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This paper describes the solution of Bazinga Team for Tmall Recommendation Prize 2014. With real-world user action data provided by Tmall, one of the largest B2C online retail platforms in China, this competition requires to predict future user purchases on Tmall website. Predictions are judged on F1Score, which considers both precision and recall for fair evaluation. The data set provided by Tmall contains more than half billion action records from over ten million distinct users. Such massive data volume poses a big challenge, and drives competitors to write every single program in MapReduce fashion and run it on distributed cluster. We model the purchase prediction problem as standard machine learning problem, and mainly employ regression and classification methods as single models. Individual models are then aggregated in a two-stage approach, using linear regression for blending, and finally a linear ensemble of blended models. The competition is approaching the end but still in running during writing this paper. In the end, our team achieves F1Score 6.11 and ranks 7th (out of 7,276 teams in total). | Large Scale Purchase Prediction with Historical User Actions on B2C
Online Retail Platform | 2,700 |
In this paper, we study the generalization performance of regularized multi-task learning (RMTL) in a vector-valued framework, where MTL is considered as a learning process for vector-valued functions. We are mainly concerned with two theoretical questions: 1) under what conditions does RMTL perform better with a smaller task sample size than STL? 2) under what conditions is RMTL generalizable and can guarantee the consistency of each task during simultaneous learning? In particular, we investigate two types of task-group relatedness: the observed discrepancy-dependence measure (ODDM) and the empirical discrepancy-dependence measure (EDDM), both of which detect the dependence between two groups of multiple related tasks (MRTs). We then introduce the Cartesian product-based uniform entropy number (CPUEN) to measure the complexities of vector-valued function classes. By applying the specific deviation and the symmetrization inequalities to the vector-valued framework, we obtain the generalization bound for RMTL, which is the upper bound of the joint probability of the event that there is at least one task with a large empirical discrepancy between the expected and empirical risks. Finally, we present a sufficient condition to guarantee the consistency of each task in the simultaneous learning process, and we discuss how task relatedness affects the generalization performance of RMTL. Our theoretical findings answer the aforementioned two questions. | Task-group Relatedness and Generalization Bounds for Regularized
Multi-task Learning | 2,701 |
Structural support vector machines (SSVMs) are amongst the best performing models for structured computer vision tasks, such as semantic image segmentation or human pose estimation. Training SSVMs, however, is computationally costly, because it requires repeated calls to a structured prediction subroutine (called \emph{max-oracle}), which has to solve an optimization problem itself, e.g. a graph cut. In this work, we introduce a new algorithm for SSVM training that is more efficient than earlier techniques when the max-oracle is computationally expensive, as it is frequently the case in computer vision tasks. The main idea is to (i) combine the recent stochastic Block-Coordinate Frank-Wolfe algorithm with efficient hyperplane caching, and (ii) use an automatic selection rule for deciding whether to call the exact max-oracle or to rely on an approximate one based on the cached hyperplanes. We show experimentally that this strategy leads to faster convergence to the optimum with respect to the number of requires oracle calls, and that this translates into faster convergence with respect to the total runtime when the max-oracle is slow compared to the other steps of the algorithm. A publicly available C++ implementation is provided at http://pub.ist.ac.at/~vnk/papers/SVM.html . | A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training
Structural SVMs with a Costly max-Oracle | 2,702 |
In this paper, the Dempster-Shafer method is employed as the theoretical basis for creating data classification systems. Testing is carried out using three popular (multiple attribute) benchmark datasets that have two, three and four classes. In each case, a subset of the available data is used for training to establish thresholds, limits or likelihoods of class membership for each attribute, and hence create mass functions that establish probability of class membership for each attribute of the test data. Classification of each data item is achieved by combination of these probabilities via Dempster's Rule of Combination. Results for the first two datasets show extremely high classification accuracy that is competitive with other popular methods. The third dataset is non-numerical and difficult to classify, but good results can be achieved provided the system and mass functions are designed carefully and the right attributes are chosen for combination. In all cases the Dempster-Shafer method provides comparable performance to other more popular algorithms, but the overhead of generating accurate mass functions increases the complexity with the addition of new attributes. Overall, the results suggest that the D-S approach provides a suitable framework for the design of classification systems and that automating the mass function design and calculation would increase the viability of the algorithm for complex classification problems. | Data classification using the Dempster-Shafer method | 2,703 |
This paper presents a new solution for choosing the K parameter in the k-nearest neighbor (KNN) algorithm, the solution depending on the idea of ensemble learning, in which a weak KNN classifier is used each time with a different K, starting from one to the square root of the size of the training set. The results of the weak classifiers are combined using the weighted sum rule. The proposed solution was tested and compared to other solutions using a group of experiments in real life problems. The experimental results show that the proposed classifier outperforms the traditional KNN classifier that uses a different number of neighbors, is competitive with other classifiers, and is a promising classifier with strong potential for a wide range of applications. | Solving the Problem of the K Parameter in the KNN Classifier Using an
Ensemble Learning Approach | 2,704 |
This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in some dimensions in the feature space. The proposed metric is proved mathematically to be a metric. To test its viability for different applications, the KNN used the proposed metric for classifying test examples chosen from a number of real datasets. Compared to some other well known metrics, the experimental results show that the proposed metric is a promising distance measure for the KNN classifier with strong potential for a wide range of applications. | Dimensionality Invariant Similarity Measure | 2,705 |
In this paper, we propose the problem of domain transfer structured output learn- ing and the first solution to solve it. The problem is defined on two different data domains sharing the same input and output spaces, named as source domain and target domain. The outputs are structured, and for the data samples of the source domain, the corresponding outputs are available, while for most data samples of the target domain, the corresponding outputs are missing. The input distributions of the two domains are significantly different. The problem is to learn a predictor for the target domain to predict the structured outputs from the input. Due to the limited number of outputs available for the samples form the target domain, it is difficult to directly learn the predictor from the target domain, thus it is necessary to use the output information available in source domain. We propose to learn the target domain predictor by adapting a auxiliary predictor trained by using source domain data to the target domain. The adaptation is implemented by adding a delta function on the basis of the auxiliary predictor. An algorithm is developed to learn the parameter of the delta function to minimize loss functions associat- ed with the predicted outputs against the true outputs of the data samples with available outputs of the target domain. | Domain Transfer Structured Output Learning | 2,706 |
Much of the energy consumption in buildings is due to HVAC systems, which has motivated several recent studies on making these systems more energy- efficient. Occupancy and activity are two important aspects, which need to be correctly estimated for optimal HVAC control. However, state-of-the-art methods to estimate occupancy and classify activity require infrastructure and/or wearable sensors which suffers from lower acceptability due to higher cost. Encouragingly, with the advancement of the smartphones, these are becoming more achievable. Most of the existing occupancy estimation tech- niques have the underlying assumption that the phone is always carried by its user. However, phones are often left at desk while attending meeting or other events, which generates estimation error for the existing phone based occupancy algorithms. Similarly, in the recent days the emerging theory of Sparse Random Classifier (SRC) has been applied for activity classification on smartphone, however, there are rooms to improve the on-phone process- ing. We propose a novel sensor fusion method which offers almost 100% accuracy for occupancy estimation. We also propose an activity classifica- tion algorithm, which offers similar accuracy as of the state-of-the-art SRC algorithms while offering 50% reduction in processing. | Novel Methods for Activity Classification and Occupany Prediction
Enabling Fine-grained HVAC Control | 2,707 |
The sensitivity of Adaboost to random label noise is a well-studied problem. LogitBoost, BrownBoost and RobustBoost are boosting algorithms claimed to be less sensitive to noise than AdaBoost. We present the results of experiments evaluating these algorithms on both synthetic and real datasets. We compare the performance on each of datasets when the labels are corrupted by different levels of independent label noise. In presence of random label noise, we found that BrownBoost and RobustBoost perform significantly better than AdaBoost and LogitBoost, while the difference between each pair of algorithms is insignificant. We provide an explanation for the difference based on the margin distributions of the algorithms. | Non-Convex Boosting Overcomes Random Label Noise | 2,708 |
In this paper, we propose to learn a Mahalanobis distance to perform alignment of multivariate time series. The learning examples for this task are time series for which the true alignment is known. We cast the alignment problem as a structured prediction task, and propose realistic losses between alignments for which the optimization is tractable. We provide experiments on real data in the audio to audio context, where we show that the learning of a similarity measure leads to improvements in the performance of the alignment task. We also propose to use this metric learning framework to perform feature selection and, from basic audio features, build a combination of these with better performance for the alignment. | Metric Learning for Temporal Sequence Alignment | 2,709 |
A particularly successful role for Inductive Logic Programming (ILP) is as a tool for discovering useful relational features for subsequent use in a predictive model. Conceptually, the case for using ILP to construct relational features rests on treating these features as functions, the automated discovery of which necessarily requires some form of first-order learning. Practically, there are now several reports in the literature that suggest that augmenting any existing features with ILP-discovered relational features can substantially improve the predictive power of a model. While the approach is straightforward enough, much still needs to be done to scale it up to explore more fully the space of possible features that can be constructed by an ILP system. This is in principle, infinite and in practice, extremely large. Applications have been confined to heuristic or random selections from this space. In this paper, we address this computational difficulty by allowing features to be constructed in a distributed manner. That is, there is a network of computational units, each of which employs an ILP engine to construct some small number of features and then builds a (local) model. We then employ a consensus-based algorithm, in which neighboring nodes share information to update local models. For a category of models (those with convex loss functions), it can be shown that the algorithm will result in all nodes converging to a consensus model. In practice, it may be slow to achieve this convergence. Nevertheless, our results on synthetic and real datasets that suggests that in relatively short time the "best" node in the network reaches a model whose predictive accuracy is comparable to that obtained using more computational effort in a non-distributed setting (the best node is identified as the one whose weights converge first). | Consensus-Based Modelling using Distributed Feature Construction | 2,710 |
This work focuses on active learning of distance metrics from relative comparison information. A relative comparison specifies, for a data point triplet $(x_i,x_j,x_k)$, that instance $x_i$ is more similar to $x_j$ than to $x_k$. Such constraints, when available, have been shown to be useful toward defining appropriate distance metrics. In real-world applications, acquiring constraints often require considerable human effort. This motivates us to study how to select and query the most useful relative comparisons to achieve effective metric learning with minimum user effort. Given an underlying class concept that is employed by the user to provide such constraints, we present an information-theoretic criterion that selects the triplet whose answer leads to the highest expected gain in information about the classes of a set of examples. Directly applying the proposed criterion requires examining $O(n^3)$ triplets with $n$ instances, which is prohibitive even for datasets of moderate size. We show that a randomized selection strategy can be used to reduce the selection pool from $O(n^3)$ to $O(n)$, allowing us to scale up to larger-size problems. Experiments show that the proposed method consistently outperforms two baseline policies. | Active Metric Learning from Relative Comparisons | 2,711 |
We develop a novel probabilistic approach for multi-label classification that is based on the mixtures-of-experts architecture combined with recently introduced conditional tree-structured Bayesian networks. Our approach captures different input-output relations from multi-label data using the efficient tree-structured classifiers, while the mixtures-of-experts architecture aims to compensate for the tree-structured restrictions and build a more accurate model. We develop and present algorithms for learning the model from data and for performing multi-label predictions on future data instances. Experiments on multiple benchmark datasets demonstrate that our approach achieves highly competitive results and outperforms the existing state-of-the-art multi-label classification methods. | A Mixtures-of-Experts Framework for Multi-Label Classification | 2,712 |
With the availability of high precision digital sensors and cheap storage medium, it is not uncommon to find large amounts of data collected on almost all measurable attributes, both in nature and man-made habitats. Weather in particular has been an area of keen interest for researchers to develop more accurate and reliable prediction models. This paper presents a set of experiments which involve the use of prevalent machine learning techniques to build models to predict the day of the week given the weather data for that particular day i.e. temperature, wind, rain etc., and test their reliability across four cities in Australia {Brisbane, Adelaide, Perth, Hobart}. The results provide a comparison of accuracy of these machine learning techniques and their reliability to predict the day of the week by analysing the weather data. We then apply the models to predict weather conditions based on the available data. | Predictive Capacity of Meteorological Data - Will it rain tomorrow | 2,713 |
We consider the approximation capability of orthogonal super greedy algorithms (OSGA) and its applications in supervised learning. OSGA is concerned with selecting more than one atoms in each iteration step, which, of course, greatly reduces the computational burden when compared with the conventional orthogonal greedy algorithm (OGA). We prove that even for function classes that are not the convex hull of the dictionary, OSGA does not degrade the approximation capability of OGA provided the dictionary is incoherent. Based on this, we deduce a tight generalization error bound for OSGA learning. Our results show that in the realm of supervised learning, OSGA provides a possibility to further reduce the computational burden of OGA in the premise of maintaining its prominent generalization capability. | Learning and approximation capability of orthogonal super greedy
algorithm | 2,714 |
We consider \textit{anytime} linear prediction in the common machine learning setting, where features are in groups that have costs. We achieve anytime (or interruptible) predictions by sequencing the computation of feature groups and reporting results using the computed features at interruption. We extend Orthogonal Matching Pursuit (OMP) and Forward Regression (FR) to learn the sequencing greedily under this group setting with costs. We theoretically guarantee that our algorithms achieve near-optimal linear predictions at each budget when a feature group is chosen. With a novel analysis of OMP, we improve its theoretical bound to the same strength as that of FR. In addition, we develop a novel algorithm that consumes cost $4B$ to approximate the optimal performance of \textit{any} cost $B$, and prove that with cost less than $4B$, such an approximation is impossible. To our knowledge, these are the first anytime bounds at \textit{all} budgets. We test our algorithms on two real-world data-sets and evaluate them in terms of anytime linear prediction performance against cost-weighted Group Lasso and alternative greedy algorithms. | Efficient Feature Group Sequencing for Anytime Linear Prediction | 2,715 |
Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been extensively studied and well accepted by the scientific community, SSC algorithms are relatively new but gaining more attention in recent years due to better adaptability. In the paper, a comprehensive survey on existing SSC algorithms and the recent development are presented. The SSC algorithms are classified systematically into three main categories, namely, conventional SSC (CSSC), independent SSC (ISSC) and extended SSC (XSSC). The characteristics of these algorithms are highlighted and the potential future development of SSC is also discussed. | A Survey on Soft Subspace Clustering | 2,716 |
The traditional prototype based clustering methods, such as the well-known fuzzy c-mean (FCM) algorithm, usually need sufficient data to find a good clustering partition. If the available data is limited or scarce, most of the existing prototype based clustering algorithms will no longer be effective. While the data for the current clustering task may be scarce, there is usually some useful knowledge available in the related scenes/domains. In this study, the concept of transfer learning is applied to prototype based fuzzy clustering (PFC). Specifically, the idea of leveraging knowledge from the source domain is exploited to develop a set of transfer prototype based fuzzy clustering (TPFC) algorithms. Three prototype based fuzzy clustering algorithms, namely, FCM, fuzzy k-plane clustering (FKPC) and fuzzy subspace clustering (FSC), have been chosen to incorporate with knowledge leveraging mechanism to develop the corresponding transfer clustering algorithms. Novel objective functions are proposed to integrate the knowledge of source domain with the data of target domain for clustering in the target domain. The proposed algorithms have been validated on different synthetic and real-world datasets and the results demonstrate their effectiveness when compared with both the original prototype based fuzzy clustering algorithms and the related clustering algorithms like multi-task clustering and co-clustering. | Transfer Prototype-based Fuzzy Clustering | 2,717 |
This document discusses the Information Theoretically Efficient Model (ITEM), a computerized system to generate an information theoretically efficient multinomial logistic regression from a general dataset. More specifically, this model is designed to succeed even where the logit transform of the dependent variable is not necessarily linear in the independent variables. This research shows that for large datasets, the resulting models can be produced on modern computers in a tractable amount of time. These models are also resistant to overfitting, and as such they tend to produce interpretable models with only a limited number of features, all of which are designed to be well behaved. | The Information Theoretically Efficient Model (ITEM): A model for
computerized analysis of large datasets | 2,718 |
We study the best-arm identification problem in linear bandit, where the rewards of the arms depend linearly on an unknown parameter $\theta^*$ and the objective is to return the arm with the largest reward. We characterize the complexity of the problem and introduce sample allocation strategies that pull arms to identify the best arm with a fixed confidence, while minimizing the sample budget. In particular, we show the importance of exploiting the global linear structure to improve the estimate of the reward of near-optimal arms. We analyze the proposed strategies and compare their empirical performance. Finally, as a by-product of our analysis, we point out the connection to the $G$-optimality criterion used in optimal experimental design. | Best-Arm Identification in Linear Bandits | 2,719 |
By exploiting the duality between boosting and online learning, we present a boosting framework which proves to be extremely powerful thanks to employing the vast knowledge available in the online learning area. Using this framework, we develop various algorithms to address multiple practically and theoretically interesting questions including sparse boosting, smooth-distribution boosting, agnostic learning and some generalization to double-projection online learning algorithms, as a by-product. | A Boosting Framework on Grounds of Online Learning | 2,720 |
Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem there are two main issues that need to be addressed: (i) Finding an appropriate measure function than can be fairly fast and robustly computed for high-dimensional data. (ii) A search strategy to optimize the measure over the subset space in a reasonable amount of time. In this article mutual information between features and class labels is considered to be the measure function. Two series expansions for mutual information are proposed, and it is shown that most heuristic criteria suggested in the literature are truncated approximations of these expansions. It is well-known that searching the whole subset space is an NP-hard problem. Here, instead of the conventional sequential search algorithms, we suggest a parallel search strategy based on semidefinite programming (SDP) that can search through the subset space in polynomial time. By exploiting the similarities between the proposed algorithm and an instance of the maximum-cut problem in graph theory, the approximation ratio of this algorithm is derived and is compared with the approximation ratio of the backward elimination method. The experiments show that it can be misleading to judge the quality of a measure solely based on the classification accuracy, without taking the effect of the non-optimum search strategy into account. | A Semidefinite Programming Based Search Strategy for Feature Selection
with Mutual Information Measure | 2,721 |
In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reduc- ing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradi- ent descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization. | Maximum mutual information regularized classification | 2,722 |
In cognitive radio (CR) technology, the trend of sensing is no longer to only detect the presence of active primary users. A large number of applications demand for more comprehensive knowledge on primary user behaviors in spatial, temporal, and frequency domains. To satisfy such requirements, we study the statistical relationship among primary users by introducing a Bayesian network (BN) based framework. How to learn such a BN structure is a long standing issue, not fully understood even in the statistical learning community. Besides, another key problem in this learning scenario is that the CR has to identify how many variables are in the BN, which is usually considered as prior knowledge in statistical learning applications. To solve such two issues simultaneously, this paper proposes a BN structure learning scheme consisting of an efficient structure learning algorithm and a blind variable identification scheme. The proposed approach incurs significantly lower computational complexity compared with previous ones, and is capable of determining the structure without assuming much prior knowledge about variables. With this result, cognitive users could efficiently understand the statistical pattern of primary networks, such that more efficient cognitive protocols could be designed across different network layers. | Cognitive Learning of Statistical Primary Patterns via Bayesian Network | 2,723 |
Kernel-based approaches for sequence classification have been successfully applied to a variety of domains, including the text categorization, image classification, speech analysis, biological sequence analysis, time series and music classification, where they show some of the most accurate results. Typical kernel functions for sequences in these domains (e.g., bag-of-words, mismatch, or subsequence kernels) are restricted to {\em discrete univariate} (i.e. one-dimensional) string data, such as sequences of words in the text analysis, codeword sequences in the image analysis, or nucleotide or amino acid sequences in the DNA and protein sequence analysis. However, original sequence data are often of real-valued multivariate nature, i.e. are not univariate and discrete as required by typical $k$-mer based sequence kernel functions. In this work, we consider the problem of the {\em multivariate} sequence classification such as classification of multivariate music sequences, or multidimensional protein sequence representations. To this end, we extend {\em univariate} kernel functions typically used in sequence analysis and propose efficient {\em multivariate} similarity kernel method (MVDFQ-SK) based on (1) a direct feature quantization (DFQ) of each sequence dimension in the original {\em real-valued} multivariate sequences and (2) applying novel multivariate discrete kernel measures on these multivariate discrete DFQ sequence representations to more accurately capture similarity relationships among sequences and improve classification performance. Experiments using the proposed MVDFQ-SK kernel method show excellent classification performance on three challenging music classification tasks as well as protein sequence classification with significant 25-40% improvements over univariate kernel methods and existing state-of-the-art sequence classification methods. | Efficient multivariate sequence classification | 2,724 |
The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials are used to estimate the Volterra kernels. Existing literature proposes algorithms for a fixed number of Volterra kernels, and Laguerre series. This paper presents a novel algorithm for generalized calculation of the finite order Volterra-Laguerre (VL) series for a MIMO system. An example addresses the utility of the algorithm in practical application. | Generalized Laguerre Reduction of the Volterra Kernel for Practical
Identification of Nonlinear Dynamic Systems | 2,725 |
We consider a setting where a system learns to rank a fixed set of $m$ items. The goal is produce good item rankings for users with diverse interests who interact online with the system for $T$ rounds. We consider a novel top-$1$ feedback model: at the end of each round, the relevance score for only the top ranked object is revealed. However, the performance of the system is judged on the entire ranked list. We provide a comprehensive set of results regarding learnability under this challenging setting. For PairwiseLoss and DCG, two popular ranking measures, we prove that the minimax regret is $\Theta(T^{2/3})$. Moreover, the minimax regret is achievable using an efficient strategy that only spends $O(m \log m)$ time per round. The same efficient strategy achieves $O(T^{2/3})$ regret for Precision@$k$. Surprisingly, we show that for normalized versions of these ranking measures, i.e., AUC, NDCG \& MAP, no online ranking algorithm can have sublinear regret. | Online Ranking with Top-1 Feedback | 2,726 |
Stochastic discriminative EM (sdEM) is an online-EM-type algorithm for discriminative training of probabilistic generative models belonging to the exponential family. In this work, we introduce and justify this algorithm as a stochastic natural gradient descent method, i.e. a method which accounts for the information geometry in the parameter space of the statistical model. We show how this learning algorithm can be used to train probabilistic generative models by minimizing different discriminative loss functions, such as the negative conditional log-likelihood and the Hinge loss. The resulting models trained by sdEM are always generative (i.e. they define a joint probability distribution) and, in consequence, allows to deal with missing data and latent variables in a principled way either when being learned or when making predictions. The performance of this method is illustrated by several text classification problems for which a multinomial naive Bayes and a latent Dirichlet allocation based classifier are learned using different discriminative loss functions. | Stochastic Discriminative EM | 2,727 |
Inthischapterwediscusshowtolearnanoptimalmanifoldpresentationto regularize nonegative matrix factorization (NMF) for data representation problems. NMF,whichtriestorepresentanonnegativedatamatrixasaproductoftwolowrank nonnegative matrices, has been a popular method for data representation due to its ability to explore the latent part-based structure of data. Recent study shows that lots of data distributions have manifold structures, and we should respect the manifold structure when the data are represented. Recently, manifold regularized NMF used a nearest neighbor graph to regulate the learning of factorization parameter matrices and has shown its advantage over traditional NMF methods for data representation problems. However, how to construct an optimal graph to present the manifold prop- erly remains a difficultproblem due to the graph modelselection, noisy features, and nonlinear distributed data. In this chapter, we introduce three effective methods to solve these problems of graph construction for manifold regularized NMF. Multiple graph learning is proposed to solve the problem of graph model selection, adaptive graph learning via feature selection is proposed to solve the problem of constructing a graph from noisy features, while multi-kernel learning-based graph construction is used to solve the problem of learning a graph from nonlinearly distributed data. | Learning manifold to regularize nonnegative matrix factorization | 2,728 |
Conditional random fields (CRFs) are usually specified by graphical models but in this paper we propose to use probabilistic logic programs and specify them generatively. Our intension is first to provide a unified approach to CRFs for complex modeling through the use of a Turing complete language and second to offer a convenient way of realizing generative-discriminative pairs in machine learning to compare generative and discriminative models and choose the best model. We implemented our approach as the D-PRISM language by modifying PRISM, a logic-based probabilistic modeling language for generative modeling, while exploiting its dynamic programming mechanism for efficient probability computation. We tested D-PRISM with logistic regression, a linear-chain CRF and a CRF-CFG and empirically confirmed their excellent discriminative performance compared to their generative counterparts, i.e.\ naive Bayes, an HMM and a PCFG. We also introduced new CRF models, CRF-BNCs and CRF-LCGs. They are CRF versions of Bayesian network classifiers and probabilistic left-corner grammars respectively and easily implementable in D-PRISM. We empirically showed that they outperform their generative counterparts as expected. | A Logic-based Approach to Generatively Defined Discriminative Modeling | 2,729 |
Sparse-Group Lasso (SGL) has been shown to be a powerful regression technique for simultaneously discovering group and within-group sparse patterns by using a combination of the $\ell_1$ and $\ell_2$ norms. However, in large-scale applications, the complexity of the regularizers entails great computational challenges. In this paper, we propose a novel Two-Layer Feature REduction method (TLFre) for SGL via a decomposition of its dual feasible set. The two-layer reduction is able to quickly identify the inactive groups and the inactive features, respectively, which are guaranteed to be absent from the sparse representation and can be removed from the optimization. Existing feature reduction methods are only applicable for sparse models with one sparsity-inducing regularizer. To our best knowledge, TLFre is the first one that is capable of dealing with multiple sparsity-inducing regularizers. Moreover, TLFre has a very low computational cost and can be integrated with any existing solvers. We also develop a screening method---called DPC (DecomPosition of Convex set)---for the nonnegative Lasso problem. Experiments on both synthetic and real data sets show that TLFre and DPC improve the efficiency of SGL and nonnegative Lasso by several orders of magnitude. | Two-Layer Feature Reduction for Sparse-Group Lasso via Decomposition of
Convex Sets | 2,730 |
The capacity of a learning machine is measured by its Vapnik-Chervonenkis dimension, and learning machines with a low VC dimension generalize better. It is well known that the VC dimension of SVMs can be very large or unbounded, even though they generally yield state-of-the-art learning performance. In this paper, we show how to learn a hyperplane regressor by minimizing an exact, or \boldmath{$\Theta$} bound on its VC dimension. The proposed approach, termed as the Minimal Complexity Machine (MCM) Regressor, involves solving a simple linear programming problem. Experimental results show, that on a number of benchmark datasets, the proposed approach yields regressors with error rates much less than those obtained with conventional SVM regresssors, while often using fewer support vectors. On some benchmark datasets, the number of support vectors is less than one tenth the number used by SVMs, indicating that the MCM does indeed learn simpler representations. | Learning a hyperplane regressor by minimizing an exact bound on the VC
dimension | 2,731 |
Naive Bayes classifiers, a family of classifiers that are based on the popular Bayes' probability theorem, are known for creating simple yet well performing models, especially in the fields of document classification and disease prediction. In this article, we will look at the main concepts of naive Bayes classification in the context of document categorization. | Naive Bayes and Text Classification I - Introduction and Theory | 2,732 |
In machine learning and pattern recognition, feature selection has been a hot topic in the literature. Unsupervised feature selection is challenging due to the loss of labels which would supply the related information.How to define an appropriate metric is the key for feature selection. We propose a filter method for unsupervised feature selection which is based on the Confidence Machine. Confidence Machine offers an estimation of confidence on a feature'reliability. In this paper, we provide the math model of Confidence Machine in the context of feature selection, which maximizes the relevance and minimizes the redundancy of the selected feature. We compare our method against classic feature selection methods Laplacian Score, Pearson Correlation and Principal Component Analysis on benchmark data sets. The experimental results demonstrate the efficiency and effectiveness of our method. | Feature Selection Based on Confidence Machine | 2,733 |
In this paper, we describe a new vector similarity measure associated with a convex cost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle between the two surface normals is the similarity measure. Convex cost function can be the negative entropy function, total variation (TV) function and filtered variation function. The convex cost function need not be differentiable everywhere. In general, we need to compute the gradient of the cost function to compute the surface normals. If the gradient does not exist at a given vector, it is possible to use the subgradients and the normal producing the smallest angle between the two vectors is used to compute the similarity measure. | Cosine Similarity Measure According to a Convex Cost Function | 2,734 |
We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is not yet well-understood. In this paper we provide strong theoretical guarantees regarding learning with random decision trees. We analyze and compare three different variants of the algorithm that have minimal memory requirements: majority voting, threshold averaging and probabilistic averaging. The random structure of the tree enables us to adapt these methods to a differentially-private setting thus we also propose differentially-private versions of all three schemes. We give upper-bounds on the generalization error and mathematically explain how the accuracy depends on the number of random decision trees. Furthermore, we prove that only logarithmic (in the size of the dataset) number of independently selected random decision trees suffice to correctly classify most of the data, even when differential-privacy guarantees must be maintained. We empirically show that majority voting and threshold averaging give the best accuracy, also for conservative users requiring high privacy guarantees. Furthermore, we demonstrate that a simple majority voting rule is an especially good candidate for the differentially-private classifier since it is much less sensitive to the choice of forest parameters than other methods. | Differentially- and non-differentially-private random decision trees | 2,735 |
In this paper, we compare three initialization schemes for the KMEANS clustering algorithm: 1) random initialization (KMEANSRAND), 2) KMEANS++, and 3) KMEANSD++. Both KMEANSRAND and KMEANS++ have a major that the value of k needs to be set by the user of the algorithms. (Kang 2013) recently proposed a novel use of determinantal point processes for sampling the initial centroids for the KMEANS algorithm (we call it KMEANSD++). They, however, do not provide any evaluation establishing that KMEANSD++ is better than other algorithms. In this paper, we show that the performance of KMEANSD++ is comparable to KMEANS++ (both of which are better than KMEANSRAND) with KMEANSD++ having an additional that it can automatically approximate the value of k. | Notes on using Determinantal Point Processes for Clustering with
Applications to Text Clustering | 2,736 |
Feature selection involes identifying the most relevant subset of input features, with a view to improving generalization of predictive models by reducing overfitting. Directly searching for the most relevant combination of attributes is NP-hard. Variable selection is of critical importance in many applications, such as micro-array data analysis, where selecting a small number of discriminative features is crucial to developing useful models of disease mechanisms, as well as for prioritizing targets for drug discovery. The recently proposed Minimal Complexity Machine (MCM) provides a way to learn a hyperplane classifier by minimizing an exact (\boldmath{$\Theta$}) bound on its VC dimension. It is well known that a lower VC dimension contributes to good generalization. For a linear hyperplane classifier in the input space, the VC dimension is upper bounded by the number of features; hence, a linear classifier with a small VC dimension is parsimonious in the set of features it employs. In this paper, we use the linear MCM to learn a classifier in which a large number of weights are zero; features with non-zero weights are the ones that are chosen. Selected features are used to learn a kernel SVM classifier. On a number of benchmark datasets, the features chosen by the linear MCM yield comparable or better test set accuracy than when methods such as ReliefF and FCBF are used for the task. The linear MCM typically chooses one-tenth the number of attributes chosen by the other methods; on some very high dimensional datasets, the MCM chooses about $0.6\%$ of the features; in comparison, ReliefF and FCBF choose 70 to 140 times more features, thus demonstrating that minimizing the VC dimension may provide a new, and very effective route for feature selection and for learning sparse representations. | Feature Selection through Minimization of the VC dimension | 2,737 |
A Relational Dependency Network (RDN) is a directed graphical model widely used for multi-relational data. These networks allow cyclic dependencies, necessary to represent relational autocorrelations. We describe an approach for learning both the RDN's structure and its parameters, given an input relational database: First learn a Bayesian network (BN), then transform the Bayesian network to an RDN. Thus fast Bayes net learning can provide fast RDN learning. The BN-to-RDN transform comprises a simple, local adjustment of the Bayes net structure and a closed-form transform of the Bayes net parameters. This method can learn an RDN for a dataset with a million tuples in minutes. We empirically compare our approach to state-of-the art RDN learning methods that use functional gradient boosting, on five benchmark datasets. Learning RDNs via BNs scales much better to large datasets than learning RDNs with boosting, and provides competitive accuracy in predictions. | Fast Learning of Relational Dependency Networks | 2,738 |
Standard Multi-Armed Bandit (MAB) problems assume that the arms are independent. However, in many application scenarios, the information obtained by playing an arm provides information about the remainder of the arms. Hence, in such applications, this informativeness can and should be exploited to enable faster convergence to the optimal solution. In this paper, we introduce and formalize the Global MAB (GMAB), in which arms are globally informative through a global parameter, i.e., choosing an arm reveals information about all the arms. We propose a greedy policy for the GMAB which always selects the arm with the highest estimated expected reward, and prove that it achieves bounded parameter-dependent regret. Hence, this policy selects suboptimal arms only finitely many times, and after a finite number of initial time steps, the optimal arm is selected in all of the remaining time steps with probability one. In addition, we also study how the informativeness of the arms about each other's rewards affects the speed of learning. Specifically, we prove that the parameter-free (worst-case) regret is sublinear in time, and decreases with the informativeness of the arms. We also prove a sublinear in time Bayesian risk bound for the GMAB which reduces to the well-known Bayesian risk bound for linearly parameterized bandits when the arms are fully informative. GMABs have applications ranging from drug and treatment discovery to dynamic pricing. | Global Bandits with Holder Continuity | 2,739 |
Estimating the parameters of probabilistic models of language such as maxent models and probabilistic neural models is computationally difficult since it involves evaluating partition functions by summing over an entire vocabulary, which may be millions of word types in size. Two closely related strategies---noise contrastive estimation (Mnih and Teh, 2012; Mnih and Kavukcuoglu, 2013; Vaswani et al., 2013) and negative sampling (Mikolov et al., 2012; Goldberg and Levy, 2014)---have emerged as popular solutions to this computational problem, but some confusion remains as to which is more appropriate and when. This document explicates their relationships to each other and to other estimation techniques. The analysis shows that, although they are superficially similar, NCE is a general parameter estimation technique that is asymptotically unbiased, while negative sampling is best understood as a family of binary classification models that are useful for learning word representations but not as a general-purpose estimator. | Notes on Noise Contrastive Estimation and Negative Sampling | 2,740 |
We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables. We parametrize this transformation so that computing the Jacobian determinant and inverse transform is trivial, yet we maintain the ability to learn complex non-linear transformations, via a composition of simple building blocks, each based on a deep neural network. The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy. We show that this approach yields good generative models on four image datasets and can be used for inpainting. | NICE: Non-linear Independent Components Estimation | 2,741 |
This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this problem do not have theoretical guarantees and can get stuck in bad local optima. We present the first polynomial time algorithm which provably learns the parameters of a mixture of two Mallows models. A key component of our algorithm is a novel use of tensor decomposition techniques to learn the top-k prefix in both the rankings. Before this work, even the question of identifiability in the case of a mixture of two Mallows models was unresolved. | Learning Mixtures of Ranking Models | 2,742 |
We present Factorbird, a prototype of a parameter server approach for factorizing large matrices with Stochastic Gradient Descent-based algorithms. We designed Factorbird to meet the following desiderata: (a) scalability to tall and wide matrices with dozens of billions of non-zeros, (b) extensibility to different kinds of models and loss functions as long as they can be optimized using Stochastic Gradient Descent (SGD), and (c) adaptability to both batch and streaming scenarios. Factorbird uses a parameter server in order to scale to models that exceed the memory of an individual machine, and employs lock-free Hogwild!-style learning with a special partitioning scheme to drastically reduce conflicting updates. We also discuss other aspects of the design of our system such as how to efficiently grid search for hyperparameters at scale. We present experiments of Factorbird on a matrix built from a subset of Twitter's interaction graph, consisting of more than 38 billion non-zeros and about 200 million rows and columns, which is to the best of our knowledge the largest matrix on which factorization results have been reported in the literature. | Factorbird - a Parameter Server Approach to Distributed Matrix
Factorization | 2,743 |
CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they need an access to the {\it full} matrix, a requirement that can be difficult to fulfill in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only $O(n r\ln r)$ observed entries are needed by the proposed algorithm to perfectly recover a rank $r$ matrix of size $n\times n$, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm. | CUR Algorithm for Partially Observed Matrices | 2,744 |
The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely orthogonal tensor decompositions, Independent Component Analysis (ICA), topic models, spectral clustering, and Gaussian mixture learning---we generalize the eigendecomposition from quadratic forms to a broad class of "orthogonally decomposable" functions. We identify a key role of convexity in our extension, and we generalize two traditional characterizations of eigenvectors: First, the eigenvectors of a quadratic form arise from the optima structure of the quadratic form on the sphere. Second, the eigenvectors are the fixed points of the power iteration. In our setting, we consider a simple first order generalization of the power method which we call gradient iteration. It leads to efficient and easily implementable methods for basis recovery. It includes influential Machine Learning methods such as cumulant-based FastICA and the tensor power iteration for orthogonally decomposable tensors as special cases. We provide a complete theoretical analysis of gradient iteration using the structure theory of discrete dynamical systems to show almost sure convergence and fast (super-linear) convergence rates. The analysis also extends to the case when the observed function is only approximately orthogonally decomposable, with bounds that are polynomial in dimension and other relevant parameters, such as perturbation size. Our perturbation results can be considered as a non-linear version of the classical Davis-Kahan theorem for perturbations of eigenvectors of symmetric matrices. | Eigenvectors of Orthogonally Decomposable Functions | 2,745 |
We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d samples. While there have been recent results for specific graph classes, these involve fairly extensive technical arguments that are specialized to each specific graph class. In contrast, we isolate two key graph-structural ingredients that can then be used to specify sample complexity lower-bounds. Presence of these structural properties makes the graph class hard to learn. We derive corollaries of our main result that not only recover existing recent results, but also provide lower bounds for novel graph classes not considered previously. We also extend our framework to the random graph setting and derive corollaries for Erd\H{o}s-R\'{e}nyi graphs in a certain dense setting. | On the Information Theoretic Limits of Learning Ising Models | 2,746 |
It has been a long-standing goal in machine learning, as well as in AI more generally, to develop life-long learning systems that learn many different tasks over time, and reuse insights from tasks learned, "learning to learn" as they do so. In this work we pose and provide efficient algorithms for several natural theoretical formulations of this goal. Specifically, we consider the problem of learning many different target functions over time, that share certain commonalities that are initially unknown to the learning algorithm. Our aim is to learn new internal representations as the algorithm learns new target functions, that capture this commonality and allow subsequent learning tasks to be solved more efficiently and from less data. We develop efficient algorithms for two very different kinds of commonalities that target functions might share: one based on learning common low-dimensional and unions of low-dimensional subspaces and one based on learning nonlinear Boolean combinations of features. Our algorithms for learning Boolean feature combinations additionally have a dual interpretation, and can be viewed as giving an efficient procedure for constructing near-optimal sparse Boolean autoencoders under a natural "anchor-set" assumption. | Efficient Representations for Life-Long Learning and Autoencoding | 2,747 |
We investigate the problem of incorporating higher-level symbolic score-like information into Automatic Music Transcription (AMT) systems to improve their performance. We use recurrent neural networks (RNNs) and their variants as music language models (MLMs) and present a generative architecture for combining these models with predictions from a frame level acoustic classifier. We also compare different neural network architectures for acoustic modeling. The proposed model computes a distribution over possible output sequences given the acoustic input signal and we present an algorithm for performing a global search for good candidate transcriptions. The performance of the proposed model is evaluated on piano music from the MAPS dataset and we observe that the proposed model consistently outperforms existing transcription methods. | A Hybrid Recurrent Neural Network For Music Transcription | 2,748 |
A common phenomena in modern recommendation systems is the use of feedback from one user to infer the `value' of an item to other users. This results in an exploration vs. exploitation trade-off, in which items of possibly low value have to be presented to users in order to ascertain their value. Existing approaches to solving this problem focus on the case where the number of items are small, or admit some underlying structure -- it is unclear, however, if good recommendation is possible when dealing with content-rich settings with unstructured content. We consider this problem under a simple natural model, wherein the number of items and the number of item-views are of the same order, and an `access-graph' constrains which user is allowed to see which item. Our main insight is that the presence of the access-graph in fact makes good recommendation possible -- however this requires the exploration policy to be designed to take advantage of the access-graph. Our results demonstrate the importance of `serendipity' in exploration, and how higher graph-expansion translates to a higher quality of recommendations; it also suggests a reason why in some settings, simple policies like Twitter's `Latest-First' policy achieve a good performance. From a technical perspective, our model presents a way to study exploration-exploitation tradeoffs in settings where the number of `trials' and `strategies' are large (potentially infinite), and more importantly, of the same order. Our algorithms admit competitive-ratio guarantees which hold for the worst-case user, under both finite-population and infinite-horizon settings, and are parametrized in terms of properties of the underlying graph. Conversely, we also demonstrate that improperly-designed policies can be highly sub-optimal, and that in many settings, our results are order-wise optimal. | Online Collaborative-Filtering on Graphs | 2,749 |
The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear transformations or the analysis of learning algorithms whenever hypotheses are chosen from composite classes, as is the case for multi-layer models. | A chain rule for the expected suprema of Gaussian processes | 2,750 |
We study a new type of K-armed bandit problem where the expected return of one arm may depend on the returns of other arms. We present a new algorithm for this general class of problems and show that under certain circumstances it is possible to achieve finite expected cumulative regret. We also give problem-dependent lower bounds on the cumulative regret showing that at least in special cases the new algorithm is nearly optimal. | Bounded Regret for Finite-Armed Structured Bandits | 2,751 |
Orthogonal greedy learning (OGL) is a stepwise learning scheme that adds a new atom from a dictionary via the steepest gradient descent and build the estimator via orthogonal projecting the target function to the space spanned by the selected atoms in each greedy step. Here, "greed" means choosing a new atom according to the steepest gradient descent principle. OGL then avoids the overfitting/underfitting by selecting an appropriate iteration number. In this paper, we point out that the overfitting/underfitting can also be avoided via redefining "greed" in OGL. To this end, we introduce a new greedy metric, called $\delta$-greedy thresholds, to refine "greed" and theoretically verifies its feasibility. Furthermore, we reveals that such a greedy metric can bring an adaptive termination rule on the premise of maintaining the prominent learning performance of OGL. Our results show that the steepest gradient descent is not the unique greedy metric of OGL and some other more suitable metric may lessen the hassle of model-selection of OGL. | Greedy metrics in orthogonal greedy learning | 2,752 |
Consider a stationary discrete random process with alphabet size d, which is assumed to be the output process of an unknown stationary Hidden Markov Model (HMM). Given the joint probabilities of finite length strings of the process, we are interested in finding a finite state generative model to describe the entire process. In particular, we focus on two classes of models: HMMs and quasi-HMMs, which is a strictly larger class of models containing HMMs. In the main theorem, we show that if the random process is generated by an HMM of order less or equal than k, and whose transition and observation probability matrix are in general position, namely almost everywhere on the parameter space, both the minimal quasi-HMM realization and the minimal HMM realization can be efficiently computed based on the joint probabilities of all the length N strings, for N > 4 lceil log_d(k) rceil +1. In this paper, we also aim to compare and connect the two lines of literature: realization theory of HMMs, and the recent development in learning latent variable models with tensor decomposition techniques. | Minimal Realization Problems for Hidden Markov Models | 2,753 |
Clinical trial adaptation refers to any adjustment of the trial protocol after the onset of the trial. The main goal is to make the process of introducing new medical interventions to patients more efficient by reducing the cost and the time associated with evaluating their safety and efficacy. The principal question is how should adaptation be performed so as to minimize the chance of distorting the outcome of the trial. We propose a novel method for achieving this. Unlike previous work our approach focuses on trial adaptation by sample size adjustment. We adopt a recently proposed stratification framework based on collected auxiliary data and show that this information together with the primary measured variables can be used to make a probabilistically informed choice of the particular sub-group a sample should be removed from. Experiments on simulated data are used to illustrate the effectiveness of our method and its application in practice. | Sample-targeted clinical trial adaptation | 2,754 |
An important use of private data is to build machine learning classifiers. While there is a burgeoning literature on differentially private classification algorithms, we find that they are not practical in real applications due to two reasons. First, existing differentially private classifiers provide poor accuracy on real world datasets. Second, there is no known differentially private algorithm for empirically evaluating the private classifier on a private test dataset. In this paper, we develop differentially private algorithms that mirror real world empirical machine learning workflows. We consider the private classifier training algorithm as a blackbox. We present private algorithms for selecting features that are input to the classifier. Though adding a preprocessing step takes away some of the privacy budget from the actual classification process (thus potentially making it noisier and less accurate), we show that our novel preprocessing techniques significantly increase classifier accuracy on three real-world datasets. We also present the first private algorithms for empirically constructing receiver operating characteristic (ROC) curves on a private test set. | Differentially Private Algorithms for Empirical Machine Learning | 2,755 |
In the convex optimization approach to online regret minimization, many methods have been developed to guarantee a $O(\sqrt{T})$ bound on regret for subdifferentiable convex loss functions with bounded subgradients, by using a reduction to linear loss functions. This suggests that linear loss functions tend to be the hardest ones to learn against, regardless of the underlying decision spaces. We investigate this question in a systematic fashion looking at the interplay between the set of possible moves for both the decision maker and the adversarial environment. This allows us to highlight sharp distinctive behaviors about the learnability of piecewise linear loss functions. On the one hand, when the decision set of the decision maker is a polyhedron, we establish $\Omega(\sqrt{T})$ lower bounds on regret for a large class of piecewise linear loss functions with important applications in online linear optimization, repeated zero-sum Stackelberg games, online prediction with side information, and online two-stage optimization. On the other hand, we exhibit $o(\sqrt{T})$ learning rates, achieved by the Follow-The-Leader algorithm, in online linear optimization when the boundary of the decision maker's decision set is curved and when $0$ does not lie in the convex hull of the environment's decision set. Hence, the curvature of the decision maker's decision set is a determining factor for the optimal learning rate. These results hold in a completely adversarial setting. | No-Regret Learnability for Piecewise Linear Losses | 2,756 |
In many real-world applications, data are represented by matrices or high-order tensors. Despite the promising performance, the existing two-dimensional discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection, making the model less flexible. In this paper, we propose a novel Compound Rank-k Projection (CRP) algorithm for bilinear analysis. CRP deals with matrices directly without transforming them into vectors, and it therefore preserves the correlations within the matrix and decreases the computation complexity. Different from the existing two dimensional discriminant analysis algorithms, objective function values of CRP increase monotonically.In addition, CRP utilizes multiple rank-k projection models to enable a larger search space in which the optimal solution can be found. In this way, the discriminant ability is enhanced. | Compound Rank-k Projections for Bilinear Analysis | 2,757 |
In this paper, we propose a novel semi-supervised feature selection framework by mining correlations among multiple tasks and apply it to different multimedia applications. Instead of independently computing the importance of features for each task, our algorithm leverages shared knowledge from multiple related tasks, thus, improving the performance of feature selection. Note that we build our algorithm on assumption that different tasks share common structures. The proposed algorithm selects features in a batch mode, by which the correlations between different features are taken into consideration. Besides, considering the fact that labeling a large amount of training data in real world is both time-consuming and tedious, we adopt manifold learning which exploits both labeled and unlabeled training data for feature space analysis. Since the objective function is non-smooth and difficult to solve, we propose an iterative algorithm with fast convergence. Extensive experiments on different applications demonstrate that our algorithm outperforms other state-of-the-art feature selection algorithms. | Semi-supervised Feature Analysis by Mining Correlations among Multiple
Tasks | 2,758 |
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections of the original variables to obtain a low dimensional feature representation with maximal variance. One limitation is that it is very difficult to interpret the results of PCA. In addition, the classical PCA is vulnerable to certain noisy data. In this paper, we propose a convex sparse principal component analysis (CSPCA) algorithm and apply it to feature analysis. First we show that PCA can be formulated as a low-rank regression optimization problem. Based on the discussion, the l 2 , 1 -norm minimization is incorporated into the objective function to make the regression coefficients sparse, thereby robust to the outliers. In addition, based on the sparse model used in CSPCA, an optimal weight is assigned to each of the original feature, which in turn provides the output with good interpretability. With the output of our CSPCA, we can effectively analyze the importance of each feature under the PCA criteria. The objective function is convex, and we propose an iterative algorithm to optimize it. We apply the CSPCA algorithm to feature selection and conduct extensive experiments on six different benchmark datasets. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art unsupervised feature selection algorithms. | A Convex Sparse PCA for Feature Analysis | 2,759 |
Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their simplicity and efficacy. The classical k-means algorithm partitions a number of data points into several subsets by iteratively updating the clustering centers and the associated data points. By contrast, a weighted undirected graph is constructed in min-cut algorithms which partition the vertices of the graph into two sets. However, existing clustering algorithms tend to cluster minority of data points into a subset, which shall be avoided when the target dataset is balanced. To achieve more accurate clustering for balanced dataset, we propose to leverage exclusive lasso on k-means and min-cut to regulate the balance degree of the clustering results. By optimizing our objective functions that build atop the exclusive lasso, we can make the clustering result as much balanced as possible. Extensive experiments on several large-scale datasets validate the advantage of the proposed algorithms compared to the state-of-the-art clustering algorithms. | Balanced k-Means and Min-Cut Clustering | 2,760 |
Spectral clustering is a key research topic in the field of machine learning and data mining. Most of the existing spectral clustering algorithms are built upon Gaussian Laplacian matrices, which are sensitive to parameters. We propose a novel parameter free, distance consistent Locally Linear Embedding. The proposed distance consistent LLE promises that edges between closer data points have greater weight.Furthermore, we propose a novel improved spectral clustering via embedded label propagation. Our algorithm is built upon two advancements of the state of the art:1) label propagation,which propagates a node\'s labels to neighboring nodes according to their proximity; and 2) manifold learning, which has been widely used in its capacity to leverage the manifold structure of data points. First we perform standard spectral clustering on original data and assign each cluster to k nearest data points. Next, we propagate labels through dense, unlabeled data regions. Extensive experiments with various datasets validate the superiority of the proposed algorithm compared to current state of the art spectral algorithms. | Improved Spectral Clustering via Embedded Label Propagation | 2,761 |
While there are many studies on weight regularization, the study on structure regularization is rare. Many existing systems on structured prediction focus on increasing the level of structural dependencies within the model. However, this trend could have been misdirected, because our study suggests that complex structures are actually harmful to generalization ability in structured prediction. To control structure-based overfitting, we propose a structure regularization framework via \emph{structure decomposition}, which decomposes training samples into mini-samples with simpler structures, deriving a model with better generalization power. We show both theoretically and empirically that structure regularization can effectively control overfitting risk and lead to better accuracy. As a by-product, the proposed method can also substantially accelerate the training speed. The method and the theoretical results can apply to general graphical models with arbitrary structures. Experiments on well-known tasks demonstrate that our method can easily beat the benchmark systems on those highly-competitive tasks, achieving state-of-the-art accuracies yet with substantially faster training speed. | Structure Regularization for Structured Prediction: Theories and
Experiments | 2,762 |
We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previously best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous state of the art and show a consistent exponential improvement in several different scenarios. | Revenue Optimization in Posted-Price Auctions with Strategic Buyers | 2,763 |
Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning in the original space. However, the manifold in reduced-dimensional subspace is likely to exhibit altered properties in contrast with the original space. Thus, applying manifold information obtained from the original space to the clustering process in a low-dimensional subspace is prone to inferior performance. Aiming to address this issue, we propose a novel convex algorithm that mines the manifold structure in the low-dimensional subspace. In addition, our unified learning process makes the manifold learning particularly tailored for the clustering. Compared with other related methods, the proposed algorithm results in more structured clustering result. To validate the efficacy of the proposed algorithm, we perform extensive experiments on several benchmark datasets in comparison with some state-of-the-art clustering approaches. The experimental results demonstrate that the proposed algorithm has quite promising clustering performance. | A Convex Formulation for Spectral Shrunk Clustering | 2,764 |
The growing amount of high dimensional data in different machine learning applications requires more efficient and scalable optimization algorithms. In this work, we consider combining two techniques, parallelism and Nesterov's acceleration, to design faster algorithms for L1-regularized loss. We first simplify BOOM, a variant of gradient descent, and study it in a unified framework, which allows us to not only propose a refined measurement of sparsity to improve BOOM, but also show that BOOM is provably slower than FISTA. Moving on to parallel coordinate descent methods, we then propose an efficient accelerated version of Shotgun, improving the convergence rate from $O(1/t)$ to $O(1/t^2)$. Our algorithm enjoys a concise form and analysis compared to previous work, and also allows one to study several connected work in a unified way. | Accelerated Parallel Optimization Methods for Large Scale Machine
Learning | 2,765 |
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case viewpoint, which is in general more robust for classification. However, the original problem of WLDA is non-convex and difficult to optimize. In this paper, we reformulate the optimization problem of WLDA into a sequence of semidefinite feasibility problems. To efficiently solve the semidefinite feasibility problems, we design a new scalable optimization method with quasi-Newton methods and eigen-decomposition being the core components. The proposed method is orders of magnitude faster than standard interior-point based SDP solvers. Experiments on a variety of classification problems demonstrate that our approach achieves better performance than standard LDA. Our method is also much faster and more scalable than standard interior-point SDP solvers based WLDA. The computational complexity for an SDP with $m$ constraints and matrices of size $d$ by $d$ is roughly reduced from $\mathcal{O}(m^3+md^3+m^2d^2)$ to $\mathcal{O}(d^3)$ ($m>d$ in our case). | Worst-Case Linear Discriminant Analysis as Scalable Semidefinite
Feasibility Problems | 2,766 |
This report discusses two new indices for comparing clusterings of a set of points. The motivation for looking at new ways for comparing clusterings stems from the fact that the existing clustering indices are based on set cardinality alone and do not consider the positions of data points. The new indices, namely, the Random Walk index (RWI) and Variation of Information with Neighbors (VIN), are both inspired by the clustering metric Variation of Information (VI). VI possesses some interesting theoretical properties which are also desirable in a metric for comparing clusterings. We define our indices and discuss some of their explored properties which appear relevant for a clustering index. We also include the results of these indices on clusterings of some example data sets. | Graph Sensitive Indices for Comparing Clusterings | 2,767 |
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity caused by the factorization model, there is a limited theoretical understanding of this formulation. In this paper, we establish a theoretical guarantee for the factorization formulation to correctly recover the underlying low-rank matrix. In particular, we show that under similar conditions to those in previous works, many standard optimization algorithms converge to the global optima of a factorization formulation, and recover the true low-rank matrix. We study the local geometry of a properly regularized factorization formulation and prove that any stationary point in a certain local region is globally optimal. A major difference of our work from the existing results is that we do not need resampling in either the algorithm or its analysis. Compared to other works on nonconvex optimization, one extra difficulty lies in analyzing nonconvex constrained optimization when the constraint (or the corresponding regularizer) is not "consistent" with the gradient direction. One technical contribution is the perturbation analysis for non-symmetric matrix factorization. | Guaranteed Matrix Completion via Non-convex Factorization | 2,768 |
We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable independence, ii) redundancy in network parametrization, and iii) uniformity. These assumptions enable us to explain the complexity of the fully decoupled neural network through the prism of the results from random matrix theory. We show that for large-size decoupled networks the lowest critical values of the random loss function form a layered structure and they are located in a well-defined band lower-bounded by the global minimum. The number of local minima outside that band diminishes exponentially with the size of the network. We empirically verify that the mathematical model exhibits similar behavior as the computer simulations, despite the presence of high dependencies in real networks. We conjecture that both simulated annealing and SGD converge to the band of low critical points, and that all critical points found there are local minima of high quality measured by the test error. This emphasizes a major difference between large- and small-size networks where for the latter poor quality local minima have non-zero probability of being recovered. Finally, we prove that recovering the global minimum becomes harder as the network size increases and that it is in practice irrelevant as global minimum often leads to overfitting. | The Loss Surfaces of Multilayer Networks | 2,769 |
Optunity is a free software package dedicated to hyperparameter optimization. It contains various types of solvers, ranging from undirected methods to direct search, particle swarm and evolutionary optimization. The design focuses on ease of use, flexibility, code clarity and interoperability with existing software in all machine learning environments. Optunity is written in Python and contains interfaces to environments such as R and MATLAB. Optunity uses a BSD license and is freely available online at http://www.optunity.net. | Easy Hyperparameter Search Using Optunity | 2,770 |
In this work we consider the learning setting where, in addition to the training set, the learner receives a collection of auxiliary hypotheses originating from other tasks. We focus on a broad class of ERM-based linear algorithms that can be instantiated with any non-negative smooth loss function and any strongly convex regularizer. We establish generalization and excess risk bounds, showing that, if the algorithm is fed with a good combination of source hypotheses, generalization happens at the fast rate $\mathcal{O}(1/m)$ instead of the usual $\mathcal{O}(1/\sqrt{m})$. On the other hand, if the source hypotheses combination is a misfit for the target task, we recover the usual learning rate. As a byproduct of our study, we also prove a new bound on the Rademacher complexity of the smooth loss class under weaker assumptions compared to previous works. | Fast Rates by Transferring from Auxiliary Hypotheses | 2,771 |
The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster centers required. To reduce the number of input points we could average the points locally and use the means or the local centers as the input for clustering. However since the required number of local centers is very high, running the clustering algorithm on the entire dataset to obtain these representational points is very time consuming. To remedy this problem, in this paper we are proposing two subclustering schemes where by we subdivide the dataset into smaller sets and run the clustering algorithm on the smaller datasets to obtain the required number of datapoints to run our clustering algorithm with. As we are subdividing the given dataset, we could run clustering algorithm on each smaller piece of the dataset in parallel. We found that both parallel and serial execution of this method to be much faster than the original clustering algorithm and error in running the clustering algorithm on a reduced set to be very less. | A parallel sampling based clustering | 2,772 |
In this paper, we theoretically justify an approach popular among participants of the Higgs Boson Machine Learning Challenge to optimize approximate median significance (AMS). The approach is based on the following two-stage procedure. First, a real-valued function is learned by minimizing a surrogate loss for binary classification, such as logistic loss, on the training sample. Then, a threshold is tuned on a separate validation sample, by direct optimization of AMS. We show that the regret of the resulting (thresholded) classifier measured with respect to the squared AMS, is upperbounded by the regret of the underlying real-valued function measured with respect to the logistic loss. Hence, we prove that minimizing logistic surrogate is a consistent method of optimizing AMS. | Consistent optimization of AMS by logistic loss minimization | 2,773 |
In this report, we describe a Theano-based AlexNet (Krizhevsky et al., 2012) implementation and its naive data parallelism on multiple GPUs. Our performance on 2 GPUs is comparable with the state-of-art Caffe library (Jia et al., 2014) run on 1 GPU. To the best of our knowledge, this is the first open-source Python-based AlexNet implementation to-date. | Theano-based Large-Scale Visual Recognition with Multiple GPUs | 2,774 |
A widely-used tool for binary classification is the Support Vector Machine (SVM), a supervised learning technique that finds the "maximum margin" linear separator between the two classes. While SVMs have been well studied in the batch (offline) setting, there is considerably less work on the streaming (online) setting, which requires only a single pass over the data using sub-linear space. Existing streaming algorithms are not yet competitive with the batch implementation. In this paper, we use the formulation of the SVM as a minimum enclosing ball (MEB) problem to provide a streaming SVM algorithm based off of the blurred ball cover originally proposed by Agarwal and Sharathkumar. Our implementation consistently outperforms existing streaming SVM approaches and provides higher accuracies than libSVM on several datasets, thus making it competitive with the standard SVM batch implementation. | Accurate Streaming Support Vector Machines | 2,775 |
Deep learning has attracted great attention recently and yielded the state of the art performance in dimension reduction and classification problems. However, it cannot effectively handle the structured output prediction, e.g. sequential labeling. In this paper, we propose a deep learning structure, which can learn discriminative features for sequential labeling problems. More specifically, we add the inter-relationship between labels in our deep learning structure, in order to incorporate the context information from the sequential data. Thus, our model is more powerful than linear Conditional Random Fields (CRFs) because the objective function learns latent non-linear features so that target labeling can be better predicted. We pretrain the deep structure with stacked restricted Boltzmann machines (RBMs) for feature learning and optimize our objective function with online learning algorithm, a mixture of perceptron training and stochastic gradient descent. We test our model on different challenge tasks, and show that our model outperforms significantly over the completive baselines. | Sequential Labeling with online Deep Learning | 2,776 |
The purpose of this report is in examining the generalization performance of Support Vector Machines (SVM) as a tool for pattern recognition and object classification. The work is motivated by the growing popularity of the method that is claimed to guarantee a good generalization performance for the task in hand. The method is implemented in MATLAB. SVMs based on various kernels are tested for classifying data from various domains. | An Evaluation of Support Vector Machines as a Pattern Recognition Tool | 2,777 |
In this paper, we propose a new max-margin based discriminative feature learning method. Specifically, we aim at learning a low-dimensional feature representation, so as to maximize the global margin of the data and make the samples from the same class as close as possible. In order to enhance the robustness to noise, a $l_{2,1}$ norm constraint is introduced to make the transformation matrix in group sparsity. In addition, for multi-class classification tasks, we further intend to learn and leverage the correlation relationships among multiple class tasks for assisting in learning discriminative features. The experimental results demonstrate the power of the proposed method against the related state-of-the-art methods. | Max-Margin based Discriminative Feature Learning | 2,778 |
We consider learning from data of variable quality that may be obtained from different heterogeneous sources. Addressing learning from heterogeneous data in its full generality is a challenging problem. In this paper, we adopt instead a model in which data is observed through heterogeneous noise, where the noise level reflects the quality of the data source. We study how to use stochastic gradient algorithms to learn in this model. Our study is motivated by two concrete examples where this problem arises naturally: learning with local differential privacy based on data from multiple sources with different privacy requirements, and learning from data with labels of variable quality. The main contribution of this paper is to identify how heterogeneous noise impacts performance. We show that given two datasets with heterogeneous noise, the order in which to use them in standard SGD depends on the learning rate. We propose a method for changing the learning rate as a function of the heterogeneity, and prove new regret bounds for our method in two cases of interest. Experiments on real data show that our method performs better than using a single learning rate and using only the less noisy of the two datasets when the noise level is low to moderate. | Learning from Data with Heterogeneous Noise using SGD | 2,779 |
Online multiple-output regression is an important machine learning technique for modeling, predicting, and compressing multi-dimensional correlated data streams. In this paper, we propose a novel online multiple-output regression method, called MORES, for stream data. MORES can \emph{dynamically} learn the structure of the coefficients change in each update step to facilitate the model's continuous refinement. We observe that limited expressive ability of the regression model, especially in the preliminary stage of online update, often leads to the variables in the residual errors being dependent. In light of this point, MORES intends to \emph{dynamically} learn and leverage the structure of the residual errors to improve the prediction accuracy. Moreover, we define three statistical variables to \emph{exactly} represent all the seen samples for \emph{incrementally} calculating prediction loss in each online update round, which can avoid loading all the training data into memory for updating model, and also effectively prevent drastic fluctuation of the model in the presence of noise. Furthermore, we introduce a forgetting factor to set different weights on samples so as to track the data streams' evolving characteristics quickly from the latest samples. Experiments on one synthetic dataset and three real-world datasets validate the effectiveness of the proposed method. In addition, the update speed of MORES is at least 2000 samples processed per second on the three real-world datasets, more than 15 times faster than the state-of-the-art online learning algorithm. | Dynamic Structure Embedded Online Multiple-Output Regression for Stream
Data | 2,780 |
In large scale machine learning and data mining problems with high feature dimensionality, the Euclidean distance between data points can be uninformative, and Distance Metric Learning (DML) is often desired to learn a proper similarity measure (using side information such as example data pairs being similar or dissimilar). However, high dimensionality and large volume of pairwise constraints in modern big data can lead to prohibitive computational cost for both the original DML formulation in Xing et al. (2002) and later extensions. In this paper, we present a distributed algorithm for DML, and a large-scale implementation on a parameter server architecture. Our approach builds on a parallelizable reformulation of Xing et al. (2002), and an asynchronous stochastic gradient descent optimization procedure. To our knowledge, this is the first distributed solution to DML, and we show that, on a system with 256 CPU cores, our program is able to complete a DML task on a dataset with 1 million data points, 22-thousand features, and 200 million labeled data pairs, in 15 hours; and the learned metric shows great effectiveness in properly measuring distances. | Large Scale Distributed Distance Metric Learning | 2,781 |
The notion of metric plays a key role in machine learning problems such as classification, clustering or ranking. However, it is worth noting that there is a severe lack of theoretical guarantees that can be expected on the generalization capacity of the classifier associated to a given metric. The theoretical framework of $(\epsilon, \gamma, \tau)$-good similarity functions (Balcan et al., 2008) has been one of the first attempts to draw a link between the properties of a similarity function and those of a linear classifier making use of it. In this paper, we extend and complete this theory by providing a new generalization bound for the associated classifier based on the algorithmic robustness framework. | Algorithmic Robustness for Learning via $(ε, γ, τ)$-Good
Similarity Functions | 2,782 |
Many modern multiclass and multilabel problems are characterized by increasingly large output spaces. For these problems, label embeddings have been shown to be a useful primitive that can improve computational and statistical efficiency. In this work we utilize a correspondence between rank constrained estimation and low dimensional label embeddings that uncovers a fast label embedding algorithm which works in both the multiclass and multilabel settings. The result is a randomized algorithm whose running time is exponentially faster than naive algorithms. We demonstrate our techniques on two large-scale public datasets, from the Large Scale Hierarchical Text Challenge and the Open Directory Project, where we obtain state of the art results. | Fast Label Embeddings via Randomized Linear Algebra | 2,783 |
We describe a general framework for online adaptation of optimization hyperparameters by `hot swapping' their values during learning. We investigate this approach in the context of adaptive learning rate selection using an explore-exploit strategy from the multi-armed bandit literature. Experiments on a benchmark neural network show that the hot swapping approach leads to consistently better solutions compared to well-known alternatives such as AdaDelta and stochastic gradient with exhaustive hyperparameter search. | Hot Swapping for Online Adaptation of Optimization Hyperparameters | 2,784 |
Energy-based models are popular in machine learning due to the elegance of their formulation and their relationship to statistical physics. Among these, the Restricted Boltzmann Machine (RBM), and its staple training algorithm contrastive divergence (CD), have been the prototype for some recent advancements in the unsupervised training of deep neural networks. However, CD has limited theoretical motivation, and can in some cases produce undesirable behavior. Here, we investigate the performance of Minimum Probability Flow (MPF) learning for training RBMs. Unlike CD, with its focus on approximating an intractable partition function via Gibbs sampling, MPF proposes a tractable, consistent, objective function defined in terms of a Taylor expansion of the KL divergence with respect to sampling dynamics. Here we propose a more general form for the sampling dynamics in MPF, and explore the consequences of different choices for these dynamics for training RBMs. Experimental results show MPF outperforming CD for various RBM configurations. | Understanding Minimum Probability Flow for RBMs Under Various Kinds of
Dynamics | 2,785 |
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm. | Adam: A Method for Stochastic Optimization | 2,786 |
We study the problem of clustering with relative constraints, where each constraint specifies relative similarities among instances. In particular, each constraint $(x_i, x_j, x_k)$ is acquired by posing a query: is instance $x_i$ more similar to $x_j$ than to $x_k$? We consider the scenario where answers to such queries are based on an underlying (but unknown) class concept, which we aim to discover via clustering. Different from most existing methods that only consider constraints derived from yes and no answers, we also incorporate don't know responses. We introduce a Discriminative Clustering method with Relative Constraints (DCRC) which assumes a natural probabilistic relationship between instances, their underlying cluster memberships, and the observed constraints. The objective is to maximize the model likelihood given the constraints, and in the meantime enforce cluster separation and cluster balance by also making use of the unlabeled instances. We evaluated the proposed method using constraints generated from ground-truth class labels, and from (noisy) human judgments from a user study. Experimental results demonstrate: 1) the usefulness of relative constraints, in particular when don't know answers are considered; 2) the improved performance of the proposed method over state-of-the-art methods that utilize either relative or pairwise constraints; and 3) the robustness of our method in the presence of noisy constraints, such as those provided by human judgement. | Discriminative Clustering with Relative Constraints | 2,787 |
Word2vec, as an efficient tool for learning vector representation of words has shown its effectiveness in many natural language processing tasks. Mikolov et al. issued Skip-Gram and Negative Sampling model for developing this toolbox. Perozzi et al. introduced the Skip-Gram model into the study of social network for the first time, and designed an algorithm named DeepWalk for learning node embedding on a graph. We prove that the DeepWalk algorithm is actually factoring a matrix M where each entry M_{ij} is logarithm of the average probability that node i randomly walks to node j in fix steps. | Comprehend DeepWalk as Matrix Factorization | 2,788 |
We showed in this work how the Hassanat distance metric enhances the performance of the nearest neighbour classifiers. The results demonstrate the superiority of this distance metric over the traditional and most-used distances, such as Manhattan distance and Euclidian distance. Moreover, we proved that the Hassanat distance metric is invariant to data scale, noise and outliers. Throughout this work, it is clearly notable that both ENN and IINC performed very well with the distance investigated, as their accuracy increased significantly by 3.3% and 3.1% respectively, with no significant advantage of the ENN over the IINC in terms of accuracy. Correspondingly, it can be noted from our results that there is no optimal algorithm that can solve all real-life problems perfectly; this is supported by the no-free-lunch theorem | On Enhancing The Performance Of Nearest Neighbour Classifiers Using
Hassanat Distance Metric | 2,789 |
Support Vector Machine (SVM) is an effective model for many classification problems. However, SVM needs the solution of a quadratic program which require specialized code. In addition, SVM has many parameters, which affects the performance of SVM classifier. Recently, the Generalized Eigenvalue Proximal SVM (GEPSVM) has been presented to solve the SVM complexity. In real world applications data may affected by error or noise, working with this data is a challenging problem. In this paper, an approach has been proposed to overcome this problem. This method is called DSA-GEPSVM. The main improvements are carried out based on the following: 1) a novel fuzzy values in the linear case. 2) A new Kernel function in the nonlinear case. 3) Differential Search Algorithm (DSA) is reformulated to find near optimal values of the GEPSVM parameters and its kernel parameters. The experimental results show that the proposed approach is able to find the suitable parameter values, and has higher classification accuracy compared with some other algorithms. | Differential Search Algorithm-based Parametric Optimization of Fuzzy
Generalized Eigenvalue Proximal Support Vector Machine | 2,790 |
Learning a kernel matrix from relative comparison human feedback is an important problem with applications in collaborative filtering, object retrieval, and search. For learning a kernel over a large number of objects, existing methods face significant scalability issues inhibiting the application of these methods to settings where a kernel is learned in an online and timely fashion. In this paper we propose a novel framework called Efficient online Relative comparison Kernel LEarning (ERKLE), for efficiently learning the similarity of a large set of objects in an online manner. We learn a kernel from relative comparisons via stochastic gradient descent, one query response at a time, by taking advantage of the sparse and low-rank properties of the gradient to efficiently restrict the kernel to lie in the space of positive semidefinite matrices. In addition, we derive a passive-aggressive online update for minimally satisfying new relative comparisons as to not disrupt the influence of previously obtained comparisons. Experimentally, we demonstrate a considerable improvement in speed while obtaining improved or comparable accuracy compared to current methods in the online learning setting. | Efficient Online Relative Comparison Kernel Learning | 2,791 |
High-content screening uses large collections of unlabeled cell image data to reason about genetics or cell biology. Two important tasks are to identify those cells which bear interesting phenotypes, and to identify sub-populations enriched for these phenotypes. This exploratory data analysis usually involves dimensionality reduction followed by clustering, in the hope that clusters represent a phenotype. We propose the use of stacked de-noising auto-encoders to perform dimensionality reduction for high-content screening. We demonstrate the superior performance of our approach over PCA, Local Linear Embedding, Kernel PCA and Isomap. | Deep Autoencoders for Dimensionality Reduction of High-Content Screening
Data | 2,792 |
In a variety of problems, the number and state of multiple moving targets are unknown and are subject to be inferred from their measurements obtained by a sensor with limited sensing ability. This type of problems is raised in a variety of applications, including monitoring of endangered species, cleaning, and surveillance. Particle filters are widely used to estimate target state from its prior information and its measurements that recently become available, especially for the cases when the measurement model and the prior distribution of state of interest are non-Gaussian. However, the problem of estimating number of total targets and their state becomes intractable when the number of total targets and the measurement-target association are unknown. This paper presents a novel Gaussian particle filter technique that combines Kalman filter and particle filter for estimating the number and state of total targets based on the measurement obtained online. The estimation is represented by a set of weighted particles, different from classical particle filter, where each particle is a Gaussian distribution instead of a point mass. | A Gaussian Particle Filter Approach for Sensors to Track Multiple Moving
Targets | 2,793 |
The Vapnik-Chervonenkis (VC) dimension measures the complexity of a learning machine, and a low VC dimension leads to good generalization. The recently proposed Minimal Complexity Machine (MCM) learns a hyperplane classifier by minimizing an exact bound on the VC dimension. This paper extends the MCM classifier to the fuzzy domain. The use of a fuzzy membership is known to reduce the effect of outliers, and to reduce the effect of noise on learning. Experimental results show, that on a number of benchmark datasets, the the fuzzy MCM classifier outperforms SVMs and the conventional MCM in terms of generalization, and that the fuzzy MCM uses fewer support vectors. On several benchmark datasets, the fuzzy MCM classifier yields excellent test set accuracies while using one-tenth the number of support vectors used by SVMs. | Learning a Fuzzy Hyperplane Fat Margin Classifier with Minimum VC
dimension | 2,794 |
We propose novel methods for max-cost Discrete Function Evaluation Problem (DFEP) under budget constraints. We are motivated by applications such as clinical diagnosis where a patient is subjected to a sequence of (possibly expensive) tests before a decision is made. Our goal is to develop strategies for minimizing max-costs. The problem is known to be NP hard and greedy methods based on specialized impurity functions have been proposed. We develop a broad class of \emph{admissible} impurity functions that admit monomials, classes of polynomials, and hinge-loss functions that allow for flexible impurity design with provably optimal approximation bounds. This flexibility is important for datasets when max-cost can be overly sensitive to "outliers." Outliers bias max-cost to a few examples that require a large number of tests for classification. We design admissible functions that allow for accuracy-cost trade-off and result in $O(\log n)$ guarantees of the optimal cost among trees with corresponding classification accuracy levels. | Max-Cost Discrete Function Evaluation Problem under a Budget | 2,795 |
Clustering is an essential problem in machine learning and data mining. One vital factor that impacts clustering performance is how to learn or design the data representation (or features). Fortunately, recent advances in deep learning can learn unsupervised features effectively, and have yielded state of the art performance in many classification problems, such as character recognition, object recognition and document categorization. However, little attention has been paid to the potential of deep learning for unsupervised clustering problems. In this paper, we propose a deep belief network with nonparametric clustering. As an unsupervised method, our model first leverages the advantages of deep learning for feature representation and dimension reduction. Then, it performs nonparametric clustering under a maximum margin framework -- a discriminative clustering model and can be trained online efficiently in the code space. Lastly model parameters are refined in the deep belief network. Thus, this model can learn features for clustering and infer model complexity in an unified framework. The experimental results show the advantage of our approach over competitive baselines. | Deep Learning with Nonparametric Clustering | 2,796 |
We consider classification and regression tasks where we have missing data and assume that the (clean) data resides in a low rank subspace. Finding a hidden subspace is known to be computationally hard. Nevertheless, using a non-proper formulation we give an efficient agnostic algorithm that classifies as good as the best linear classifier coupled with the best low-dimensional subspace in which the data resides. A direct implication is that our algorithm can linearly (and non-linearly through kernels) classify provably as well as the best classifier that has access to the full data. | Classification with Low Rank and Missing Data | 2,797 |
Sparsity-inducing penalties are useful tools to design multiclass support vector machines (SVMs). In this paper, we propose a convex optimization approach for efficiently and exactly solving the multiclass SVM learning problem involving a sparse regularization and the multiclass hinge loss formulated by Crammer and Singer. We provide two algorithms: the first one dealing with the hinge loss as a penalty term, and the other one addressing the case when the hinge loss is enforced through a constraint. The related convex optimization problems can be efficiently solved thanks to the flexibility offered by recent primal-dual proximal algorithms and epigraphical splitting techniques. Experiments carried out on several datasets demonstrate the interest of considering the exact expression of the hinge loss rather than a smooth approximation. The efficiency of the proposed algorithms w.r.t. several state-of-the-art methods is also assessed through comparisons of execution times. | A Proximal Approach for Sparse Multiclass SVM | 2,798 |
In this paper, we propose the problem of optimizing multivariate performance measures from multi-view data, and an effective method to solve it. This problem has two features: the data points are presented by multiple views, and the target of learning is to optimize complex multivariate performance measures. We propose to learn a linear discriminant functions for each view, and combine them to construct a overall multivariate mapping function for mult-view data. To learn the parameters of the linear dis- criminant functions of different views to optimize multivariate performance measures, we formulate a optimization problem. In this problem, we propose to minimize the complexity of the linear discriminant functions of each view, encourage the consistences of the responses of different views over the same data points, and minimize the upper boundary of a given multivariate performance measure. To optimize this problem, we employ the cutting-plane method in an iterative algorithm. In each iteration, we update a set of constrains, and optimize the mapping function parameter of each view one by one. | Multi-view learning for multivariate performance measures optimization | 2,799 |
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