With the increasing size of today's data sets, finding 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 capability 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.

Supervised statistical classification is a vital tool for satellite image processing. It is useful not only when a discrete result, such as feature extraction or surface type, is required, but also for continuum retrievals by dividing the quantity of interest into discrete ranges. Because of the high resolution of modern satellite instruments and because of the requirement for real-time processing, any algorithm has to be fast to be useful. Here we describe an algorithm based on kernel estimation called Adaptive Gaussian Filtering that incorporates several innovations to produce superior efficiency as compared to three other popular methods: k-nearest-neighbour (KNN), Learning Vector Quantization (LVQ) and Support Vector Machines (SVM). This efficiency is gained with no compromises: accuracy is maintained, while estimates of the conditional probabilities are returned. These are useful not only to gauge the accuracy of an estimate in the absence of its true value, but also to re-calibrate a retrieved image and as a proxy for a discretized continuum variable. The algorithm is demonstrated and compared with the other three on a pair of synthetic test classes and to map the waterways of the Netherlands. Software may be found at: http://libagf.sourceforge.net.

A successful class of image denoising methods is based on Bayesian approaches working in wavelet representations. However, analytical estimates can be obtained only for particular combinations of analytical models of signal and noise, thus precluding its straightforward extension to deal with other arbitrary noise sources. In this paper, we propose an alternative non-explicit way to take into account the relations among natural image wavelet coefficients for denoising: we use support vector regression (SVR) in the wavelet domain to enforce these relations in the estimated signal. Since relations among the coefficients are specific to the signal, the regularization property of SVR is exploited to remove the noise, which does not share this feature. The specific signal relations are encoded in an anisotropic kernel obtained from mutual information measures computed on a representative image database. Training considers minimizing the Kullback-Leibler divergence (KLD) between the estimated and actual probability functions of signal and noise in order to enforce similarity. Due to its non-parametric nature, the method can eventually cope with different noise sources without the need of an explicit re-formulation, as it is strictly necessary under parametric Bayesian formalisms. Results under several noise levels and noise sources show that: (1) the proposed method outperforms conventional wavelet methods that assume coefficient independence, (2) it is similar to state-of-the-art methods that do explicitly include these relations when the noise source is Gaussian, and (3) it gives better numerical and visual performance when more complex, realistic noise sources are considered. Therefore, the proposed machine learning approach can be seen as a more flexible (model-free) alternative to the explicit description of wavelet coefficient relations for image denoising.

We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel which would enable a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in two-sample hypothesis testing on synthetic as well as real-world data.

In past few years, several techniques have been proposed for training of linear Support Vector Machine (SVM) in limited-memory setting, where a dual block-coordinate descent (dual-BCD) method was used to balance cost spent on I/O and computation. In this paper, we consider the more general setting of regularized \emph{Empirical Risk Minimization (ERM)} when data cannot fit into memory. In particular, we generalize the existing block minimization framework based on strong duality and \emph{Augmented Lagrangian} technique to achieve global convergence for ERM with arbitrary convex loss function and regularizer. The block minimization framework is flexible in the sense that, given a solver working under sufficient memory, one can integrate it with the framework to obtain a solver globally convergent under limited-memory condition. We conduct experiments on L1-regularized classification and regression problems to corroborate our convergence theory and compare the proposed framework to algorithms adopted from online and distributed settings, which shows superiority of the proposed approach on data of size ten times larger than the memory capacity.

In user-facing applications, displaying calibrated confidence measures---probabilities that correspond to true frequency---can be as important as obtaining high accuracy. We are interested in calibration for structured prediction problems such as speech recognition, optical character recognition, and medical diagnosis. Structured prediction presents new challenges for calibration: the output space is large, and users may issue many types of probability queries (e.g., marginals) on the structured output. We extend the notion of calibration so as to handle various subtleties pertaining to the structured setting, and then provide a simple recalibration method that trains a binary classifier to predict probabilities of interest. We explore a range of features appropriate for structured recalibration, and demonstrate their efficacy on three real-world datasets.

This paper presents a new semi-supervised framework with convolutional neural networks (CNNs) for text categorization. Unlike the previous approaches that rely on word embeddings, our method learns embeddings of small text regions from unlabeled data for integration into a supervised CNN. The proposed scheme for embedding learning is based on the idea of two-view semi-supervised learning, which is intended to be useful for the task of interest even though the training is done on unlabeled data. Our models achieve better results than previous approaches on sentiment classification and topic classification tasks.

With recent advancement in data collection and storage, we have large amounts of information at our disposal, especially with respect to the number of explanatory variables or'features'. When these features contain redundant or noisy information, estimating the functional connection between the response and these features can become quite challenging, and that often hampers the quality of learning. One way to overcome this is by finding a smaller set of features or explanatory variables that can perform the learning task sufficiently well. In this paper, we discuss feature elimination in statistical learning with kernel machines. Kernel machines (KM) are a class of learning methods for pattern analysis and regression, under transformations of the input feature space, of which the linear support vector machine (SVM) is the simplest case. In general, the term'kernel machine' is reserved for the more general version of the SVM problem with nonlinear transformation of the feature space. The popularity of these algorithms is motivated by the fact that these are easyto-compute techniques that enable estimation under weak or no assumptions on the distribution [see Steinwart and Chirstmann, 2008].

A deep generative model is developed for representation and analysis of images, based on a hierarchical convolutional dictionary-learning framework. Stochastic {\em unpooling} is employed to link consecutive layers in the model, yielding top-down image generation. A Bayesian support vector machine is linked to the top-layer features, yielding max-margin discrimination. Deep deconvolutional inference is employed when testing, to infer the latent features, and the top-layer features are connected with the max-margin classifier for discrimination tasks. The model is efficiently trained using a Monte Carlo expectation-maximization (MCEM) algorithm, with implementation on graphical processor units (GPUs) for efficient large-scale learning, and fast testing. Excellent results are obtained on several benchmark datasets, including ImageNet, demonstrating that the proposed model achieves results that are highly competitive with similarly sized convolutional neural networks.

Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the results from binary classifiers together. An inherent difficulty of this framework is that the class prediction can be ambiguous due to boundary crossing. To fix this issue, we propose a noncrossing ordinal classification method which materializes the framework by imposing noncrossing constraints. An asymptotic study of the proposed method is conducted. We show by simulated and data examples that the proposed method can improve the classification performance for ordinal data without the ambiguity caused by boundary crossings.