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We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of unbounded loss functions, under the assumption that a moment of the loss is bounded. These bounds are useful in the analysis of importance weighting and other learning tasks such as unbounded regression.
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Relative Deviation Learning Bounds and Generalization with Unbounded
Loss Functions
| 2,500
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We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the marginal likelihood or a variational free energy. The space and time complexity are linear in training set size, and the algorithm can be applied to large regression problems on discrete or continuous domains. Empirical evaluation shows state-of-art performance in discrete cases and competitive results in the continuous case.
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Efficient Optimization for Sparse Gaussian Process Regression
| 2,501
|
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top principal components of a dataset with a large number of rows (examples) and columns (features). Our algorithm leverages both structured and unstructured random projections to retain good accuracy while being computationally efficient. We demonstrate the technique on the winning submission the KDD 2010 Cup.
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Combining Structured and Unstructured Randomness in Large Scale PCA
| 2,502
|
Sophisticated automatic incident detection (AID) technology plays a key role in contemporary transportation systems. Though many papers were devoted to study incident classification algorithms, few study investigated how to enhance feature representation of incidents to improve AID performance. In this paper, we propose to use an unsupervised feature learning algorithm to generate higher level features to represent incidents. We used real incident data in the experiments and found that effective feature mapping function can be learnt from the data crosses the test sites. With the enhanced features, detection rate (DR), false alarm rate (FAR) and mean time to detect (MTTD) are significantly improved in all of the three representative cases. This approach also provides an alternative way to reduce the amount of labeled data, which is expensive to obtain, required in training better incident classifiers since the feature learning is unsupervised.
|
An Unsupervised Feature Learning Approach to Improve Automatic Incident
Detection
| 2,503
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Scalable machine learning over big data is an important problem that is receiving a lot of attention in recent years. On popular distributed environments such as Hadoop running on a cluster of commodity machines, communication costs are substantial and algorithms need to be designed suitably considering those costs. In this paper we give a novel approach to the distributed training of linear classifiers (involving smooth losses and L2 regularization) that is designed to reduce the total communication costs. At each iteration, the nodes minimize locally formed approximate objective functions; then the resulting minimizers are combined to form a descent direction to move. Our approach gives a lot of freedom in the formation of the approximate objective function as well as in the choice of methods to solve them. The method is shown to have $O(log(1/\epsilon))$ time convergence. The method can be viewed as an iterative parameter mixing method. A special instantiation yields a parallel stochastic gradient descent method with strong convergence. When communication times between nodes are large, our method is much faster than the Terascale method (Agarwal et al., 2011), which is a state of the art distributed solver based on the statistical query model (Chuet al., 2006) that computes function and gradient values in a distributed fashion. We also evaluate against other recent distributed methods and demonstrate superior performance of our method.
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An efficient distributed learning algorithm based on effective local
functional approximations
| 2,504
|
We present new methods for multilabel classification, relying on ensemble learning on a collection of random output graphs imposed on the multilabel and a kernel-based structured output learner as the base classifier. For ensemble learning, differences among the output graphs provide the required base classifier diversity and lead to improved performance in the increasing size of the ensemble. We study different methods of forming the ensemble prediction, including majority voting and two methods that perform inferences over the graph structures before or after combining the base models into the ensemble. We compare the methods against the state-of-the-art machine learning approaches on a set of heterogeneous multilabel benchmark problems, including multilabel AdaBoost, convex multitask feature learning, as well as single target learning approaches represented by Bagging and SVM. In our experiments, the random graph ensembles are very competitive and robust, ranking first or second on most of the datasets. Overall, our results show that random graph ensembles are viable alternatives to flat multilabel and multitask learners.
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Multilabel Classification through Random Graph Ensembles
| 2,505
|
Pattern recognition techniques have been employed in a myriad of industrial, medical, commercial and academic applications. To tackle such a diversity of data, many techniques have been devised. However, despite the long tradition of pattern recognition research, there is no technique that yields the best classification in all scenarios. Therefore, the consideration of as many as possible techniques presents itself as an fundamental practice in applications aiming at high accuracy. Typical works comparing methods either emphasize the performance of a given algorithm in validation tests or systematically compare various algorithms, assuming that the practical use of these methods is done by experts. In many occasions, however, researchers have to deal with their practical classification tasks without an in-depth knowledge about the underlying mechanisms behind parameters. Actually, the adequate choice of classifiers and parameters alike in such practical circumstances constitutes a long-standing problem and is the subject of the current paper. We carried out a study on the performance of nine well-known classifiers implemented by the Weka framework and compared the dependence of the accuracy with their configuration parameter configurations. The analysis of performance with default parameters revealed that the k-nearest neighbors method exceeds by a large margin the other methods when high dimensional datasets are considered. When other configuration of parameters were allowed, we found that it is possible to improve the quality of SVM in more than 20% even if parameters are set randomly. Taken together, the investigation conducted in this paper suggests that, apart from the SVM implementation, Weka's default configuration of parameters provides an performance close the one achieved with the optimal configuration.
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A systematic comparison of supervised classifiers
| 2,506
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We study exploration in Multi-Armed Bandits in a setting where $k$ players collaborate in order to identify an $\epsilon$-optimal arm. Our motivation comes from recent employment of bandit algorithms in computationally intensive, large-scale applications. Our results demonstrate a non-trivial tradeoff between the number of arm pulls required by each of the players, and the amount of communication between them. In particular, our main result shows that by allowing the $k$ players to communicate only once, they are able to learn $\sqrt{k}$ times faster than a single player. That is, distributing learning to $k$ players gives rise to a factor $\sqrt{k}$ parallel speed-up. We complement this result with a lower bound showing this is in general the best possible. On the other extreme, we present an algorithm that achieves the ideal factor $k$ speed-up in learning performance, with communication only logarithmic in $1/\epsilon$.
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Distributed Exploration in Multi-Armed Bandits
| 2,507
|
The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the division step, we partition the kernel SVM problem into smaller subproblems by clustering the data, so that each subproblem can be solved independently and efficiently. We show theoretically that the support vectors identified by the subproblem solution are likely to be support vectors of the entire kernel SVM problem, provided that the problem is partitioned appropriately by kernel clustering. In the conquer step, the local solutions from the subproblems are used to initialize a global coordinate descent solver, which converges quickly as suggested by our analysis. By extending this idea, we develop a multilevel Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction strategy, which outperforms state-of-the-art methods in terms of training speed, testing accuracy, and memory usage. As an example, on the covtype dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in obtaining the exact SVM solution (to within $10^{-6}$ relative error) which achieves 96.15% prediction accuracy. Moreover, with our proposed early prediction strategy, DC-SVM achieves about 96% accuracy in only 12 minutes, which is more than 100 times faster than LIBSVM.
|
A Divide-and-Conquer Solver for Kernel Support Vector Machines
| 2,508
|
Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical results, however, disclosed that maximizing the minimum margin does not necessarily lead to better generalization performances, and instead, the margin distribution has been proven to be more crucial. In this paper, we propose the Large margin Distribution Machine (LDM), which tries to achieve a better generalization performance by optimizing the margin distribution. We characterize the margin distribution by the first- and second-order statistics, i.e., the margin mean and variance. The LDM is a general learning approach which can be used in any place where SVM can be applied, and its superiority is verified both theoretically and empirically in this paper.
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Large Margin Distribution Machine
| 2,509
|
It is surprising that last two decades many works in time series data mining and clustering were concerned with measures of similarity of time series but not with measures of association that can be used for measuring possible direct and inverse relationships between time series. Inverse relationships can exist between dynamics of prices and sell volumes, between growth patterns of competitive companies, between well production data in oilfields, between wind velocity and air pollution concentration etc. The paper develops a theoretical basis for analysis and construction of time series shape association measures. Starting from the axioms of time series shape association measures it studies the methods of construction of measures satisfying these axioms. Several general methods of construction of such measures suitable for measuring time series shape similarity and shape association are proposed. Time series shape association measures based on Minkowski distance and data standardization methods are considered. The cosine similarity and the Pearsons correlation coefficient are obtained as particular cases of the proposed general methods that can be used also for construction of new association measures in data analysis.
|
Constructing Time Series Shape Association Measures: Minkowski Distance
and Data Standardization
| 2,510
|
We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear transformations are effectively applied not only to the received rewards but also to the true transition probabilities of the underlying Markov decision process. When appropriate utility functions are chosen, the agents' behaviors express key features of human behavior as predicted by prospect theory (Kahneman and Tversky, 1979), for example different risk-preferences for gains and losses as well as the shape of subjective probability curves. We derive a risk-sensitive Q-learning algorithm, which is necessary for modeling human behavior when transition probabilities are unknown, and prove its convergence. As a proof of principle for the applicability of the new framework we apply it to quantify human behavior in a sequential investment task. We find, that the risk-sensitive variant provides a significantly better fit to the behavioral data and that it leads to an interpretation of the subject's responses which is indeed consistent with prospect theory. The analysis of simultaneously measured fMRI signals show a significant correlation of the risk-sensitive TD error with BOLD signal change in the ventral striatum. In addition we find a significant correlation of the risk-sensitive Q-values with neural activity in the striatum, cingulate cortex and insula, which is not present if standard Q-values are used.
|
Risk-sensitive Reinforcement Learning
| 2,511
|
We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these disparate approaches by maintaining an independent Hessian approximation for each contributing function in the sum. We maintain computational tractability and limit memory requirements even for high dimensional optimization problems by storing and manipulating these quadratic approximations in a shared, time evolving, low dimensional subspace. Each update step requires only a single contributing function or minibatch evaluation (as in SGD), and each step is scaled using an approximate inverse Hessian and little to no adjustment of hyperparameters is required (as is typical for quasi-Newton methods). This algorithm contrasts with earlier stochastic second order techniques that treat the Hessian of each contributing function as a noisy approximation to the full Hessian, rather than as a target for direct estimation. We experimentally demonstrate improved convergence on seven diverse optimization problems. The algorithm is released as open source Python and MATLAB packages.
|
Fast large-scale optimization by unifying stochastic gradient and
quasi-Newton methods
| 2,512
|
Missing value imputation is an important practical problem. There is a large body of work on it, but there does not exist any work that formulates the problem in a structured output setting. Also, most applications have constraints on the imputed data, for example on the distribution associated with each variable. None of the existing imputation methods use these constraints. In this paper we propose a structured output approach for missing value imputation that also incorporates domain constraints. We focus on large margin models, but it is easy to extend the ideas to probabilistic models. We deal with the intractable inference step in learning via a piecewise training technique that is simple, efficient, and effective. Comparison with existing state-of-the-art and baseline imputation methods shows that our method gives significantly improved performance on the Hamming loss measure.
|
A Structured Prediction Approach for Missing Value Imputation
| 2,513
|
In structured output learning, obtaining labelled data for real-world applications is usually costly, while unlabelled examples are available in abundance. Semi-supervised structured classification has been developed to handle large amounts of unlabelled structured data. In this work, we consider semi-supervised structural SVMs with domain constraints. The optimization problem, which in general is not convex, contains the loss terms associated with the labelled and unlabelled examples along with the domain constraints. We propose a simple optimization approach, which alternates between solving a supervised learning problem and a constraint matching problem. Solving the constraint matching problem is difficult for structured prediction, and we propose an efficient and effective hill-climbing method to solve it. The alternating optimization is carried out within a deterministic annealing framework, which helps in effective constraint matching, and avoiding local minima which are not very useful. The algorithm is simple to implement and achieves comparable generalization performance on benchmark datasets.
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Large Margin Semi-supervised Structured Output Learning
| 2,514
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The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible to use the extra examples to speed up the computation time required to perform the learning task? We give the first positive answer to this question for a {\em natural supervised learning problem} --- we consider agnostic PAC learning of halfspaces over $3$-sparse vectors in $\{-1,1,0\}^n$. This class is inefficiently learnable using $O\left(n/\epsilon^2\right)$ examples. Our main contribution is a novel, non-cryptographic, methodology for establishing computational-statistical gaps, which allows us to show that, under a widely believed assumption that refuting random $\mathrm{3CNF}$ formulas is hard, it is impossible to efficiently learn this class using only $O\left(n/\epsilon^2\right)$ examples. We further show that under stronger hardness assumptions, even $O\left(n^{1.499}/\epsilon^2\right)$ examples do not suffice. On the other hand, we show a new algorithm that learns this class efficiently using $\tilde{\Omega}\left(n^2/\epsilon^2\right)$ examples. This formally establishes the tradeoff between sample and computational complexity for a natural supervised learning problem.
|
More data speeds up training time in learning halfspaces over sparse
vectors
| 2,515
|
We consider the problem of quantitatively evaluating missing value imputation algorithms. Given a dataset with missing values and a choice of several imputation algorithms to fill them in, there is currently no principled way to rank the algorithms using a quantitative metric. We develop a framework based on treating imputation evaluation as a problem of comparing two distributions and show how it can be used to compute quantitative metrics. We present an efficient procedure for applying this framework to practical datasets, demonstrate several metrics derived from the existing literature on comparing distributions, and propose a new metric called Neighborhood-based Dissimilarity Score which is fast to compute and provides similar results. Results are shown on several datasets, metrics, and imputations algorithms.
|
A Quantitative Evaluation Framework for Missing Value Imputation
Algorithms
| 2,516
|
The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very complex as it requires the complete data matrix to be calculated and stored. Further, the kernelized nature of the kernel $k$-means algorithm hinders the parallelization of its computations on modern infrastructures for distributed computing. In this paper, we are defining a family of kernel-based low-dimensional embeddings that allows for scaling kernel $k$-means on MapReduce via an efficient and unified parallelization strategy. Afterwards, we propose two methods for low-dimensional embedding that adhere to our definition of the embedding family. Exploiting the proposed parallelization strategy, we present two scalable MapReduce algorithms for kernel $k$-means. We demonstrate the effectiveness and efficiency of the proposed algorithms through an empirical evaluation on benchmark data sets.
|
Embed and Conquer: Scalable Embeddings for Kernel k-Means on MapReduce
| 2,517
|
The task of assigning label sequences to a set of observed sequences is common in computational linguistics. Several models for sequence labeling have been proposed over the last few years. Here, we focus on discriminative models for sequence labeling. Many batch and online (updating model parameters after visiting each example) learning algorithms have been proposed in the literature. On large datasets, online algorithms are preferred as batch learning methods are slow. These online algorithms were designed to solve either a primal or a dual problem. However, there has been no systematic comparison of these algorithms in terms of their speed, generalization performance (accuracy/likelihood) and their ability to achieve steady state generalization performance fast. With this aim, we compare different algorithms and make recommendations, useful for a practitioner. We conclude that the selection of an algorithm for sequence labeling depends on the evaluation criterion used and its implementation simplicity.
|
An Empirical Evaluation of Sequence-Tagging Trainers
| 2,518
|
Echo State Networks (ESNs) are a special type of the temporally deep network model, the Recurrent Neural Network (RNN), where the recurrent matrix is carefully designed and both the recurrent and input matrices are fixed. An ESN uses the linearity of the activation function of the output units to simplify the learning of the output matrix. In this paper, we devise a special technique that take advantage of this linearity in the output units of an ESN, to learn the input and recurrent matrices. This has not been done in earlier ESNs due to their well known difficulty in learning those matrices. Compared to the technique of BackPropagation Through Time (BPTT) in learning general RNNs, our proposed method exploits linearity of activation function in the output units to formulate the relationships amongst the various matrices in an RNN. These relationships results in the gradient of the cost function having an analytical form and being more accurate. This would enable us to compute the gradients instead of obtaining them by recursion as in BPTT. Experimental results on phone state classification show that learning one or both the input and recurrent matrices in an ESN yields superior results compared to traditional ESNs that do not learn these matrices, especially when longer time steps are used.
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Learning Input and Recurrent Weight Matrices in Echo State Networks
| 2,519
|
Many researches have been devoted to learn a Mahalanobis distance metric, which can effectively improve the performance of kNN classification. Most approaches are iterative and computational expensive and linear rigidity still critically limits metric learning algorithm to perform better. We proposed a computational economical framework to learn multiple metrics in closed-form.
|
Multiple Closed-Form Local Metric Learning for K-Nearest Neighbor
Classifier
| 2,520
|
In this paper, we push forward the idea of machine learning systems whose operators can be modified and fine-tuned for each problem. This allows us to propose a learning paradigm where users can write (or adapt) their operators, according to the problem, data representation and the way the information should be navigated. To achieve this goal, data instances, background knowledge, rules, programs and operators are all written in the same functional language, Erlang. Since changing operators affect how the search space needs to be explored, heuristics are learnt as a result of a decision process based on reinforcement learning where each action is defined as a choice of operator and rule. As a result, the architecture can be seen as a 'system for writing machine learning systems' or to explore new operators where the policy reuse (as a kind of transfer learning) is allowed. States and actions are represented in a Q matrix which is actually a table, from which a supervised model is learnt. This makes it possible to have a more flexible mapping between old and new problems, since we work with an abstraction of rules and actions. We include some examples sharing reuse and the application of the system gErl to IQ problems. In order to evaluate gErl, we will test it against some structured problems: a selection of IQ test tasks and some experiments on some structured prediction problems (list patterns).
|
On the definition of a general learning system with user-defined
operators
| 2,521
|
The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community is to reweight the training samples to minimize that discrepancy. In specific, many methods are based on developing Density-ratio (DR) estimation techniques that apply to both regression and classification problems. Although these methods work well for regression problems, their performance on classification problems is not satisfactory. This is due to a key observation that these methods focus on matching the sample marginal distributions without paying attention to preserving the separation between classes in the reweighted space. In this paper, we propose a novel method for Discriminative Density-ratio (DDR) estimation that addresses the aforementioned problem and aims at estimating the density-ratio of joint distributions in a class-wise manner. The proposed algorithm is an iterative procedure that alternates between estimating the class information for the test data and estimating new density ratio for each class. To incorporate the estimated class information of the test data, a soft matching technique is proposed. In addition, we employ an effective criterion which adopts mutual information as an indicator to stop the iterative procedure while resulting in a decision boundary that lies in a sparse region. Experiments on synthetic and benchmark datasets demonstrate the superiority of the proposed method in terms of both accuracy and robustness.
|
Discriminative Density-ratio Estimation
| 2,522
|
A hierarchical clustering method is stable if small perturbations on the data set produce small perturbations in the result. These perturbations are measured using the Gromov-Hausdorff metric. We study the problem of stability on linkage-based hierarchical clustering methods. We obtain that, under some basic conditions, standard linkage-based methods are semi-stable. This means that they are stable if the input data is close enough to an ultrametric space. We prove that, apart from exotic examples, introducing any unchaining condition in the algorithm always produces unstable methods.
|
Gromov-Hausdorff stability of linkage-based hierarchical clustering
methods
| 2,523
|
Feature selection plays a pivotal role in learning, particularly in areas were parsimonious features can provide insight into the underlying process, such as biology. Recent approaches for non-linear feature selection employing greedy optimisation of Centred Kernel Target Alignment(KTA), while exhibiting strong results in terms of generalisation accuracy and sparsity, can become computationally prohibitive for high-dimensional datasets. We propose randSel, a randomised feature selection algorithm, with attractive scaling properties. Our theoretical analysis of randSel provides strong probabilistic guarantees for the correct identification of relevant features. Experimental results on real and artificial data, show that the method successfully identifies effective features, performing better than a number of competitive approaches.
|
Learning Non-Linear Feature Maps
| 2,524
|
Challenging optimization problems, which elude acceptable solution via conventional calculus methods, arise commonly in different areas of industrial design and practice. Hard optimization problems are those who manifest the following behavior: a) high number of independent input variables; b) very complex or irregular multi-modal fitness; c) computational expensive fitness evaluation. This paper will focus on some theoretical issues that have strong implications for practice. I will stress how an interpretation of the No Free Lunch theorem leads naturally to a general Bayesian optimization framework. The choice of a prior over the space of functions is a critical and inevitable step in every black-box optimization.
|
No Free Lunch Theorem and Bayesian probability theory: two sides of the
same coin. Some implications for black-box optimization and metaheuristics
| 2,525
|
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an analytic expression for the unnormalized probability function and no tractable approximation. This makes it difficult to estimate the quality of these models, once they have been trained, or to monitor their quality (e.g. for early stopping) while training. A previously proposed method is based on constructing a non-parametric density estimator of the model's probability function from samples generated by the model. We revisit this idea, propose a more efficient estimator, and prove that it provides a lower bound on the true test log-likelihood, and an unbiased estimator as the number of generated samples goes to infinity, although one that incorporates the effect of poor mixing. We further propose a biased variant of the estimator that can be used reliably with a finite number of samples for the purpose of model comparison.
|
Bounding the Test Log-Likelihood of Generative Models
| 2,526
|
Novelty detection plays an important role in machine learning and signal processing. This paper studies novelty detection in a new setting where the data object is represented as a bag of instances and associated with multiple class labels, referred to as multi-instance multi-label (MIML) learning. Contrary to the common assumption in MIML that each instance in a bag belongs to one of the known classes, in novelty detection, we focus on the scenario where bags may contain novel-class instances. The goal is to determine, for any given instance in a new bag, whether it belongs to a known class or a novel class. Detecting novelty in the MIML setting captures many real-world phenomena and has many potential applications. For example, in a collection of tagged images, the tag may only cover a subset of objects existing in the images. Discovering an object whose class has not been previously tagged can be useful for the purpose of soliciting a label for the new object class. To address this novel problem, we present a discriminative framework for detecting new class instances. Experiments demonstrate the effectiveness of our proposed method, and reveal that the presence of unlabeled novel instances in training bags is helpful to the detection of such instances in testing stage.
|
Novelty Detection Under Multi-Instance Multi-Label Framework
| 2,527
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We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from computational learning theory, we refrain from any statistical assumptions and define the performance with respect to the class of general parametric predictors. In particular, we present generic lower and upper bounds on this relative performance by transforming the prediction task into a parameter learning problem. We first introduce the lower bounds on this relative performance in the mixture of experts framework, where we show that for any sequential algorithm, there always exists a sequence for which the performance of the sequential algorithm is lower bounded by zero. We then introduce a sequential learning algorithm to predict such arbitrary and unknown sequences, and calculate upper bounds on its total squared prediction error for every bounded sequence. We further show that in some scenarios we achieve matching lower and upper bounds demonstrating that our algorithms are optimal in a strong minimax sense such that their performances cannot be improved further. As an interesting result we also prove that for the worst case scenario, the performance of randomized algorithms can be achieved by sequential algorithms so that randomized algorithms does not improve the performance.
|
A Unified Approach to Universal Prediction: Generalized Upper and Lower
Bounds
| 2,528
|
We consider the problem of learning reject option classifiers. The goodness of a reject option classifier is quantified using $0-d-1$ loss function wherein a loss $d \in (0,.5)$ is assigned for rejection. In this paper, we propose {\em double ramp loss} function which gives a continuous upper bound for $(0-d-1)$ loss. Our approach is based on minimizing regularized risk under the double ramp loss using {\em difference of convex (DC) programming}. We show the effectiveness of our approach through experiments on synthetic and benchmark datasets. Our approach performs better than the state of the art reject option classification approaches.
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Double Ramp Loss Based Reject Option Classifier
| 2,529
|
We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms that improve the convergence performance of the conventional algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and extends the stability bound on the step size. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyzes and simulation results. We show the extended stability bound of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.
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A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic
Cost
| 2,530
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TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target) belongs to a computably enumerable (c.e.) or co-computably enumerable (co-c.e.) set of computable probability mass functions, then there is an algorithm to almost surely identify the target in the limit. The technical tool is the strong law of large numbers. If the set is finite and the elements of the sequence are dependent while the sequence is typical in the sense of Martin-L\"of for at least one measure belonging to a c.e. or co-c.e. set of computable measures, then there is an algorithm to identify in the limit a computable measure for which the sequence is typical (there may be more than one such measure). The technical tool is the theory of Kolmogorov complexity. We give the algorithms and consider the associated predictions.
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Algorithmic Identification of Probabilities
| 2,531
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The ICDM Challenge 2013 is to apply machine learning to the problem of hotel ranking, aiming to maximize purchases according to given hotel characteristics, location attractiveness of hotels, user's aggregated purchase history and competitive online travel agency information for each potential hotel choice. This paper describes the solution of team "binghsu & MLRush & BrickMover". We conduct simple feature engineering work and train different models by each individual team member. Afterwards, we use listwise ensemble method to combine each model's output. Besides describing effective model and features, we will discuss about the lessons we learned while using deep learning in this competition.
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Combination of Diverse Ranking Models for Personalized Expedia Hotel
Searches
| 2,532
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In this paper, we first prove a high probability bound rather than an expectation bound for stochastic optimization with smooth loss. Furthermore, the existing analysis requires the knowledge of optimal classifier for tuning the step size in order to achieve the desired bound. However, this information is usually not accessible in advanced. We also propose a strategy to address the limitation.
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Stochastic Optimization of Smooth Loss
| 2,533
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Recent advances have made it feasible to apply the stochastic variational paradigm to a collapsed representation of latent Dirichlet allocation (LDA). While the stochastic variational paradigm has successfully been applied to an uncollapsed representation of the hierarchical Dirichlet process (HDP), no attempts to apply this type of inference in a collapsed setting of non-parametric topic modeling have been put forward so far. In this paper we explore such a collapsed stochastic variational Bayes inference for the HDP. The proposed online algorithm is easy to implement and accounts for the inference of hyper-parameters. First experiments show a promising improvement in predictive performance.
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Practical Collapsed Stochastic Variational Inference for the HDP
| 2,534
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We propose a novel approach for designing kernels for support vector machines (SVMs) when the class label is linked to the observation through a latent state and the likelihood function of the observation given the state (the sensing model) is available. We show that the Bayes-optimum decision boundary is a hyperplane under a mapping defined by the likelihood function. Combining this with the maximum margin principle yields kernels for SVMs that leverage knowledge of the sensing model in an optimal way. We derive the optimum kernel for the bag-of-words (BoWs) sensing model and demonstrate its superior performance over other kernels in document and image classification tasks. These results indicate that such optimum sensing-aware kernel SVMs can match the performance of rather sophisticated state-of-the-art approaches.
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Sensing-Aware Kernel SVM
| 2,535
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Structured prediction plays a central role in machine learning applications from computational biology to computer vision. These models require significantly more computation than unstructured models, and, in many applications, algorithms may need to make predictions within a computational budget or in an anytime fashion. In this work we propose an anytime technique for learning structured prediction that, at training time, incorporates both structural elements and feature computation trade-offs that affect test-time inference. We apply our technique to the challenging problem of scene understanding in computer vision and demonstrate efficient and anytime predictions that gradually improve towards state-of-the-art classification performance as the allotted time increases.
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SpeedMachines: Anytime Structured Prediction
| 2,536
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We consider the problem of image representation for the tasks of unsupervised learning and semi-supervised learning. In those learning tasks, the raw image vectors may not provide enough representation for their intrinsic structures due to their highly dense feature space. To overcome this problem, the raw image vectors should be mapped to a proper representation space which can capture the latent structure of the original data and represent the data explicitly for further learning tasks such as clustering. Inspired by the recent research works on deep neural network and representation learning, in this paper, we introduce the multiple-layer auto-encoder into image representation, we also apply the locally invariant ideal to our image representation with auto-encoders and propose a novel method, called Graph regularized Auto-Encoder (GAE). GAE can provide a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. Extensive experiments on image clustering show encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-word cases.
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Image Representation Learning Using Graph Regularized Auto-Encoders
| 2,537
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Model interpretation is one of the key aspects of the model evaluation process. The explanation of the relationship between model variables and outputs is relatively easy for statistical models, such as linear regressions, thanks to the availability of model parameters and their statistical significance. For "black box" models, such as random forest, this information is hidden inside the model structure. This work presents an approach for computing feature contributions for random forest classification models. It allows for the determination of the influence of each variable on the model prediction for an individual instance. By analysing feature contributions for a training dataset, the most significant variables can be determined and their typical contribution towards predictions made for individual classes, i.e., class-specific feature contribution "patterns", are discovered. These patterns represent a standard behaviour of the model and allow for an additional assessment of the model reliability for a new data. Interpretation of feature contributions for two UCI benchmark datasets shows the potential of the proposed methodology. The robustness of results is demonstrated through an extensive analysis of feature contributions calculated for a large number of generated random forest models.
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Interpreting random forest classification models using a feature
contribution method
| 2,538
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The permutahedron is the convex polytope with vertex set consisting of the vectors $(\pi(1),\dots, \pi(n))$ for all permutations (bijections) $\pi$ over $\{1,\dots, n\}$. We study a bandit game in which, at each step $t$, an adversary chooses a hidden weight weight vector $s_t$, a player chooses a vertex $\pi_t$ of the permutahedron and suffers an observed loss of $\sum_{i=1}^n \pi(i) s_t(i)$. A previous algorithm CombBand of Cesa-Bianchi et al (2009) guarantees a regret of $O(n\sqrt{T \log n})$ for a time horizon of $T$. Unfortunately, CombBand requires at each step an $n$-by-$n$ matrix permanent approximation to within improved accuracy as $T$ grows, resulting in a total running time that is super linear in $T$, making it impractical for large time horizons. We provide an algorithm of regret $O(n^{3/2}\sqrt{T})$ with total time complexity $O(n^3T)$. The ideas are a combination of CombBand and a recent algorithm by Ailon (2013) for online optimization over the permutahedron in the full information setting. The technical core is a bound on the variance of the Plackett-Luce noisy sorting process's "pseudo loss". The bound is obtained by establishing positive semi-definiteness of a family of 3-by-3 matrices generated from rational functions of exponentials of 3 parameters.
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Bandit Online Optimization Over the Permutahedron
| 2,539
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Recurrent Neural Networks (RNN) have recently achieved the best performance in off-line Handwriting Text Recognition. At the same time, learning RNN by gradient descent leads to slow convergence, and training times are particularly long when the training database consists of full lines of text. In this paper, we propose an easy way to accelerate stochastic gradient descent in this set-up, and in the general context of learning to recognize sequences. The principle is called Curriculum Learning, or shaping. The idea is to first learn to recognize short sequences before training on all available training sequences. Experiments on three different handwritten text databases (Rimes, IAM, OpenHaRT) show that a simple implementation of this strategy can significantly speed up the training of RNN for Text Recognition, and even significantly improve performance in some cases.
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Curriculum Learning for Handwritten Text Line Recognition
| 2,540
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A key challenge in designing convolutional network models is sizing them appropriately. Many factors are involved in these decisions, including number of layers, feature maps, kernel sizes, etc. Complicating this further is the fact that each of these influence not only the numbers and dimensions of the activation units, but also the total number of parameters. In this paper we focus on assessing the independent contributions of three of these linked variables: The numbers of layers, feature maps, and parameters. To accomplish this, we employ a recursive convolutional network whose weights are tied between layers; this allows us to vary each of the three factors in a controlled setting. We find that while increasing the numbers of layers and parameters each have clear benefit, the number of feature maps (and hence dimensionality of the representation) appears ancillary, and finds most of its benefit through the introduction of more weights. Our results (i) empirically confirm the notion that adding layers alone increases computational power, within the context of convolutional layers, and (ii) suggest that precise sizing of convolutional feature map dimensions is itself of little concern; more attention should be paid to the number of parameters in these layers instead.
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Understanding Deep Architectures using a Recursive Convolutional Network
| 2,541
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In this paper we present a model for email authorship identification (EAI) by employing a Cluster-based Classification (CCM) technique. Traditionally, stylometric features have been successfully employed in various authorship analysis tasks; we extend the traditional feature-set to include some more interesting and effective features for email authorship identification (e.g. the last punctuation mark used in an email, the tendency of an author to use capitalization at the start of an email, or the punctuation after a greeting or farewell). We also included Info Gain feature selection based content features. It is observed that the use of such features in the authorship identification process has a positive impact on the accuracy of the authorship identification task. We performed experiments to justify our arguments and compared the results with other base line models. Experimental results reveal that the proposed CCM-based email authorship identification model, along with the proposed feature set, outperforms the state-of-the-art support vector machine (SVM)-based models, as well as the models proposed by Iqbal et al. [1, 2]. The proposed model attains an accuracy rate of 94% for 10 authors, 89% for 25 authors, and 81% for 50 authors, respectively on Enron dataset, while 89.5% accuracy has been achieved on authors' constructed real email dataset. The results on Enron dataset have been achieved on quite a large number of authors as compared to the models proposed by Iqbal et al. [1, 2].
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CEAI: CCM based Email Authorship Identification Model
| 2,542
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In this paper we present two related, kernel-based Distance Metric Learning (DML) methods. Their respective models non-linearly map data from their original space to an output space, and subsequent distance measurements are performed in the output space via a Mahalanobis metric. The dimensionality of the output space can be directly controlled to facilitate the learning of a low-rank metric. Both methods allow for simultaneous inference of the associated metric and the mapping to the output space, which can be used to visualize the data, when the output space is 2- or 3-dimensional. Experimental results for a collection of classification tasks illustrate the advantages of the proposed methods over other traditional and kernel-based DML approaches.
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Kernel-based Distance Metric Learning in the Output Space
| 2,543
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This paper presents a RKHS, in general, of vector-valued functions intended to be used as hypothesis space for multi-task classification. It extends similar hypothesis spaces that have previously considered in the literature. Assuming this space, an improved Empirical Rademacher Complexity-based generalization bound is derived. The analysis is itself extended to an MKL setting. The connection between the proposed hypothesis space and a Group-Lasso type regularizer is discussed. Finally, experimental results, with some SVM-based Multi-Task Learning problems, underline the quality of the derived bounds and validate the paper's analysis.
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Multi-Task Classification Hypothesis Space with Improved Generalization
Bounds
| 2,544
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Regularized regression techniques for linear regression have been created the last few ten years to reduce the flaws of ordinary least squares regression with regard to prediction accuracy. In this paper, new methods for using regularized regression in model choice are introduced, and we distinguish the conditions in which regularized regression develops our ability to discriminate models. We applied all the five methods that use penalty-based (regularization) shrinkage to handle Oxazolines and Oxazoles derivatives descriptor dataset with far more predictors than observations. The lasso, ridge, elasticnet, lars and relaxed lasso further possess the desirable property that they simultaneously select relevant predictive descriptors and optimally estimate their effects. Here, we comparatively evaluate the performance of five regularized linear regression methods The assessment of the performance of each model by means of benchmark experiments is an established exercise. Cross-validation and resampling methods are generally used to arrive point evaluates the efficiencies which are compared to recognize methods with acceptable features. Predictive accuracy was evaluated using the root mean squared error (RMSE) and Square of usual correlation between predictors and observed mean inhibitory concentration of antitubercular activity (R square). We found that all five regularized regression models were able to produce feasible models and efficient capturing the linearity in the data. The elastic net and lars had similar accuracies as well as lasso and relaxed lasso had similar accuracies but outperformed ridge regression in terms of the RMSE and R square metrics.
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Performance Analysis Of Regularized Linear Regression Models For
Oxazolines And Oxazoles Derivitive Descriptor Dataset
| 2,545
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We argue for the use of active learning methods for player modelling. In active learning, the learning algorithm chooses where to sample the search space so as to optimise learning progress. We hypothesise that player modelling based on active learning could result in vastly more efficient learning, but will require big changes in how data is collected. Some example active player modelling scenarios are described. A particular form of active learning is also equivalent to an influential formalisation of (human and machine) curiosity, and games with active learning could therefore be seen as being curious about the player. We further hypothesise that this form of curiosity is symmetric, and therefore that games that explore their players based on the principles of active learning will turn out to select game configurations that are interesting to the player that is being explored.
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Active Player Modelling
| 2,546
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Online Passive-Aggressive (PA) learning is an effective framework for performing max-margin online learning. But the deterministic formulation and estimated single large-margin model could limit its capability in discovering descriptive structures underlying complex data. This pa- per presents online Bayesian Passive-Aggressive (BayesPA) learning, which subsumes the online PA and extends naturally to incorporate latent variables and perform nonparametric Bayesian inference, thus providing great flexibility for explorative analysis. We apply BayesPA to topic modeling and derive efficient online learning algorithms for max-margin topic models. We further develop nonparametric methods to resolve the number of topics. Experimental results on real datasets show that our approaches significantly improve time efficiency while maintaining comparable results with the batch counterparts.
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Online Bayesian Passive-Aggressive Learning
| 2,547
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This paper proposes a new method for the K-armed dueling bandit problem, a variation on the regular K-armed bandit problem that offers only relative feedback about pairs of arms. Our approach extends the Upper Confidence Bound algorithm to the relative setting by using estimates of the pairwise probabilities to select a promising arm and applying Upper Confidence Bound with the winner as a benchmark. We prove a finite-time regret bound of order O(log t). In addition, our empirical results using real data from an information retrieval application show that it greatly outperforms the state of the art.
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Relative Upper Confidence Bound for the K-Armed Dueling Bandit Problem
| 2,548
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Policy Gradient methods that explore directly in parameter space are among the most effective and robust direct policy search methods and have drawn a lot of attention lately. The basic method from this field, Policy Gradients with Parameter-based Exploration, uses two samples that are symmetric around the current hypothesis to circumvent misleading reward in \emph{asymmetrical} reward distributed problems gathered with the usual baseline approach. The exploration parameters are still updated by a baseline approach - leaving the exploration prone to asymmetric reward distributions. In this paper we will show how the exploration parameters can be sampled quasi symmetric despite having limited instead of free parameters for exploration. We give a transformation approximation to get quasi symmetric samples with respect to the exploration without changing the overall sampling distribution. Finally we will demonstrate that sampling symmetrically also for the exploration parameters is superior in needs of samples and robustness than the original sampling approach.
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Efficient Baseline-free Sampling in Parameter Exploring Policy
Gradients: Super Symmetric PGPE
| 2,549
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In this article we propose feature graph architectures (FGA), which are deep learning systems employing a structured initialisation and training method based on a feature graph which facilitates improved generalisation performance compared with a standard shallow architecture. The goal is to explore alternative perspectives on the problem of deep network training. We evaluate FGA performance for deep SVMs on some experimental datasets, and show how generalisation and stability results may be derived for these models. We describe the effect of permutations on the model accuracy, and give a criterion for the optimal permutation in terms of feature correlations. The experimental results show that the algorithm produces robust and significant test set improvements over a standard shallow SVM training method for a range of datasets. These gains are achieved with a moderate increase in time complexity.
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Feature Graph Architectures
| 2,550
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Mixtures of Experts combine the outputs of several "expert" networks, each of which specializes in a different part of the input space. This is achieved by training a "gating" network that maps each input to a distribution over the experts. Such models show promise for building larger networks that are still cheap to compute at test time, and more parallelizable at training time. In this this work, we extend the Mixture of Experts to a stacked model, the Deep Mixture of Experts, with multiple sets of gating and experts. This exponentially increases the number of effective experts by associating each input with a combination of experts at each layer, yet maintains a modest model size. On a randomly translated version of the MNIST dataset, we find that the Deep Mixture of Experts automatically learns to develop location-dependent ("where") experts at the first layer, and class-specific ("what") experts at the second layer. In addition, we see that the different combinations are in use when the model is applied to a dataset of speech monophones. These demonstrate effective use of all expert combinations.
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Learning Factored Representations in a Deep Mixture of Experts
| 2,551
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In this paper, we propose an extremely simple deep model for the unsupervised nonlinear dimensionality reduction -- deep distributed random samplings, which performs like a stack of unsupervised bootstrap aggregating. First, its network structure is novel: each layer of the network is a group of mutually independent $k$-centers clusterings. Second, its learning method is extremely simple: the $k$ centers of each clustering are only $k$ randomly selected examples from the training data; for small-scale data sets, the $k$ centers are further randomly reconstructed by a simple cyclic-shift operation. Experimental results on nonlinear dimensionality reduction show that the proposed method can learn abstract representations on both large-scale and small-scale problems, and meanwhile is much faster than deep neural networks on large-scale problems.
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Learning Deep Representations By Distributed Random Samplings
| 2,552
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Scalability properties of deep neural networks raise key research questions, particularly as the problems considered become larger and more challenging. This paper expands on the idea of conditional computation introduced by Bengio, et. al., where the nodes of a deep network are augmented by a set of gating units that determine when a node should be calculated. By factorizing the weight matrix into a low-rank approximation, an estimation of the sign of the pre-nonlinearity activation can be efficiently obtained. For networks using rectified-linear hidden units, this implies that the computation of a hidden unit with an estimated negative pre-nonlinearity can be ommitted altogether, as its value will become zero when nonlinearity is applied. For sparse neural networks, this can result in considerable speed gains. Experimental results using the MNIST and SVHN data sets with a fully-connected deep neural network demonstrate the performance robustness of the proposed scheme with respect to the error introduced by the conditional computation process.
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Low-Rank Approximations for Conditional Feedforward Computation in Deep
Neural Networks
| 2,553
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Darwin's theory of evolution is considered to be one of the greatest scientific gems in modern science. It not only gives us a description of how living things evolve, but also shows how a population evolves through time and also, why only the fittest individuals continue the generation forward. The paper basically gives a high level analysis of the works of Valiant[1]. Though, we know the mechanisms of evolution, but it seems that there does not exist any strong quantitative and mathematical theory of the evolution of certain mechanisms. What is defined exactly as the fitness of an individual, why is that only certain individuals in a population tend to mutate, how computation is done in finite time when we have exponentially many examples: there seems to be a lot of questions which need to be answered. [1] basically treats Darwinian theory as a form of computational learning theory, which calculates the net fitness of the hypotheses and thus distinguishes functions and their classes which could be evolvable using polynomial amount of resources. Evolution is considered as a function of the environment and the previous evolutionary stages that chooses the best hypothesis using learning techniques that makes mutation possible and hence, gives a quantitative idea that why only the fittest individuals tend to survive and have the power to mutate.
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Evolution and Computational Learning Theory: A survey on Valiant's paper
| 2,554
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Not all instances in a data set are equally beneficial for inferring a model of the data. Some instances (such as outliers) are detrimental to inferring a model of the data. Several machine learning techniques treat instances in a data set differently during training such as curriculum learning, filtering, and boosting. However, an automated method for determining how beneficial an instance is for inferring a model of the data does not exist. In this paper, we present an automated method that orders the instances in a data set by complexity based on the their likelihood of being misclassified (instance hardness). The underlying assumption of this method is that instances with a high likelihood of being misclassified represent more complex concepts in a data set. Ordering the instances in a data set allows a learning algorithm to focus on the most beneficial instances and ignore the detrimental ones. We compare ordering the instances in a data set in curriculum learning, filtering and boosting. We find that ordering the instances significantly increases classification accuracy and that filtering has the largest impact on classification accuracy. On a set of 52 data sets, ordering the instances increases the average accuracy from 81% to 84%.
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A Comparative Evaluation of Curriculum Learning with Filtering and
Boosting
| 2,555
|
Bootstrapping is a useful technique for estimating the uncertainty of a predictor, for example, confidence intervals for prediction. It is typically used on small to moderate sized datasets, due to its high computation cost. This work describes a highly scalable online bootstrapping strategy, implemented inside Vowpal Wabbit, that is several times faster than traditional strategies. Our experiments indicate that, in addition to providing a black box-like method for estimating uncertainty, our implementation of online bootstrapping may also help to train models with better prediction performance due to model averaging.
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Efficient Online Bootstrapping for Large Scale Learning
| 2,556
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Neural networks have recently been proposed for multi-label classification because they are able to capture and model label dependencies in the output layer. In this work, we investigate limitations of BP-MLL, a neural network (NN) architecture that aims at minimizing pairwise ranking error. Instead, we propose to use a comparably simple NN approach with recently proposed learning techniques for large-scale multi-label text classification tasks. In particular, we show that BP-MLL's ranking loss minimization can be efficiently and effectively replaced with the commonly used cross entropy error function, and demonstrate that several advances in neural network training that have been developed in the realm of deep learning can be effectively employed in this setting. Our experimental results show that simple NN models equipped with advanced techniques such as rectified linear units, dropout, and AdaGrad perform as well as or even outperform state-of-the-art approaches on six large-scale textual datasets with diverse characteristics.
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Large-scale Multi-label Text Classification - Revisiting Neural Networks
| 2,557
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We present the first deep learning model to successfully learn control policies directly from high-dimensional sensory input using reinforcement learning. The model is a convolutional neural network, trained with a variant of Q-learning, whose input is raw pixels and whose output is a value function estimating future rewards. We apply our method to seven Atari 2600 games from the Arcade Learning Environment, with no adjustment of the architecture or learning algorithm. We find that it outperforms all previous approaches on six of the games and surpasses a human expert on three of them.
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Playing Atari with Deep Reinforcement Learning
| 2,558
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Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional \nway{} classification framing of image understanding, particularly in terms of the promise for zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. In this paper, we propose a simple method for constructing an image embedding system from any existing \nway{} image classifier and a semantic word embedding model, which contains the $\n$ class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional training. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.
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Zero-Shot Learning by Convex Combination of Semantic Embeddings
| 2,559
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Recently, it has been observed that when representations are learnt in a way that encourages sparsity, improved performance is obtained on classification tasks. These methods involve combinations of activation functions, sampling steps and different kinds of penalties. To investigate the effectiveness of sparsity by itself, we propose the k-sparse autoencoder, which is an autoencoder with linear activation function, where in hidden layers only the k highest activities are kept. When applied to the MNIST and NORB datasets, we find that this method achieves better classification results than denoising autoencoders, networks trained with dropout, and RBMs. k-sparse autoencoders are simple to train and the encoding stage is very fast, making them well-suited to large problem sizes, where conventional sparse coding algorithms cannot be applied.
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k-Sparse Autoencoders
| 2,560
|
Recent non-linear feature selection approaches employing greedy optimisation of Centred Kernel Target Alignment(KTA) exhibit strong results in terms of generalisation accuracy and sparsity. However, they are computationally prohibitive for large datasets. We propose randSel, a randomised feature selection algorithm, with attractive scaling properties. Our theoretical analysis of randSel provides strong probabilistic guarantees for correct identification of relevant features. RandSel's characteristics make it an ideal candidate for identifying informative learned representations. We've conducted experimentation to establish the performance of this approach, and present encouraging results, including a 3rd position result in the recent ICML black box learning challenge as well as competitive results for signal peptide prediction, an important problem in bioinformatics.
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Principled Non-Linear Feature Selection
| 2,561
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We present new initialization methods for the expectation-maximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known $K$-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the gap between simple random, e.g. uniform, and complex methods, that crucially depend on the right choice of hyperparameters. Our extensive experiments indicate the usefulness of our methods compared to common techniques and methods, which e.g. apply the original $K$-means++ and Gonzalez directly, with respect to artificial as well as real-world data sets.
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Adaptive Seeding for Gaussian Mixture Models
| 2,562
|
Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are robust and widely applicable across many different optimization landscapes. In this paper we develop a collection of unit tests for stochastic optimization. Each unit test rapidly evaluates an optimization algorithm on a small-scale, isolated, and well-understood difficulty, rather than in real-world scenarios where many such issues are entangled. Passing these unit tests is not sufficient, but absolutely necessary for any algorithms with claims to generality or robustness. We give initial quantitative and qualitative results on numerous established algorithms. The testing framework is open-source, extensible, and easy to apply to new algorithms.
|
Unit Tests for Stochastic Optimization
| 2,563
|
Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used to decide whether the approximation provided by the CD algorithm is good enough, though several authors (Schulz et al., 2010; Fischer & Igel, 2010) have raised doubts concerning the feasibility of this procedure. However, not many alternatives to the reconstruction error have been used in the literature. In this manuscript we investigate simple alternatives to the reconstruction error in order to detect as soon as possible the decrease in the log-likelihood during learning.
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Stopping Criteria in Contrastive Divergence: Alternatives to the
Reconstruction Error
| 2,564
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Within the framework of AdaBoost.MH, we propose to train vector-valued decision trees to optimize the multi-class edge without reducing the multi-class problem to $K$ binary one-against-all classifications. The key element of the method is a vector-valued decision stump, factorized into an input-independent vector of length $K$ and label-independent scalar classifier. At inner tree nodes, the label-dependent vector is discarded and the binary classifier can be used for partitioning the input space into two regions. The algorithm retains the conceptual elegance, power, and computational efficiency of binary AdaBoost. In experiments it is on par with support vector machines and with the best existing multi-class boosting algorithm AOSOLogitBoost, and it is significantly better than other known implementations of AdaBoost.MH.
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The return of AdaBoost.MH: multi-class Hamming trees
| 2,565
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Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the clustering methods, so this paper introduce one way to calculate the error rate of clustering methods. Clustering algorithms can be divided into several categories including partitioning clustering algorithms, hierarchical algorithms and density based algorithms. Generally speaking we should compare clustering algorithms by Scalability, Ability to work with different attribute, Clusters formed by conventional, Having minimal knowledge of the computer to recognize the input parameters, Classes for dealing with noise and extra deposition that same error rate for clustering a new data, Thus, there is no effect on the input data, different dimensions of high levels, K-means is one of the simplest approach to clustering that clustering is an unsupervised problem.
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Comparison three methods of clustering: k-means, spectral clustering and
hierarchical clustering
| 2,566
|
Transfer Learning is concerned with the application of knowledge gained from solving a problem to a different but related problem domain. In this paper, we propose a method and efficient algorithm for ranking and selecting representations from a Restricted Boltzmann Machine trained on a source domain to be transferred onto a target domain. Experiments carried out using the MNIST, ICDAR and TiCC image datasets show that the proposed adaptive feature ranking and transfer learning method offers statistically significant improvements on the training of RBMs. Our method is general in that the knowledge chosen by the ranking function does not depend on its relation to any specific target domain, and it works with unsupervised learning and knowledge-based transfer.
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Adaptive Feature Ranking for Unsupervised Transfer Learning
| 2,567
|
Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an unknown target distribution. These methods rely on a singular value decomposition of a matrix $H_S$, called the Hankel matrix, that records the frequencies of (some of) the observed strings. The accuracy of the learned distribution depends both on the quantity of information embedded in $H_S$ and on the distance between $H_S$ and its mean $H_r$. Existing concentration bounds seem to indicate that the concentration over $H_r$ gets looser with the size of $H_r$, suggesting to make a trade-off between the quantity of used information and the size of $H_r$. We propose new dimension-free concentration bounds for several variants of Hankel matrices. Experiments demonstrate that these bounds are tight and that they significantly improve existing bounds. These results suggest that the concentration rate of the Hankel matrix around its mean does not constitute an argument for limiting its size.
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Dimension-free Concentration Bounds on Hankel Matrices for Spectral
Learning
| 2,568
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Time-series classification is an important domain of machine learning and a plethora of methods have been developed for the task. In comparison to existing approaches, this study presents a novel method which decomposes a time-series dataset into latent patterns and membership weights of local segments to those patterns. The process is formalized as a constrained objective function and a tailored stochastic coordinate descent optimization is applied. The time-series are projected to a new feature representation consisting of the sums of the membership weights, which captures frequencies of local patterns. Features from various sliding window sizes are concatenated in order to encapsulate the interaction of patterns from different sizes. Finally, a large-scale experimental comparison against 6 state of the art baselines and 43 real life datasets is conducted. The proposed method outperforms all the baselines with statistically significant margins in terms of prediction accuracy.
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Invariant Factorization Of Time-Series
| 2,569
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Transductive graph-based semi-supervised learning methods usually build an undirected graph utilizing both labeled and unlabeled samples as vertices. Those methods propagate label information of labeled samples to neighbors through their edges in order to get the predicted labels of unlabeled samples. Most popular semi-supervised learning approaches are sensitive to initial label distribution happened in imbalanced labeled datasets. The class boundary will be severely skewed by the majority classes in an imbalanced classification. In this paper, we proposed a simple and effective approach to alleviate the unfavorable influence of imbalance problem by iteratively selecting a few unlabeled samples and adding them into the minority classes to form a balanced labeled dataset for the learning methods afterwards. The experiments on UCI datasets and MNIST handwritten digits dataset showed that the proposed approach outperforms other existing state-of-art methods.
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Iterative Nearest Neighborhood Oversampling in Semisupervised Learning
from Imbalanced Data
| 2,570
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A rekindled the interest in auto-encoder algorithms has been spurred by recent work on deep learning. Current efforts have been directed towards effective training of auto-encoder architectures with a large number of coding units. Here, we propose a learning algorithm for auto-encoders based on a rate-distortion objective that minimizes the mutual information between the inputs and the outputs of the auto-encoder subject to a fidelity constraint. The goal is to learn a representation that is minimally committed to the input data, but that is rich enough to reconstruct the inputs up to certain level of distortion. Minimizing the mutual information acts as a regularization term whereas the fidelity constraint can be understood as a risk functional in the conventional statistical learning setting. The proposed algorithm uses a recently introduced measure of entropy based on infinitely divisible matrices that avoids the plug in estimation of densities. Experiments using over-complete bases show that the rate-distortion auto-encoders can learn a regularized input-output mapping in an implicit manner.
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Rate-Distortion Auto-Encoders
| 2,571
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When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy $F$, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An algorithm was recently introduced for attractive binary pairwise MRFs which is guaranteed to return an $\epsilon$-approximation to the global minimum of $F$ in polynomial time provided the maximum degree $\Delta=O(\log n)$, where $n$ is the number of variables. Here we significantly improve this algorithm and derive several results including a new approach based on analyzing first derivatives of $F$, which leads to performance that is typically far superior and yields a fully polynomial-time approximation scheme (FPTAS) for attractive models without any degree restriction. Further, the method applies to general (non-attractive) models, though with no polynomial time guarantee in this case, leading to the important result that approximating $\log$ of the Bethe partition function, $\log Z_B=-\min F$, for a general model to additive $\epsilon$-accuracy may be reduced to a discrete MAP inference problem. We explore an application to predicting equipment failure on an urban power network and demonstrate that the Bethe approximation can perform well even when BP fails to converge.
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Approximating the Bethe partition function
| 2,572
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Multiple Kernel Learning(MKL) on Support Vector Machines(SVMs) has been a popular front of research in recent times due to its success in application problems like Object Categorization. This success is due to the fact that MKL has the ability to choose from a variety of feature kernels to identify the optimal kernel combination. But the initial formulation of MKL was only able to select the best of the features and misses out many other informative kernels presented. To overcome this, the Lp norm based formulation was proposed by Kloft et. al. This formulation is capable of choosing a non-sparse set of kernels through a control parameter p. Unfortunately, the parameter p does not have a direct meaning to the number of kernels selected. We have observed that stricter control over the number of kernels selected gives us an edge over these techniques in terms of accuracy of classification and also helps us to fine tune the algorithms to the time requirements at hand. In this work, we propose a Controlled Sparsity Kernel Learning (CSKL) formulation that can strictly control the number of kernels which we wish to select. The CSKL formulation introduces a parameter t which directly corresponds to the number of kernels selected. It is important to note that a search in t space is finite and fast as compared to p. We have also provided an efficient Reduced Gradient Descent based algorithm to solve the CSKL formulation, which is proven to converge. Through our experiments on the Caltech101 Object Categorization dataset, we have also shown that one can achieve better accuracies than the previous formulations through the right choice of t.
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Controlled Sparsity Kernel Learning
| 2,573
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Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements--eigenfunctions of a GP prior--and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements--eigenfunctions--and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machine.
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EigenGP: Gaussian Process Models with Adaptive Eigenfunctions
| 2,574
|
Motivated by applications in energy management, this paper presents the Multi-Armed Risk-Aware Bandit (MARAB) algorithm. With the goal of limiting the exploration of risky arms, MARAB takes as arm quality its conditional value at risk. When the user-supplied risk level goes to 0, the arm quality tends toward the essential infimum of the arm distribution density, and MARAB tends toward the MIN multi-armed bandit algorithm, aimed at the arm with maximal minimal value. As a first contribution, this paper presents a theoretical analysis of the MIN algorithm under mild assumptions, establishing its robustness comparatively to UCB. The analysis is supported by extensive experimental validation of MIN and MARAB compared to UCB and state-of-art risk-aware MAB algorithms on artificial and real-world problems.
|
Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits
| 2,575
|
In recent years, there has been growing focus on the study of automated recommender systems. Music recommendation systems serve as a prominent domain for such works, both from an academic and a commercial perspective. A fundamental aspect of music perception is that music is experienced in temporal context and in sequence. In this work we present DJ-MC, a novel reinforcement-learning framework for music recommendation that does not recommend songs individually but rather song sequences, or playlists, based on a model of preferences for both songs and song transitions. The model is learned online and is uniquely adapted for each listener. To reduce exploration time, DJ-MC exploits user feedback to initialize a model, which it subsequently updates by reinforcement. We evaluate our framework with human participants using both real song and playlist data. Our results indicate that DJ-MC's ability to recommend sequences of songs provides a significant improvement over more straightforward approaches, which do not take transitions into account.
|
DJ-MC: A Reinforcement-Learning Agent for Music Playlist Recommendation
| 2,576
|
This paper develops a theory of clustering and coding which combines a geometric model with a probabilistic model in a principled way. The geometric model is a Riemannian manifold with a Riemannian metric, ${g}_{ij}({\bf x})$, which we interpret as a measure of dissimilarity. The probabilistic model consists of a stochastic process with an invariant probability measure which matches the density of the sample input data. The link between the two models is a potential function, $U({\bf x})$, and its gradient, $\nabla U({\bf x})$. We use the gradient to define the dissimilarity metric, which guarantees that our measure of dissimilarity will depend on the probability measure. Finally, we use the dissimilarity metric to define a coordinate system on the embedded Riemannian manifold, which gives us a low-dimensional encoding of our original data.
|
Clustering, Coding, and the Concept of Similarity
| 2,577
|
We propose a novel method for approximate inference in Bayesian networks (BNs). The idea is to sample data from a BN, learn a latent tree model (LTM) from the data offline, and when online, make inference with the LTM instead of the original BN. Because LTMs are tree-structured, inference takes linear time. In the meantime, they can represent complex relationship among leaf nodes and hence the approximation accuracy is often good. Empirical evidence shows that our method can achieve good approximation accuracy at low online computational cost.
|
Latent Tree Models and Approximate Inference in Bayesian Networks
| 2,578
|
The paper investigates stochastic resource allocation problems with scarce, reusable resources and non-preemtive, time-dependent, interconnected tasks. This approach is a natural generalization of several standard resource management problems, such as scheduling and transportation problems. First, reactive solutions are considered and defined as control policies of suitably reformulated Markov decision processes (MDPs). We argue that this reformulation has several favorable properties, such as it has finite state and action spaces, it is aperiodic, hence all policies are proper and the space of control policies can be safely restricted. Next, approximate dynamic programming (ADP) methods, such as fitted Q-learning, are suggested for computing an efficient control policy. In order to compactly maintain the cost-to-go function, two representations are studied: hash tables and support vector regression (SVR), particularly, nu-SVRs. Several additional improvements, such as the application of limited-lookahead rollout algorithms in the initial phases, action space decomposition, task clustering and distributed sampling are investigated, too. Finally, experimental results on both benchmark and industry-related data are presented.
|
Adaptive Stochastic Resource Control: A Machine Learning Approach
| 2,579
|
Machine learning techniques are gaining prevalence in the production of a wide range of classifiers for complex real-world applications with nonuniform testing and misclassification costs. The increasing complexity of these applications poses a real challenge to resource management during learning and classification. In this work we introduce ACT (anytime cost-sensitive tree learner), a novel framework for operating in such complex environments. ACT is an anytime algorithm that allows learning time to be increased in return for lower classification costs. It builds a tree top-down and exploits additional time resources to obtain better estimations for the utility of the different candidate splits. Using sampling techniques, ACT approximates the cost of the subtree under each candidate split and favors the one with a minimal cost. As a stochastic algorithm, ACT is expected to be able to escape local minima, into which greedy methods may be trapped. Experiments with a variety of datasets were conducted to compare ACT to the state-of-the-art cost-sensitive tree learners. The results show that for the majority of domains ACT produces significantly less costly trees. ACT also exhibits good anytime behavior with diminishing returns.
|
Anytime Induction of Low-cost, Low-error Classifiers: a Sampling-based
Approach
| 2,580
|
In this paper we apply Conformal Prediction (CP) to the k-Nearest Neighbours Regression (k-NNR) algorithm and propose ways of extending the typical nonconformity measure used for regression so far. Unlike traditional regression methods which produce point predictions, Conformal Predictors output predictive regions that satisfy a given confidence level. The regions produced by any Conformal Predictor are automatically valid, however their tightness and therefore usefulness depends on the nonconformity measure used by each CP. In effect a nonconformity measure evaluates how strange a given example is compared to a set of other examples based on some traditional machine learning algorithm. We define six novel nonconformity measures based on the k-Nearest Neighbours Regression algorithm and develop the corresponding CPs following both the original (transductive) and the inductive CP approaches. A comparison of the predictive regions produced by our measures with those of the typical regression measure suggests that a major improvement in terms of predictive region tightness is achieved by the new measures.
|
Regression Conformal Prediction with Nearest Neighbours
| 2,581
|
Multiclass problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. Various methods, including all-pairs (APs), one-versus-all (OVA), and error correcting output code (ECOC), have been studied, to decompose multiclass problems into binary problems. However, little study has been made to optimally aggregate binary problems to determine a final answer to the multiclass problem. In this paper we present a convex optimization method for an optimal aggregation of binary classifiers to estimate class membership probabilities in multiclass problems. We model the class membership probability as a softmax function which takes a conic combination of discrepancies induced by individual binary classifiers, as an input. With this model, we formulate the regularized maximum likelihood estimation as a convex optimization problem, which is solved by the primal-dual interior point method. Connections of our method to large margin classifiers are presented, showing that the large margin formulation can be considered as a limiting case of our convex formulation. Numerical experiments on synthetic and real-world data sets demonstrate that our method outperforms existing aggregation methods as well as direct methods, in terms of the classification accuracy and the quality of class membership probability estimates.
|
Convex Optimization for Binary Classifier Aggregation in Multiclass
Problems
| 2,582
|
Over the past few years, Multi-Kernel Learning (MKL) has received significant attention among data-driven feature selection techniques in the context of kernel-based learning. MKL formulations have been devised and solved for a broad spectrum of machine learning problems, including Multi-Task Learning (MTL). Solving different MKL formulations usually involves designing algorithms that are tailored to the problem at hand, which is, typically, a non-trivial accomplishment. In this paper we present a general Multi-Task Multi-Kernel Learning (Multi-Task MKL) framework that subsumes well-known Multi-Task MKL formulations, as well as several important MKL approaches on single-task problems. We then derive a simple algorithm that can solve the unifying framework. To demonstrate the flexibility of the proposed framework, we formulate a new learning problem, namely Partially-Shared Common Space (PSCS) Multi-Task MKL, and demonstrate its merits through experimentation.
|
A Unifying Framework for Typical Multi-Task Multiple Kernel Learning
Problems
| 2,583
|
An extreme learning machine (ELM) can be regarded as a two stage feed-forward neural network (FNN) learning system which randomly assigns the connections with and within hidden neurons in the first stage and tunes the connections with output neurons in the second stage. Therefore, ELM training is essentially a linear learning problem, which significantly reduces the computational burden. Numerous applications show that such a computation burden reduction does not degrade the generalization capability. It has, however, been open that whether this is true in theory. The aim of our work is to study the theoretical feasibility of ELM by analyzing the pros and cons of ELM. In the previous part on this topic, we pointed out that via appropriate selection of the activation function, ELM does not degrade the generalization capability in the expectation sense. In this paper, we launch the study in a different direction and show that the randomness of ELM also leads to certain negative consequences. On one hand, we find that the randomness causes an additional uncertainty problem of ELM, both in approximation and learning. On the other hand, we theoretically justify that there also exists an activation function such that the corresponding ELM degrades the generalization capability. In particular, we prove that the generalization capability of ELM with Gaussian kernel is essentially worse than that of FNN with Gaussian kernel. To facilitate the use of ELM, we also provide a remedy to such a degradation. We find that the well-developed coefficient regularization technique can essentially improve the generalization capability. The obtained results reveal the essential characteristic of ELM and give theoretical guidance concerning how to use ELM.
|
Is Extreme Learning Machine Feasible? A Theoretical Assessment (Part II)
| 2,584
|
Non-negative least-mean-square (NNLMS) algorithm and its variants have been proposed for online estimation under non-negativity constraints. The transient behavior of the NNLMS, Normalized NNLMS, Exponential NNLMS and Sign-Sign NNLMS algorithms have been studied in our previous work. In this technical report, we derive closed-form expressions for the steady-state excess mean-square error (EMSE) for the four algorithms. Simulations results illustrate the accuracy of the theoretical results. This is a complementary material to our previous work.
|
Steady-state performance of non-negative least-mean-square algorithm and
its variants
| 2,585
|
Distributions over rankings are used to model data in a multitude of real world settings such as preference analysis and political elections. Modeling such distributions presents several computational challenges, however, due to the factorial size of the set of rankings over an item set. Some of these challenges are quite familiar to the artificial intelligence community, such as how to compactly represent a distribution over a combinatorially large space, and how to efficiently perform probabilistic inference with these representations. With respect to ranking, however, there is the additional challenge of what we refer to as human task complexity users are rarely willing to provide a full ranking over a long list of candidates, instead often preferring to provide partial ranking information. Simultaneously addressing all of these challenges i.e., designing a compactly representable model which is amenable to efficient inference and can be learned using partial ranking data is a difficult task, but is necessary if we would like to scale to problems with nontrivial size. In this paper, we show that the recently proposed riffled independence assumptions cleanly and efficiently address each of the above challenges. In particular, we establish a tight mathematical connection between the concepts of riffled independence and of partial rankings. This correspondence not only allows us to then develop efficient and exact algorithms for performing inference tasks using riffled independence based represen- tations with partial rankings, but somewhat surprisingly, also shows that efficient inference is not possible for riffle independent models (in a certain sense) with observations which do not take the form of partial rankings. Finally, using our inference algorithm, we introduce the first method for learning riffled independence based models from partially ranked data.
|
Riffled Independence for Efficient Inference with Partial Rankings
| 2,586
|
Anomaly detection is being regarded as an unsupervised learning task as anomalies stem from adversarial or unlikely events with unknown distributions. However, the predictive performance of purely unsupervised anomaly detection often fails to match the required detection rates in many tasks and there exists a need for labeled data to guide the model generation. Our first contribution shows that classical semi-supervised approaches, originating from a supervised classifier, are inappropriate and hardly detect new and unknown anomalies. We argue that semi-supervised anomaly detection needs to ground on the unsupervised learning paradigm and devise a novel algorithm that meets this requirement. Although being intrinsically non-convex, we further show that the optimization problem has a convex equivalent under relatively mild assumptions. Additionally, we propose an active learning strategy to automatically filter candidates for labeling. In an empirical study on network intrusion detection data, we observe that the proposed learning methodology requires much less labeled data than the state-of-the-art, while achieving higher detection accuracies.
|
Toward Supervised Anomaly Detection
| 2,587
|
We introduce a new problem, the Online Selective Anomaly Detection (OSAD), to model a specific scenario emerging from research in sleep science. Scientists have segmented sleep into several stages and stage two is characterized by two patterns (or anomalies) in the EEG time series recorded on sleep subjects. These two patterns are sleep spindle (SS) and K-complex. The OSAD problem was introduced to design a residual system, where all anomalies (known and unknown) are detected but the system only triggers an alarm when non-SS anomalies appear. The solution of the OSAD problem required us to combine techniques from both machine learning and control theory. Experiments on data from real subjects attest to the effectiveness of our approach.
|
Sleep Analytics and Online Selective Anomaly Detection
| 2,588
|
A commonly used paradigm for representing graphs is to use a vector that contains normalized frequencies of occurrence of certain motifs or sub-graphs. This vector representation can be used in a variety of applications, such as, for computing similarity between graphs. The graphlet kernel of Shervashidze et al. [32] uses induced sub-graphs of k nodes (christened as graphlets by Przulj [28]) as motifs in the vector representation, and computes the kernel via a dot product between these vectors. One can easily show that this is a valid kernel between graphs. However, such a vector representation suffers from a few drawbacks. As k becomes larger we encounter the sparsity problem; most higher order graphlets will not occur in a given graph. This leads to diagonal dominance, that is, a given graph is similar to itself but not to any other graph in the dataset. On the other hand, since lower order graphlets tend to be more numerous, using lower values of k does not provide enough discrimination ability. We propose a smoothing technique to tackle the above problems. Our method is based on a novel extension of Kneser-Ney and Pitman-Yor smoothing techniques from natural language processing to graphs. We use the relationships between lower order and higher order graphlets in order to derive our method. Consequently, our smoothing algorithm not only respects the dependency between sub-graphs but also tackles the diagonal dominance problem by distributing the probability mass across graphlets. In our experiments, the smoothed graphlet kernel outperforms graph kernels based on raw frequency counts.
|
The Structurally Smoothed Graphlet Kernel
| 2,589
|
We study algorithms for online linear optimization in Hilbert spaces, focusing on the case where the player is unconstrained. We develop a novel characterization of a large class of minimax algorithms, recovering, and even improving, several previous results as immediate corollaries. Moreover, using our tools, we develop an algorithm that provides a regret bound of $\mathcal{O}\Big(U \sqrt{T \log(U \sqrt{T} \log^2 T +1)}\Big)$, where $U$ is the $L_2$ norm of an arbitrary comparator and both $T$ and $U$ are unknown to the player. This bound is optimal up to $\sqrt{\log \log T}$ terms. When $T$ is known, we derive an algorithm with an optimal regret bound (up to constant factors). For both the known and unknown $T$ case, a Normal approximation to the conditional value of the game proves to be the key analysis tool.
|
Unconstrained Online Linear Learning in Hilbert Spaces: Minimax
Algorithms and Normal Approximations
| 2,590
|
In this paper we present methods for exemplar based clustering with outlier selection based on the facility location formulation. Given a distance function and the number of outliers to be found, the methods automatically determine the number of clusters and outliers. We formulate the problem as an integer program to which we present relaxations that allow for solutions that scale to large data sets. The advantages of combining clustering and outlier selection include: (i) the resulting clusters tend to be compact and semantically coherent (ii) the clusters are more robust against data perturbations and (iii) the outliers are contextualised by the clusters and more interpretable, i.e. it is easier to distinguish between outliers which are the result of data errors from those that may be indicative of a new pattern emergent in the data. We present and contrast three relaxations to the integer program formulation: (i) a linear programming formulation (LP) (ii) an extension of affinity propagation to outlier detection (APOC) and (iii) a Lagrangian duality based formulation (LD). Evaluation on synthetic as well as real data shows the quality and scalability of these different methods.
|
Integer Programming Relaxations for Integrated Clustering and Outlier
Detection
| 2,591
|
In the past few years co-clustering has emerged as an important data mining tool for two way data analysis. Co-clustering is more advantageous over traditional one dimensional clustering in many ways such as, ability to find highly correlated sub-groups of rows and columns. However, one of the overlooked benefits of co-clustering is that, it can be used to extract meaningful knowledge for various other knowledge extraction purposes. For example, building predictive models with high dimensional data and heterogeneous population is a non-trivial task. Co-clusters extracted from such data, which shows similar pattern in both the dimension, can be used for a more accurate predictive model building. Several applications such as finding patient-disease cohorts in health care analysis, finding user-genre groups in recommendation systems and community detection problems can benefit from co-clustering technique that utilizes the predictive power of the data to generate co-clusters for improved data analysis. In this paper, we present the novel idea of Predictive Overlapping Co-Clustering (POCC) as an optimization problem for a more effective and improved predictive analysis. Our algorithm generates optimal co-clusters by maximizing predictive power of the co-clusters subject to the constraints on the number of row and column clusters. In this paper precision, recall and f-measure have been used as evaluation measures of the resulting co-clusters. Results of our algorithm has been compared with two other well-known techniques - K-means and Spectral co-clustering, over four real data set namely, Leukemia, Internet-Ads, Ovarian cancer and MovieLens data set. The results demonstrate the effectiveness and utility of our algorithm POCC in practice.
|
Predictive Overlapping Co-Clustering
| 2,592
|
In recent years the importance of finding a meaningful pattern from huge datasets has become more challenging. Data miners try to adopt innovative methods to face this problem by applying feature selection methods. In this paper we propose a new hybrid method in which we use a combination of resampling, filtering the sample domain and wrapper subset evaluation method with genetic search to reduce dimensions of Lung-Cancer dataset that we received from UCI Repository of Machine Learning databases. Finally, we apply some well- known classification algorithms (Na\"ive Bayes, Logistic, Multilayer Perceptron, Best First Decision Tree and JRIP) to the resulting dataset and compare the results and prediction rates before and after the application of our feature selection method on that dataset. The results show a substantial progress in the average performance of five classification algorithms simultaneously and the classification error for these classifiers decreases considerably. The experiments also show that this method outperforms other feature selection methods with a lower cost.
|
Improving Performance of a Group of Classification Algorithms Using
Resampling and Feature Selection
| 2,593
|
Cluster analysis has attracted more and more attention in the field of machine learning and data mining. Numerous clustering algorithms have been proposed and are being developed due to diverse theories and various requirements of emerging applications. Therefore, it is very worth establishing an unified axiomatic framework for data clustering. In the literature, it is an open problem and has been proved very challenging. In this paper, clustering results are axiomatized by assuming that an proper clustering result should satisfy categorization axioms. The proposed axioms not only introduce classification of clustering results and inequalities of clustering results, but also are consistent with prototype theory and exemplar theory of categorization models in cognitive science. Moreover, the proposed axioms lead to three principles of designing clustering algorithm and cluster validity index, which follow many popular clustering algorithms and cluster validity indices.
|
Categorization Axioms for Clustering Results
| 2,594
|
In this paper a hybrid feature selection method is proposed which takes advantages of wrapper subset evaluation with a lower cost and improves the performance of a group of classifiers. The method uses combination of sample domain filtering and resampling to refine the sample domain and two feature subset evaluation methods to select reliable features. This method utilizes both feature space and sample domain in two phases. The first phase filters and resamples the sample domain and the second phase adopts a hybrid procedure by information gain, wrapper subset evaluation and genetic search to find the optimal feature space. Experiments carried out on different types of datasets from UCI Repository of Machine Learning databases and the results show a rise in the average performance of five classifiers (Naive Bayes, Logistic, Multilayer Perceptron, Best First Decision Tree and JRIP) simultaneously and the classification error for these classifiers decreases considerably. The experiments also show that this method outperforms other feature selection methods with a lower cost.
|
A Hybrid Feature Selection Method to Improve Performance of a Group of
Classification Algorithms
| 2,595
|
High accuracy in cancer prediction is important to improve the quality of the treatment and to improve the rate of survivability of patients. As the data volume is increasing rapidly in the healthcare research, the analytical challenge exists in double. The use of effective sampling technique in classification algorithms always yields good prediction accuracy. The SEER public use cancer database provides various prominent class labels for prognosis prediction. The main objective of this paper is to find the effect of sampling techniques in classifying the prognosis variable and propose an ideal sampling method based on the outcome of the experimentation. In the first phase of this work the traditional random sampling and stratified sampling techniques have been used. At the next level the balanced stratified sampling with variations as per the choice of the prognosis class labels have been tested. Much of the initial time has been focused on performing the pre_processing of the SEER data set. The classification model for experimentation has been built using the breast cancer, respiratory cancer and mixed cancer data sets with three traditional classifiers namely Decision Tree, Naive Bayes and K-Nearest Neighbor. The three prognosis factors survival, stage and metastasis have been used as class labels for experimental comparisons. The results shows a steady increase in the prediction accuracy of balanced stratified model as the sample size increases, but the traditional approach fluctuates before the optimum results.
|
Cancer Prognosis Prediction Using Balanced Stratified Sampling
| 2,596
|
We present tools for the analysis of Follow-The-Regularized-Leader (FTRL), Dual Averaging, and Mirror Descent algorithms when the regularizer (equivalently, prox-function or learning rate schedule) is chosen adaptively based on the data. Adaptivity can be used to prove regret bounds that hold on every round, and also allows for data-dependent regret bounds as in AdaGrad-style algorithms (e.g., Online Gradient Descent with adaptive per-coordinate learning rates). We present results from a large number of prior works in a unified manner, using a modular and tight analysis that isolates the key arguments in easily re-usable lemmas. This approach strengthens pre-viously known FTRL analysis techniques to produce bounds as tight as those achieved by potential functions or primal-dual analysis. Further, we prove a general and exact equivalence between an arbitrary adaptive Mirror Descent algorithm and a correspond- ing FTRL update, which allows us to analyze any Mirror Descent algorithm in the same framework. The key to bridging the gap between Dual Averaging and Mirror Descent algorithms lies in an analysis of the FTRL-Proximal algorithm family. Our regret bounds are proved in the most general form, holding for arbitrary norms and non-smooth regularizers with time-varying weight.
|
A Survey of Algorithms and Analysis for Adaptive Online Learning
| 2,597
|
In many applications, the training data, from which one needs to learn a classifier, is corrupted with label noise. Many standard algorithms such as SVM perform poorly in presence of label noise. In this paper we investigate the robustness of risk minimization to label noise. We prove a sufficient condition on a loss function for the risk minimization under that loss to be tolerant to uniform label noise. We show that the $0-1$ loss, sigmoid loss, ramp loss and probit loss satisfy this condition though none of the standard convex loss functions satisfy it. We also prove that, by choosing a sufficiently large value of a parameter in the loss function, the sigmoid loss, ramp loss and probit loss can be made tolerant to non-uniform label noise also if we can assume the classes to be separable under noise-free data distribution. Through extensive empirical studies, we show that risk minimization under the $0-1$ loss, the sigmoid loss and the ramp loss has much better robustness to label noise when compared to the SVM algorithm.
|
Making Risk Minimization Tolerant to Label Noise
| 2,598
|
This work investigates the use of mixed-norm regularization for sensor selection in Event-Related Potential (ERP) based Brain-Computer Interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is extended to the multi-task learning situation where several similar classification tasks related to different subjects are learned simultaneously. In this case, multi-task learning helps in leveraging data scarcity issue yielding to more robust classifiers. For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities. The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection. The multi-task approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.
|
Mixed-norm Regularization for Brain Decoding
| 2,599
|
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