Cross-Validation (CV), and out-of-sample performance-estimation protocols in general, are often employed both for (a) selecting the optimal combination of algorithms and values of hyper-parameters (called a configuration) for producing the final predictive model, and (b) estimating the predictive performance of the final model. However, the cross-validated performance of the best configuration is optimistically biased. We present an efficient bootstrap method that corrects for the bias, called Bootstrap Bias Corrected CV (BBC-CV). BBC-CV's main idea is to bootstrap the whole process of selecting the best-performing configuration on the out-of-sample predictions of each configuration, without additional training of models. In comparison to the alternatives, namely the nested cross-validation and a method by Tibshirani and Tibshirani, BBC-CV is computationally more efficient, has smaller variance and bias, and is applicable to any metric of performance (accuracy, AUC, concordance index, mean squared error). Subsequently, we employ again the idea of bootstrapping the out-of-sample predictions to speed up the CV process. Specifically, using a bootstrap-based hypothesis test we stop training of models on new folds of statistically-significantly inferior configurations. We name the method Bootstrap Corrected with Early Dropping CV (BCED-CV) that is both efficient and provides accurate performance estimates.
Krueger @cite_14 in 2015 introduced the so-called (CVST) which uses nonparametric testing together with sequential analysis in order to choose the best performing configuration on the basis of linearly increasing subsets of data. At each step, the Friedman @cite_22 or the Cochran's Q test @cite_18 (for regression and classification tasks respectively) are employed in order to detect statistically significant differences between configurations' performances. Then, the seemingly under-performing configurations are further tested through sequential analysis to determine which of them will be discharged. Finally, an early stopping criterion is employed to further speed up the CV process. The winner configuration is the one that has the best average ranking, based on performance, in the last few iterations specified in advance. The disadvantage of CVST is that it initially operates on smaller subsets, thus risking the early elimination of good models when the original dataset is already small.
@cite_18 @cite_14 @cite_22
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Context: This paper presents an approach for selecting regression test cases in the context of large-scale database applications. We focus on a black-box (specification-based) approach, relying on classification tree models to model the input domain of the system under test (SUT), in order to obtain a more practical and scalable solution. We perform an experiment in an industrial setting where the SUT is a large database application in Norway's tax department. Objective: We investigate the use of similarity-based test case selection for supporting black box regression testing of database applications. We have developed a practical approach and tool (DART) for functional black-box regression testing of database applications. In order to make the regression test approach scalable for large database applications, we needed a test case selection strategy that reduces the test execution costs and analysis effort. We used classification tree models to partition the input domain of the SUT in order to then select test cases. Rather than selecting test cases at random from each partition, we incorporated a similarity-based test case selection, hypothesizing that it would yield a higher fault detection rate. Method: An experiment was conducted to determine which similarity-based selection algorithm was the most suitable in selecting test cases in large regression test suites, and whether similarity-based selection was a worthwhile and practical alternative to simpler solutions. Results: The results show that combining similarity measurement with partition-based test case selection, by using similarity-based test case selection within each partition, can provide improved fault detection rates over simpler solutions when specific conditions are met regarding the partitions. Conclusions: Under the conditions present in the experiment the improvements were marginal. However, a detailed analysis concludes that the similarity-based selection strategy should be applied when a large number of test cases are contained in each partition and there is significant variability within partitions. If these conditions are not present, incorporating similarity measures is not worthwhile, since the gain is negligible over a random selection within each partition. We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises naturally from settings where the outcome, unlike the covariates, is expensive to obtain, a frequent scenario in modern studies involving large databases like electronic medical records (EMR). Supervised estimators like the ordinary least squares (OLS) estimator utilize only the labeled data. It is often of interest to investigate if and when the unlabeled data can be exploited to improve estimation of the regression parameter in the adopted linear model. In this paper, we propose a class of 'Efficient and Adaptive Semi-Supervised Estimators' (EASE) to improve estimation efficiency. The EASE are two-step estimators adaptive to model mis-specification, leading to improved (optimal in some cases) efficiency under model mis-specification, and equal (optimal) efficiency under a linear model. This adaptive property, often unaddressed in the existing literature, is crucial for advocating 'safe' use of the unlabeled data. The construction of EASE primarily involves a flexible 'semi-non-parametric' imputation, including a smoothing step that works well even when the number of covariates is not small; and a follow up 'refitting' step along with a cross-validation (CV) strategy both of which have useful practical as well as theoretical implications towards addressing two important issues: under-smoothing and over-fitting. We establish asymptotic results including consistency, asymptotic normality and the adaptive properties of EASE. We also provide influence function expansions and a 'double' CV strategy for inference. The results are further validated through extensive simulations, followed by application to an EMR study on auto-immunity. With the increasing size of today's data sets, nding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which uses nonparametric testing coupled with sequential analysis to determine the best parameter set on linearly increasing subsets of the data. By eliminating underperforming candidates quickly and keeping promising candidates as long as possible, the method speeds up the computation while preserving the power of the full cross-validation. Theoretical considerations underline the statistical power of our procedure. The experimental evaluation shows that our method reduces the computation time by a factor of up to 120 compared to a full cross-validation with a negligible impact on the accuracy. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. In this paper, a novel algorithm to blindly separate an instantaneous linear underdetermined mixture of nonstationary sources is proposed. It means that the number of sources exceeds the number of channels of the available data. The separation is based on the working assumption that the sources are piecewise stationary with a different variance in each block. It proceeds in two steps: 1) estimating the mixing matrix, and 2) computing the optimum beamformer in each block to maximize the signal-to-interference ratio of each separated signal with respect to the remaining signals. Estimating the mixing matrix is accomplished through a specialized tensor decomposition of the set of sample covariance matrices of the received mixture in each block. It utilizes optimum weighting, which allows statistically efficient (CRB attaining) estimation provided that the data obey the assumed Gaussian piecewise stationary model. In simulations, performance of the algorithm is successfully tested on blind separation of 16 speech signals from nine linear instantaneous mixtures of these signals. We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in the sense that the posterior probability of the true model converges to one even when the number of covariates grows nearly exponentially with the sample size. This is arguably the strongest selection consistency result that has been available in the Bayesian variable selection literature; yet the proposed method can be carried out through posterior sampling with a simple Gibbs sampler. Furthermore, we argue that the proposed method is asymptotically similar to model selection with the @math penalty. We also demonstrate through empirical work the fine performance of the proposed approach relative to some state of the art alternatives. Nonparametric detection of existence of an anomalous disk over a lattice network is investigated. If an anomalous disk exists, then all nodes belonging to the disk observe samples generated by a distribution q, whereas all other nodes observe samples generated by a distribution p that is distinct from q. If there does not exist an anomalous disk, then all nodes receive samples generated by p. The distributions p and q are arbitrary and unknown. The goal is to design statistically consistent test as the network size becomes asymptotically large. A kernel-based test is proposed based on maximum mean discrepancy (MMD) which measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space (RKHS). A sufficient condition on the minimum size of candidate anomalous disks is characterized in order to guarantee the consistency of the proposed test. A necessary condition that any universally consistent test must satisfy is further derived. Comparison of sufficient and necessary conditions yields that the proposed test is order-level optimal. We propose a new test, based on model selection methods, for testing that the expectation of a Gaussian vector with n independent components belongs to a linear subspace of R n against a nonparametric alternative. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative. The properties of the test are nonasymptotic and we prove that the test is rate optimal [up to a possible log(n) factor] over various classes of alternatives simultaneously. We also provide a simulation study in order to evaluate the procedure when the purpose is to test goodness-of-fit in a regression model. 1. Introduction. We consider the regression model The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error probability corresponds to the maximum Chernoff information over the choice of controls, and a pure stationary open-loop control policy is asymptotically optimal within the larger class of all causal control policies. For multihypothesis testing in the fixed sample size setting, lower and upper bounds on the optimal error exponent are derived. It is also shown through an example with three hypotheses that the optimal causal control policy can be strictly better than the optimal open-loop control policy. In the sequential setting, a test based on earlier work by Chernoff for binary hypothesis testing, is shown to be first-order asymptotically optimal for multihypothesis testing in a strong sense, using the notion of decision making risk in place of the overall probability of error. Another test is also designed to meet hard risk constrains while retaining asymptotic optimality. The role of past information and randomization in designing optimal control policies is discussed. MART (Friedman, 2001, 2002), an ensemble model of boosted regression trees, is known to deliver high prediction accuracy for diverse tasks, and it is widely used in practice. However, it suffers an issue which we call over-specialization, wherein trees added at later iterations tend to impact the prediction of only a few instances, and make negligible contribution towards the remaining instances. This negatively affects the performance of the model on unseen data, and also makes the model over-sensitive to the contributions of the few, initially added tress. We show that the commonly used tool to address this issue, that of shrinkage, alleviates the problem only to a certain extent and the fundamental issue of over-specialization still remains. In this work, we explore a different approach to address the problem that of employing dropouts, a tool that has been recently proposed in the context of learning deep neural networks (, 2012). We propose a novel way of employing dropouts in MART, resulting in the DART algorithm. We evaluate DART on ranking, regression and classification tasks, using large scale, publicly available datasets, and show that DART outperforms MART in each of the tasks, with a significant margin. We also show that DART overcomes the issue of over-specialization to a considerable extent. Appearing in Proceedings of the 18 International Conference on Artificial Intelligence and Statistics (AISTATS) 2015, San Diego, CA, USA. JMLR: W&CP volume 38. Copyright 2015 by the authors. In this paper we study the asymptotic properties of Bayesian multiple testing procedures for a large class of Gaussian scale mixture pri- ors. We study two types of multiple testing risks: a Bayesian risk proposed in (2011) where the data are assume to come from a mixture of normal, and a frequentist risk similar to the one proposed by Arias-Castro and Chen (2017). Following the work of van der (2016), we give general conditions on the prior such that both risks can be bounded. For the Bayesian risk, the bound is almost sharp. This result show that under these conditions, the considered class of continuous prior can be competitive with the usual two-group model (e.g. spike and slab priors). We also show that if the non-zeros component of the parameter are large enough, the minimax risk can be made asymptotically null. The separation rates obtained are consistent with the one that could be guessed from the existing literature (see van der , 2017b). For both problems, we then give conditions under which an adaptive version of the result can be obtained. Multi-layer neural networks have lead to remarkable performance on many kinds of benchmark tasks in text, speech and image processing. Nonlinear parameter estimation in hierarchical models is known to be subject to overfitting and misspecification. One approach to these estimation and related problems (local minima, colinearity, feature discovery etc.) is called Dropout (Hinton, et al 2012, 2016). The Dropout algorithm removes hidden units according to a Bernoulli random variable with probability @math prior to each update, creating random "shocks" to the network that are averaged over updates. In this paper we will show that Dropout is a special case of a more general model published originally in 1990 called the Stochastic Delta Rule, or SDR (Hanson, 1990). SDR redefines each weight in the network as a random variable with mean @math and standard deviation @math . Each weight random variable is sampled on each forward activation, consequently creating an exponential number of potential networks with shared weights. Both parameters are updated according to prediction error, thus resulting in weight noise injections that reflect a local history of prediction error and local model averaging. SDR therefore implements a more sensitive local gradient-dependent simulated annealing per weight converging in the limit to a Bayes optimal network. Tests on standard benchmarks (CIFAR) using a modified version of DenseNet shows the SDR outperforms standard Dropout in test error by approx. @math with DenseNet-BC 250 on CIFAR-100 and approx. @math in smaller networks. We also show that SDR reaches the same accuracy that Dropout attains in 100 epochs in as few as 35 epochs. In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of the well-known variance-related risk measures, and because of its computational efficiencies has gained popularity in finance and operations research. In this paper, we consider the mean-CVaR optimization problem in MDPs. We first derive a formula for computing the gradient of this risk-sensitive objective function. We then devise policy gradient and actor-critic algorithms that each uses a specific method to estimate this gradient and updates the policy parameters in the descent direction. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in an optimal stopping problem. We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative discussion assuming that the number of observations is sufficiently large, we provide simple formulas for approximately assessing two types of CV errors, which enable us to significantly reduce the necessary cost of computation. These formulas also provide a simple connection of the CV errors to the residual sums of squares between the reconstructed and the given measurements. Second, on the basis of this finding, we analytically evaluate the CV errors when the design matrix is given as a simple random matrix in the large size limit by using the replica method. Finally, these results are compared with those of numerical simulations on finite-size systems and are confirmed to be correct. We also apply the simple formulas of the first type of CV error to an actual dataset of the supernovae. We propose a new approach to appearance-based loop detection for mobile robots, using three-dimensional (3D) laser scans. Loop detection is an important problem in the simultaneous localization and mapping (SLAM) domain, and, because it can be seen as the problem of recognizing previously visited places, it is an example of the data association problem. Without a flat-floor assumption, two-dimensional laser-based approaches are bound to fail in many cases. Two of the problems with 3D approaches that we address in this paper are how to handle the greatly increased amount of data and how to efficiently obtain invariance to 3D rotations. We present a compact representation of 3D point clouds that is still discriminative enough to detect loop closures without false positives (i.e., detecting loop closure where there is none). A low false-positive rate is very important because wrong data association could have disastrous consequences in a SLAM algorithm. Our approach uses only the appearance of 3D point clouds to detect loops and requires no pose information. We exploit the normal distributions transform surface representation to create feature histograms based on surface orientation and smoothness. The surface shape histograms compress the input data by two to three orders of magnitude. Because of the high compression rate, the histograms can be matched efficiently to compare the appearance of two scans. Rotation invariance is achieved by aligning scans with respect to dominant surface orientations. We also propose to use expectation maximization to fit a gamma mixture model to the output similarity measures in order to automatically determine the threshold that separates scans at loop closures from nonoverlapping ones. We discuss the problem of determining ground truth in the context of loop detection and the difficulties in comparing the results of the few available methods based on range information. Furthermore, we present quantitative performance evaluations using three real-world data sets, one of which is highly self-similar, showing that the proposed method achieves high recall rates (percentage of correctly identified loop closures) at low false-positive rates in environments with different characteristics. © 2009 Wiley Periodicals, Inc. Despite breakthroughs in image classification due to the evolution of deep learning and, in particular, convolutional neural networks (CNNs), state-of-the-art models only possess a very limited amount of rotational invariance. Known workarounds include artificial rotations of the training data or ensemble approaches, where several models are evaluated. These approaches either increase the workload of the training or inflate the number of parameters. Further approaches add rotational invariance by globally pooling over rotationally equivariant features. Instead, we propose to incorporate rotational invariance into the feature-extraction part of the CNN directly. This allows to train on unrotated data and perform well on a rotated test set. We use rotational convolutions and introduce a rotational pooling layer that performs a pooling over the back-rotated output feature maps. We show that when training on the original, unrotated MNIST training dataset, but evaluating on rotations of the MNIST test dataset, the error rate can be reduced substantially from 58.20 to 12.20 . Similar results are shown for the CIFAR-10 and CIFAR-100 datasets. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. In large-scale data enters, software and hardware failures are frequent, resulting in failures of job executions that may cause significant resource waste and performance deterioration. To proactively minimize the resource inefficiency due to job failures, it is important to identify them in advance using key job attributes. However, so far, prevailing research on datacenter workload characterization has overlooked job failures, including their patterns, root causes, and impact. In this paper, we aim to develop prediction models and mitigation policies for unsuccessful jobs, so as to reduce the resource waste in big data enters. In particular, we base our analysis on Google cluster traces, consisting of a large number of big-data jobs with a high task fan-out. We first identify the time-varying patterns of failed jobs and the contributing system features. Based on our characterization study, we develop an on-line predictive model for job failures by applying various statistical learning techniques, namely Linear Discriminate Analysis (LDA), Quadratic Discriminate Analysis (QDA), and Logistic Regression (LR). Furthermore, we propose a delay-based mitigation policy which, after a certain grace period, proactively terminates the execution of jobs that are predicted to fail. The particular objective of postponing job terminations is to strike a good tradeoffs between resource waste and false prediction of successful jobs. Our evaluation results show that the proposed method is able to significantly reduce the resource waste by 41.9 on average, and keep false terminations of jobs low, i.e., only 1 . We provide a general framework for privacy-preserving variational Bayes (VB) for a large class of probabilistic models, called the conjugate exponential (CE) family. Our primary observation is that when models are in the CE family, we can privatise the variational posterior distributions simply by perturbing the expected sufficient statistics of the complete-data likelihood. For widely used non-CE models with binomial likelihoods, we exploit the P 'o lya-Gamma data augmentation scheme to bring such models into the CE family, such that inferences in the modified model resemble the private variational Bayes algorithm as closely as possible. The iterative nature of variational Bayes presents a further challenge since iterations increase the amount of noise needed. We overcome this by combining: (1) a relaxed notion of differential privacy, called concentrated differential privacy, which provides a tight bound on the privacy cost of multiple VB iterations and thus significantly decreases the amount of additive noise; and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic learning. We empirically demonstrate the effectiveness of our method in CE and non-CE models including latent Dirichlet allocation, Bayesian logistic regression, and sigmoid belief networks, evaluated on real-world datasets. In this paper, we propose three criteria for efficient sample selection in case of data stream regression problems within an online active learning context. The selection becomes important whenever the target values, which guide the update of the regressors as well as the implicit model structures, are costly or time-consuming to measure and also in case when very fast models updates are required to cope with stream mining real-time demands. Reducing the selected samples as much as possible while keeping the predictive accuracy of the models on a high level is, thus, a central challenge. This should be ideally achieved in unsupervised and single-pass manner. Our selection criteria rely on three aspects: 1) the extrapolation degree combined with the model's nonlinearity degree , which is measured in terms of a new specific homogeneity criterion among adjacent local approximators; 2) the uncertainty in model outputs, which can be measured in terms of confidence intervals using so-called adaptive local error bars — we integrate a weighted localization of an incremental noise level estimator and propose formulas for online merging of local error bars; 3) the uncertainty in model parameters, which is estimated by the so-called A-optimality criterion, which relies on the Fisher information matrix. The selection criteria are developed in combination with evolving generalized Takagi–Sugeno (TS) fuzzy models (containing rules in arbitrarily rotated position), as it could be shown in previous publications that these outperform conventional evolving TS models (containing axis-parallel rules). The results based on three high-dimensional real-world streaming problems show that a model update based on only 10 –20 selected samples can still achieve similar accumulated model errors over time to the case when performing a full model update on all samples. This can be achieved with a negligible sensitivity on the size of the active learning latency buffer. Random sampling with the same percentages of samples selected, however, achieved much higher error rates. Hence, the intelligence in our sample selection concept leads to an economic balance between model accuracy and measurement as well computational costs for model updates.