressively. | Totally Corrective Multiclass Boosting with Binary Weak Learners | 2,167 |
We establish an excess risk bound of O(H R_n^2 + R_n \sqrt{H L*}) for empirical risk minimization with an H-smooth loss function and a hypothesis class with Rademacher complexity R_n, where L* is the best risk achievable by the hypothesis class. For typical hypothesis classes where R_n = \sqrt{R/n}, this translates to a learning rate of O(RH/n) in the separable (L*=0) case and O(RH/n + \sqrt{L^* RH/n}) more generally. We also provide similar guarantees for online and stochastic convex optimization with a smooth non-negative objective. | Optimistic Rates for Learning with a Smooth Loss | 2,168 |
Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the L1/Lq norm with q > 1 is attractive in many applications of regression and classification in that it facilitates group sparsity in the model. The resulting optimization problem is, however, challenging to solve due to the structure of the L1/Lq -regularization. Existing work deals with special cases including q = 2,infinity, and they cannot be easily extended to the general case. In this paper, we propose an efficient algorithm based on the accelerated gradient method for solving the L1/Lq -regularized problem, which is applicable for all values of q larger than 1, thus significantly extending existing work. One key building block of the proposed algorithm is the L1/Lq -regularized Euclidean projection (EP1q). Our theoretical analysis reveals the key properties of EP1q and illustrates why EP1q for the general q is significantly more challenging to solve than the special cases. Based on our theoretical analysis, we develop an efficient algorithm for EP1q by solving two zero finding problems. Experimental results demonstrate the efficiency of the proposed algorithm. | Efficient L1/Lq Norm Regularization | 2,169 |
An instance-weighted variant of the support vector machine (SVM) has attracted considerable attention recently since they are useful in various machine learning tasks such as non-stationary data analysis, heteroscedastic data modeling, transfer learning, learning to rank, and transduction. An important challenge in these scenarios is to overcome the computational bottleneck---instance weights often change dynamically or adaptively, and thus the weighted SVM solutions must be repeatedly computed. In this paper, we develop an algorithm that can efficiently and exactly update the weighted SVM solutions for arbitrary change of instance weights. Technically, this contribution can be regarded as an extension of the conventional solution-path algorithm for a single regularization parameter to multiple instance-weight parameters. However, this extension gives rise to a significant problem that breakpoints (at which the solution path turns) have to be identified in high-dimensional space. To facilitate this, we introduce a parametric representation of instance weights. We also provide a geometric interpretation in weight space using a notion of critical region: a polyhedron in which the current affine solution remains to be optimal. Then we find breakpoints at intersections of the solution path and boundaries of polyhedrons. Through extensive experiments on various practical applications, we demonstrate the usefulness of the proposed algorithm. | Multi-parametric Solution-path Algorithm for Instance-weighted Support
Vector Machines | 2,170 |
Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm's performance. | Portfolio Allocation for Bayesian Optimization | 2,171 |
We consider the problem of energy-efficient point-to-point transmission of delay-sensitive data (e.g. multimedia data) over a fading channel. Existing research on this topic utilizes either physical-layer centric solutions, namely power-control and adaptive modulation and coding (AMC), or system-level solutions based on dynamic power management (DPM); however, there is currently no rigorous and unified framework for simultaneously utilizing both physical-layer centric and system-level techniques to achieve the minimum possible energy consumption, under delay constraints, in the presence of stochastic and a priori unknown traffic and channel conditions. In this report, we propose such a framework. We formulate the stochastic optimization problem as a Markov decision process (MDP) and solve it online using reinforcement learning. The advantages of the proposed online method are that (i) it does not require a priori knowledge of the traffic arrival and channel statistics to determine the jointly optimal power-control, AMC, and DPM policies; (ii) it exploits partial information about the system so that less information needs to be learned than when using conventional reinforcement learning algorithms; and (iii) it obviates the need for action exploration, which severely limits the adaptation speed and run-time performance of conventional reinforcement learning algorithms. Our results show that the proposed learning algorithms can converge up to two orders of magnitude faster than a state-of-the-art learning algorithm for physical layer power-control and up to three orders of magnitude faster than conventional reinforcement learning algorithms. | Fast Reinforcement Learning for Energy-Efficient Wireless Communications | 2,172 |
We propose a focus of attention mechanism to speed up the Perceptron algorithm. Focus of attention speeds up the Perceptron algorithm by lowering the number of features evaluated throughout training and prediction. Whereas the traditional Perceptron evaluates all the features of each example, the Attentive Perceptron evaluates less features for easy to classify examples, thereby achieving significant speedups and small losses in prediction accuracy. Focus of attention allows the Attentive Perceptron to stop the evaluation of features at any interim point and filter the example. This creates an attentive filter which concentrates computation at examples that are hard to classify, and quickly filters examples that are easy to classify. | The Attentive Perceptron | 2,173 |
In this paper, we consider a queue-aware distributive resource control algorithm for two-hop MIMO cooperative systems. We shall illustrate that relay buffering is an effective way to reduce the intrinsic half-duplex penalty in cooperative systems. The complex interactions of the queues at the source node and the relays are modeled as an average-cost infinite horizon Markov Decision Process (MDP). The traditional approach solving this MDP problem involves centralized control with huge complexity. To obtain a distributive and low complexity solution, we introduce a linear structure which approximates the value function of the associated Bellman equation by the sum of per-node value functions. We derive a distributive two-stage two-winner auction-based control policy which is a function of the local CSI and local QSI only. Furthermore, to estimate the best fit approximation parameter, we propose a distributive online stochastic learning algorithm using stochastic approximation theory. Finally, we establish technical conditions for almost-sure convergence and show that under heavy traffic, the proposed low complexity distributive control is global optimal. | Queue-Aware Distributive Resource Control for Delay-Sensitive Two-Hop
MIMO Cooperative Systems | 2,174 |
To classify time series by nearest neighbors, we need to specify or learn one or several distance measures. We consider variations of the Mahalanobis distance measures which rely on the inverse covariance matrix of the data. Unfortunately --- for time series data --- the covariance matrix has often low rank. To alleviate this problem we can either use a pseudoinverse, covariance shrinking or limit the matrix to its diagonal. We review these alternatives and benchmark them against competitive methods such as the related Large Margin Nearest Neighbor Classification (LMNN) and the Dynamic Time Warping (DTW) distance. As we expected, we find that the DTW is superior, but the Mahalanobis distance measures are one to two orders of magnitude faster. To get best results with Mahalanobis distance measures, we recommend learning one distance measure per class using either covariance shrinking or the diagonal approach. | Time Series Classification by Class-Specific Mahalanobis Distance
Measures | 2,175 |
This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito divergence as special cases (beta = 2,1,0, respectively). The proposed algorithms are based on a surrogate auxiliary function (a local majorization of the criterion function). We first describe a majorization-minimization (MM) algorithm that leads to multiplicative updates, which differ from standard heuristic multiplicative updates by a beta-dependent power exponent. The monotonicity of the heuristic algorithm can however be proven for beta in (0,1) using the proposed auxiliary function. Then we introduce the concept of majorization-equalization (ME) algorithm which produces updates that move along constant level sets of the auxiliary function and lead to larger steps than MM. Simulations on synthetic and real data illustrate the faster convergence of the ME approach. The paper also describes how the proposed algorithms can be adapted to two common variants of NMF : penalized NMF (i.e., when a penalty function of the factors is added to the criterion function) and convex-NMF (when the dictionary is assumed to belong to a known subspace). | Algorithms for nonnegative matrix factorization with the beta-divergence | 2,176 |
Hardness results for maximum agreement problems have close connections to hardness results for proper learning in computational learning theory. In this paper we prove two hardness results for the problem of finding a low degree polynomial threshold function (PTF) which has the maximum possible agreement with a given set of labeled examples in $\R^n \times \{-1,1\}.$ We prove that for any constants $d\geq 1, \eps > 0$, {itemize} Assuming the Unique Games Conjecture, no polynomial-time algorithm can find a degree-$d$ PTF that is consistent with a $(\half + \eps)$ fraction of a given set of labeled examples in $\R^n \times \{-1,1\}$, even if there exists a degree-$d$ PTF that is consistent with a $1-\eps$ fraction of the examples. It is $\NP$-hard to find a degree-2 PTF that is consistent with a $(\half + \eps)$ fraction of a given set of labeled examples in $\R^n \times \{-1,1\}$, even if there exists a halfspace (degree-1 PTF) that is consistent with a $1 - \eps$ fraction of the examples. {itemize} These results immediately imply the following hardness of learning results: (i) Assuming the Unique Games Conjecture, there is no better-than-trivial proper learning algorithm that agnostically learns degree-$d$ PTFs under arbitrary distributions; (ii) There is no better-than-trivial learning algorithm that outputs degree-2 PTFs and agnostically learns halfspaces (i.e. degree-1 PTFs) under arbitrary distributions. | Hardness Results for Agnostically Learning Low-Degree Polynomial
Threshold Functions | 2,177 |
A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the proposed approach, based on probably one of the simplest probabilistic models, leads to the results in the same ballpark as the state-of-the-art, at a lower computational cost. | Efficient Matrix Completion with Gaussian Models | 2,178 |
This paper considers the clustering problem for large data sets. We propose an approach based on distributed optimization. The clustering problem is formulated as an optimization problem of maximizing the classification gain. We show that the optimization problem can be reformulated and decomposed into small-scale sub optimization problems by using the Dantzig-Wolfe decomposition method. Generally speaking, the Dantzig-Wolfe method can only be used for convex optimization problems, where the duality gaps are zero. Even though, the considered optimization problem in this paper is non-convex, we prove that the duality gap goes to zero, as the problem size goes to infinity. Therefore, the Dantzig-Wolfe method can be applied here. In the proposed approach, the clustering problem is iteratively solved by a group of computers coordinated by one center processor, where each computer solves one independent small-scale sub optimization problem during each iteration, and only a small amount of data communication is needed between the computers and center processor. Numerical results show that the proposed approach is effective and efficient. | Large-Scale Clustering Based on Data Compression | 2,179 |
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions of these problems, such as SVDD, hard margin SVM, and L2-SVM, for which sublinear-time algorithms were not known before. These new algorithms use a combination of a novel sampling techniques and a new multiplicative update algorithm. We give lower bounds which show the running times of many of our algorithms to be nearly best possible in the unit-cost RAM model. We also give implementations of our algorithms in the semi-streaming setting, obtaining the first low pass polylogarithmic space and sublinear time algorithms achieving arbitrary approximation factor. | Sublinear Optimization for Machine Learning | 2,180 |
Nesterov's accelerated gradient methods (AGM) have been successfully applied in many machine learning areas. However, their empirical performance on training max-margin models has been inferior to existing specialized solvers. In this paper, we first extend AGM to strongly convex and composite objective functions with Bregman style prox-functions. Our unifying framework covers both the $\infty$-memory and 1-memory styles of AGM, tunes the Lipschiz constant adaptively, and bounds the duality gap. Then we demonstrate various ways to apply this framework of methods to a wide range of machine learning problems. Emphasis will be given on their rate of convergence and how to efficiently compute the gradient and optimize the models. The experimental results show that with our extensions AGM outperforms state-of-the-art solvers on max-margin models. | Regularized Risk Minimization by Nesterov's Accelerated Gradient
Methods: Algorithmic Extensions and Empirical Studies | 2,181 |
An importance weight quantifies the relative importance of one example over another, coming up in applications of boosting, asymmetric classification costs, reductions, and active learning. The standard approach for dealing with importance weights in gradient descent is via multiplication of the gradient. We first demonstrate the problems of this approach when importance weights are large, and argue in favor of more sophisticated ways for dealing with them. We then develop an approach which enjoys an invariance property: that updating twice with importance weight $h$ is equivalent to updating once with importance weight $2h$. For many important losses this has a closed form update which satisfies standard regret guarantees when all examples have $h=1$. We also briefly discuss two other reasonable approaches for handling large importance weights. Empirically, these approaches yield substantially superior prediction with similar computational performance while reducing the sensitivity of the algorithm to the exact setting of the learning rate. We apply these to online active learning yielding an extraordinarily fast active learning algorithm that works even in the presence of adversarial noise. | Online Importance Weight Aware Updates | 2,182 |
The note presents a modified proof of a loss bound for the exponentially weighted average forecaster with time-varying potential. The regret term of the algorithm is upper-bounded by sqrt{n ln(N)} (uniformly in n), where N is the number of experts and n is the number of steps. | On Theorem 2.3 in "Prediction, Learning, and Games" by Cesa-Bianchi and
Lugosi | 2,183 |
Recommendation systems are emerging as an important business application with significant economic impact. Currently popular systems include Amazon's book recommendations, Netflix's movie recommendations, and Pandora's music recommendations. In this paper we address the problem of estimating probabilities associated with recommendation system data using non-parametric kernel smoothing. In our estimation we interpret missing items as randomly censored observations and obtain efficient computation schemes using combinatorial properties of generating functions. We demonstrate our approach with several case studies involving real world movie recommendation data. The results are comparable with state-of-the-art techniques while also providing probabilistic preference estimates outside the scope of traditional recommender systems. | Estimating Probabilities in Recommendation Systems | 2,184 |
We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences. | A Tutorial on Bayesian Optimization of Expensive Cost Functions, with
Application to Active User Modeling and Hierarchical Reinforcement Learning | 2,185 |
In this paper, we propose a two-timescale delay-optimal dynamic clustering and power allocation design for downlink network MIMO systems. The dynamic clustering control is adaptive to the global queue state information (GQSI) only and computed at the base station controller (BSC) over a longer time scale. On the other hand, the power allocations of all the BSs in one cluster are adaptive to both intra-cluster channel state information (CCSI) and intra-cluster queue state information (CQSI), and computed at the cluster manager (CM) over a shorter time scale. We show that the two-timescale delay-optimal control can be formulated as an infinite-horizon average cost Constrained Partially Observed Markov Decision Process (CPOMDP). By exploiting the special problem structure, we shall derive an equivalent Bellman equation in terms of Pattern Selection Q-factor to solve the CPOMDP. To address the distributive requirement and the issue of exponential memory requirement and computational complexity, we approximate the Pattern Selection Q-factor by the sum of Per-cluster Potential functions and propose a novel distributive online learning algorithm to estimate the Per-cluster Potential functions (at each CM) as well as the Lagrange multipliers (LM) (at each BS). We show that the proposed distributive online learning algorithm converges almost surely (with probability 1). By exploiting the birth-death structure of the queue dynamics, we further decompose the Per-cluster Potential function into sum of Per-cluster Per-user Potential functions and formulate the instantaneous power allocation as a Per-stage QSI-aware Interference Game played among all the CMs. We also propose a QSI-aware Simultaneous Iterative Water-filling Algorithm (QSIWFA) and show that it can achieve the Nash Equilibrium (NE). | Queue-Aware Dynamic Clustering and Power Allocation for Network MIMO
Systems via Distributive Stochastic Learning | 2,186 |
To attain the best learning accuracy, people move on with difficulties and frustrations. Though one can optimize the empirical objective using a given set of samples, its generalization ability to the entire sample distribution remains questionable. Even if a fair generalization guarantee is offered, one still wants to know what is to happen if the regularizer is removed, and/or how well the artificial loss (like the hinge loss) relates to the accuracy. For such reason, this report surveys four different trials towards the learning accuracy, embracing the major advances in supervised learning theory in the past four years. Starting from the generic setting of learning, the first two trials introduce the best optimization and generalization bounds for convex learning, and the third trial gets rid of the regularizer. As an innovative attempt, the fourth trial studies the optimization when the objective is exactly the accuracy, in the special case of binary classification. This report also analyzes the last trial through experiments. | Survey & Experiment: Towards the Learning Accuracy | 2,187 |
This report explores the use of machine learning techniques to accurately predict travel times in city streets and highways using floating car data (location information of user vehicles on a road network). The aim of this report is twofold, first we present a general architecture of solving this problem, then present and evaluate few techniques on real floating car data gathered over a month on a 5 Km highway in New Delhi. | Travel Time Estimation Using Floating Car Data | 2,188 |
This article discusses in detail the rating system that won the kaggle competition "Chess Ratings: Elo vs the rest of the world". The competition provided a historical dataset of outcomes for chess games, and aimed to discover whether novel approaches can predict the outcomes of future games, more accurately than the well-known Elo rating system. The winning rating system, called Elo++ in the rest of the article, builds upon the Elo rating system. Like Elo, Elo++ uses a single rating per player and predicts the outcome of a game, by using a logistic curve over the difference in ratings of the players. The major component of Elo++ is a regularization technique that avoids overfitting these ratings. The dataset of chess games and outcomes is relatively small and one has to be careful not to draw "too many conclusions" out of the limited data. Many approaches tested in the competition showed signs of such an overfitting. The leader-board was dominated by attempts that did a very good job on a small test dataset, but couldn't generalize well on the private hold-out dataset. The Elo++ regularization takes into account the number of games per player, the recency of these games and the ratings of the opponents. Finally, Elo++ employs a stochastic gradient descent scheme for training the ratings, and uses only two global parameters (white's advantage and regularization constant) that are optimized using cross-validation. | How I won the "Chess Ratings - Elo vs the Rest of the World" Competition | 2,189 |
An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute these marginals when the underlying graph is a tree, has gained its popularity as an efficient way to approximate them in the more general case. In this paper, we focus on an aspect of the algorithm that did not get that much attention in the literature, which is the effect of the normalization of the messages. We show in particular that, for a large class of normalization strategies, it is possible to focus only on belief convergence. Following this, we express the necessary and sufficient conditions for local stability of a fixed point in terms of the graph structure and the beliefs values at the fixed point. We also explicit some connexion between the normalization constants and the underlying Bethe Free Energy. | The Role of Normalization in the Belief Propagation Algorithm | 2,190 |
We consider a retailer selling a single product with limited on-hand inventory over a finite selling season. Customer demand arrives according to a Poisson process, the rate of which is influenced by a single action taken by the retailer (such as price adjustment, sales commission, advertisement intensity, etc.). The relationship between the action and the demand rate is not known in advance. However, the retailer is able to learn the optimal action "on the fly" as she maximizes her total expected revenue based on the observed demand reactions. Using the pricing problem as an example, we propose a dynamic "learning-while-doing" algorithm that only involves function value estimation to achieve a near-optimal performance. Our algorithm employs a series of shrinking price intervals and iteratively tests prices within that interval using a set of carefully chosen parameters. We prove that the convergence rate of our algorithm is among the fastest of all possible algorithms in terms of asymptotic "regret" (the relative loss comparing to the full information optimal solution). Our result closes the performance gaps between parametric and non-parametric learning and between a post-price mechanism and a customer-bidding mechanism. Important managerial insight from this research is that the values of information on both the parametric form of the demand function as well as each customer's exact reservation price are less important than prior literature suggests. Our results also suggest that firms would be better off to perform dynamic learning and action concurrently rather than sequentially. | Close the Gaps: A Learning-while-Doing Algorithm for a Class of
Single-Product Revenue Management Problems | 2,191 |
This article presents a model which is capable of learning and abstracting new concepts based on comparing observations and finding the resemblance between the observations. In the model, the new observations are compared with the templates which have been derived from the previous experiences. In the first stage, the objects are first represented through a geometric description which is used for finding the object boundaries and a descriptor which is inspired by the human visual system and then they are fed into the model. Next, the new observations are identified through comparing them with the previously-learned templates and are used for producing new templates. The comparisons are made based on measures like Euclidean or correlation distance. The new template is created by applying onion-pealing algorithm. The algorithm consecutively uses convex hulls which are made by the points representing the objects. If the new observation is remarkably similar to one of the observed categories, it is no longer utilized in creating a new template. The existing templates are used to provide a description of the new observation. This description is provided in the templates space. Each template represents a dimension of the feature space. The degree of the resemblance each template bears to each object indicates the value associated with the object in that dimension of the templates space. In this way, the description of the new observation becomes more accurate and detailed as the time passes and the experiences increase. We have used this model for learning and recognizing the new polygons in the polygon space. Representing the polygons was made possible through employing a geometric method and a method inspired by human visual system. Various implementations of the model have been compared. The evaluation results of the model prove its efficiency in learning and deriving new templates. | A Novel Template-Based Learning Model | 2,192 |
It is a challenging task to select correlated variables in a high dimensional space. To address this challenge, the elastic net has been developed and successfully applied to many applications. Despite its great success, the elastic net does not explicitly use correlation information embedded in data to select correlated variables. To overcome this limitation, we present a novel Bayesian hybrid model, the EigenNet, that uses the eigenstructures of data to guide variable selection. Specifically, it integrates a sparse conditional classification model with a generative model capturing variable correlations in a principled Bayesian framework. We reparameterize the hybrid model in the eigenspace to avoid overfiting and to increase the computational efficiency of its MCMC sampler. Furthermore, we provide an alternative view to the EigenNet from a regularization perspective: the EigenNet has an adaptive eigenspace-based composite regularizer, which naturally generalizes the $l_{1/2}$ regularizer used by the elastic net. Experiments on synthetic and real data show that the EigenNet significantly outperforms the lasso, the elastic net, and the Bayesian lasso in terms of prediction accuracy, especially when the number of training samples is smaller than the number of variables. | EigenNet: A Bayesian hybrid of generative and conditional models for
sparse learning | 2,193 |
Ordinal regression is commonly formulated as a multi-class problem with ordinal constraints. The challenge of designing accurate classifiers for ordinal regression generally increases with the number of classes involved, due to the large number of labeled patterns that are needed. The availability of ordinal class labels, however, is often costly to calibrate or difficult to obtain. Unlabeled patterns, on the other hand, often exist in much greater abundance and are freely available. To take benefits from the abundance of unlabeled patterns, we present a novel transductive learning paradigm for ordinal regression in this paper, namely Transductive Ordinal Regression (TOR). The key challenge of the present study lies in the precise estimation of both the ordinal class label of the unlabeled data and the decision functions of the ordinal classes, simultaneously. The core elements of the proposed TOR include an objective function that caters to several commonly used loss functions casted in transductive settings, for general ordinal regression. A label swapping scheme that facilitates a strictly monotonic decrease in the objective function value is also introduced. Extensive numerical studies on commonly used benchmark datasets including the real world sentiment prediction problem are then presented to showcase the characteristics and efficacies of the proposed transductive ordinal regression. Further, comparisons to recent state-of-the-art ordinal regression methods demonstrate the introduced transductive learning paradigm for ordinal regression led to the robust and improved performance. | Transductive Ordinal Regression | 2,194 |
We consider the problem of learning an unknown product distribution $X$ over $\{0,1\}^n$ using samples $f(X)$ where $f$ is a \emph{known} transformation function. Each choice of a transformation function $f$ specifies a learning problem in this framework. Information-theoretic arguments show that for every transformation function $f$ the corresponding learning problem can be solved to accuracy $\eps$, using $\tilde{O}(n/\eps^2)$ examples, by a generic algorithm whose running time may be exponential in $n.$ We show that this learning problem can be computationally intractable even for constant $\eps$ and rather simple transformation functions. Moreover, the above sample complexity bound is nearly optimal for the general problem, as we give a simple explicit linear transformation function $f(x)=w \cdot x$ with integer weights $w_i \leq n$ and prove that the corresponding learning problem requires $\Omega(n)$ samples. As our main positive result we give a highly efficient algorithm for learning a sum of independent unknown Bernoulli random variables, corresponding to the transformation function $f(x)= \sum_{i=1}^n x_i$. Our algorithm learns to $\eps$-accuracy in poly$(n)$ time, using a surprising poly$(1/\eps)$ number of samples that is independent of $n.$ We also give an efficient algorithm that uses $\log n \cdot \poly(1/\eps)$ samples but has running time that is only $\poly(\log n, 1/\eps).$ | Learning transformed product distributions | 2,195 |
Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for classification error. In this paper, we propose a generalized sparse regularizer. Based on the proposed regularizer, we present a unified feature selection framework for general loss functions. In particular, we study the novel feature selection paradigm by optimizing multivariate performance measures. The resultant formulation is a challenging problem for high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed to solve this problem, and the convergence is presented. In addition, we adapt the proposed method to optimize multivariate measures for multiple instance learning problems. The analyses by comparing with the state-of-the-art feature selection methods show that the proposed method is superior to others. Extensive experiments on large-scale and high-dimensional real world datasets show that the proposed method outperforms $l_1$-SVM and SVM-RFE when choosing a small subset of features, and achieves significantly improved performances over SVM$^{perf}$ in terms of $F_1$-score. | A Feature Selection Method for Multivariate Performance Measures | 2,196 |
In this work we study parallelization of online learning, a core primitive in machine learning. In a parallel environment all known approaches for parallel online learning lead to delayed updates, where the model is updated using out-of-date information. In the worst case, or when examples are temporally correlated, delay can have a very adverse effect on the learning algorithm. Here, we analyze and present preliminary empirical results on a set of learning architectures based on a feature sharding approach that present various tradeoffs between delay, degree of parallelism, representation power and empirical performance. | Parallel Online Learning | 2,197 |
Supervised learning is all about the ability to generalize knowledge. Specifically, the goal of the learning is to train a classifier using training data, in such a way that it will be capable of classifying new unseen data correctly. In order to acheive this goal, it is important to carefully design the learner, so it will not overfit the training data. The later can is done usually by adding a regularization term. The statistical learning theory explains the success of this method by claiming that it restricts the complexity of the learned model. This explanation, however, is rather abstract and does not have a geometric intuition. The generalization error of a classifier may be thought of as correlated with its robustness to perturbations of the data: a classifier that copes with disturbance is expected to generalize well. Indeed, Xu et al. [2009] have shown that the SVM formulation is equivalent to a robust optimization (RO) formulation, in which an adversary displaces the training and testing points within a ball of pre-determined radius. In this work we explore a different kind of robustness, namely changing each data point with a Gaussian cloud centered at the sample. Loss is evaluated as the expectation of an underlying loss function on the cloud. This setup fits the fact that in many applications, the data is sampled along with noise. We develop an RO framework, in which the adversary chooses the covariance of the noise. In our algorithm named GURU, the tuning parameter is a spectral bound on the noise, thus it can be estimated using physical or applicative considerations. Our experiments show that this framework performs as well as SVM and even slightly better in some cases. Generalizations for Mercer kernels and for the multiclass case are presented as well. We also show that our framework may be further generalized, using the technique of convex perspective functions. | Gaussian Robust Classification | 2,198 |
We propose a new clustering technique that can be regarded as a numerical method to compute the proximity gestalt. The method analyzes edge length statistics in the MST of the dataset and provides an a contrario cluster detection criterion. The approach is fully parametric on the chosen distance and can detect arbitrarily shaped clusters. The method is also automatic, in the sense that only a single parameter is left to the user. This parameter has an intuitive interpretation as it controls the expected number of false detections. We show that the iterative application of our method can (1) provide robustness to noise and (2) solve a masking phenomenon in which a highly populated and salient cluster dominates the scene and inhibits the detection of less-populated, but still salient, clusters. | Meaningful Clustered Forest: an Automatic and Robust Clustering
Algorithm | 2,199 |
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