Measuring the relationship between any pair of variables is a rich and active area of research that is central to scientific practice. In contrast, characterizing the common information among any group of variables is typically a theoretical exercise with few practical methods for high-dimensional data. A promising solution would be a multivariate generalization of the famous Wyner common information, but this approach relies on solving an apparently intractable optimization problem. We leverage the recently introduced information sieve decomposition to formulate an incremental version of the common information problem that admits a simple fixed point solution, fast convergence, and complexity that is linear in the number of variables. This scalable approach allows us to demonstrate the usefulness of common information in high-dimensional learning problems. The sieve outperforms standard methods on dimensionality reduction tasks, solves a blind source separation problem that cannot be solved with ICA, and accurately recovers structure in brain imaging data.
The sieve could be viewed as a new objective for projection pursuit @cite_12 based on common information. The sieve stands out from standard pursuit algorithms in two ways. First, an information based orthogonality'' criteria for subsequent projections naturally emerges and, second, new factors may depend on factors learned at previous layers (note that in Fig. each learned latent factor is included in the remainder information that is optimized over in the next step). More broadly, the sieve can be viewed as a new approach to unsupervised deep representation learning @cite_36 @cite_9 . In particular, our setup can be directly viewed as an auto-encoder with a novel objective @cite_21 . From that point of view, it is clear that the sieve can also be directly leveraged for unsupervised density estimation @cite_28 .
@cite_36 @cite_28 @cite_9 @cite_21 @cite_12
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This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is special in that it allows simultaneous identification of the endmember spectral signatures and the number of endmembers. Previous SD-MMV studies mainly focus on convex relaxations. In this study, we explore the alternative of greedy pursuit, which generally provides efficient and simple algorithms. In particular, we design a greedy SD-MMV algorithm using simultaneous orthogonal matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be closely related to some existing pure pixel search algorithms, especially, the successive projection algorithm (SPA). Thus, a link between SD-MMV and pure pixel search is revealed. We then perform exact recovery analyses, and prove that the proposed greedy algorithm is robust to noise-including its identification of the (unknown) number of endmembers-under a sufficiently low noise level. The identification performance of the proposed greedy algorithm is demonstrated through both synthetic and real-data experiments. Methods for Projection Pursuit aim to facilitate the visual exploration of high-dimensional data by identifying interesting low-dimensional projections. A major challenge is the design of a suitable quality metric of projections, commonly referred to as the projection index, to be maximized by the Projection Pursuit algorithm. In this paper, we introduce a new information-theoretic strategy for tackling this problem, based on quantifying the amount of information the projection conveys to a user given their prior beliefs about the data. The resulting projection index is a subjective quantity, explicitly dependent on the intended user. As a useful illustration, we developed this idea for two particular kinds of prior beliefs. The first kind leads to PCA (Principal Component Analysis), shining new light on when PCA is (not) appropriate. The second kind leads to a novel projection index, the maximization of which can be regarded as a robust variant of PCA. We show how this projection index, though non-convex, can be effectively maximized using a modified power method as well as using a semidefinite programming relaxation. The usefulness of this new projection index is demonstrated in comparative empirical experiments against PCA and a popular Projection Pursuit method. Person re-identification is to seek a correct match for a person of interest across different camera views among a large number of impostors. It typically involves two procedures of non-linear feature extractions against dramatic appearance changes, and subsequent discriminative analysis in order to reduce intra-personal variations while enlarging inter-personal differences. In this paper, we introduce a hybrid deep architecture which combines Fisher vectors and deep neural networks to learn non-linear transformations of pedestrian images to a deep space where data can be linearly separable. The proposed method starts from Fisher vector encoding which computes a sequence of local feature extraction, aggregation, and encoding. The resulting Fisher vector output are fed into stacked supervised layer to seek non-linear transformation into a deep space. On top of the deep neural network, Linear Discriminant Analysis (LDA) is reinforced such that linearly separable latent representations can be learned in an end-to-end fashion. By optimizing an objective function modified from LDA, the network is enforced to produce feature distributions which have a low variance within the same class and high variance between classes. The objective is essentially derived from the general LDA eigenvalue problem and allows to train the network with Stochastic Gradient Descent and back-propagate LDA gradients to compute Gaussian Mixture Model (GMM) gradients in Fisher vector encoding. For empirical evaluations, we test our approach on four benchmark data sets in person re-identification (VIPeR 1, CUHK03 2, CUHK01 3, and Market 1501 4). Extensive experiments on these benchmarks show that our method can achieve state-of-the-art results. HighlightsA hybrid architecture that combines Fisher vectors and deep neural networks.An end-to-end training with linear discriminant analysis as objective.Deep features are linearly separable and class separability is maximally preserved. Abstract A new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods. A number of practical issues concerning its application are addressed. A connection to multivariate density estimation is established, and its properties are investigated through simulation studies and application to real data. The goal of exploratory projection pursuit is to use the data to find low- (one-, two-, or three-) dimensional projections that provide the most revealing views of the full-dimensional data. With these views the human gift for pattern recognition can be applied to help discover effects that may not have been anticipated in advance. Since linear effects are directly captured by the covariance structure of the variable pairs (which are straightforward to estimate) the emphasis here is on the discovery of nonlinear effects such as clustering or other general nonlinear associations among the variables. Although arbitrary ... The objective of this paper is large scale object instance retrieval, given a query image. A starting point of such systems is feature detection and description, for example using SIFT. The focus of this paper, however, is towards very large scale retrieval where, due to storage requirements, very compact image descriptors are required and no information about the original SIFT descriptors can be accessed directly at run time. We start from VLAD, the state-of-the art compact descriptor introduced by for this purpose, and make three novel contributions: first, we show that a simple change to the normalization method significantly improves retrieval performance, second, we show that vocabulary adaptation can substantially alleviate problems caused when images are added to the dataset after initial vocabulary learning. These two methods set a new state-of-the-art over all benchmarks investigated here for both mid-dimensional (20k-D to 30k-D) and small (128-D) descriptors. Our third contribution is a multiple spatial VLAD representation, MultiVLAD, that allows the retrieval and localization of objects that only extend over a small part of an image (again without requiring use of the original image SIFT descriptors). We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm). This paper presents a novel person re-identification framework based on data fusion. The pipeline of the proposed method is composed of two stages. First, a metric learning paradigm is applied on a bunch of distinct feature extractors to produce an ensemble of estimated distance measures, which are subsequently penalized according to their confidence in evidencing the correct matches from the false ones, and averaged as to draw a final decision. Second, the close persons from the gallery are selected based on the previously fused distance estimates, and utilized to build a dictionary as to reconstruct a given probe pattern. Evaluated on benchmark datasets, the proposed framework advances the state-of-the-art by interesting margins. In particular, Rank1 gains amounting to about 12 , 1 , 6 , and 12 , were scored on VIPeR, CAVIAR4REID, iLIDS, and 3DPeS, respectively. Data-driven dictionaries have produced state-of-the-art results in various classification tasks. However, when the target data has a different distribution than the source data, the learned sparse representation may not be optimal. In this paper, we investigate if it is possible to optimally represent both source and target by a common dictionary. Specifically, we describe a technique which jointly learns projections of data in the two domains, and a latent dictionary which can succinctly represent both the domains in the projected low-dimensional space. An efficient optimization technique is presented, which can be easily kernelized and extended to multiple domains. The algorithm is modified to learn a common discriminative dictionary, which can be further used for classification. The proposed approach does not require any explicit correspondence between the source and target domains, and shows good results even when there are only a few labels available in the target domain. Various recognition experiments show that the method performs on par or better than competitive state-of-the-art methods. Localizing objects in cluttered backgrounds is a challenging task in weakly supervised localization. Due to large object variations in cluttered images, objects have large ambiguity with backgrounds. However, backgrounds contain useful latent information, e.g., the sky for aeroplanes. If we can learn this latent information, object-background ambiguity can be reduced to suppress the background. In this paper, we propose the latent category learning (LCL), which is an unsupervised learning problem given only image-level class labels. Firstly, inspired by the latent semantic discovery, we use the typical probabilistic Latent Semantic Analysis (pLSA) to learn the latent categories, which can represent objects, object parts or backgrounds. Secondly, to determine which category contains the target object, we propose a category selection method evaluating each category’s discrimination. We evaluate the method on the PASCAL VOC 2007 database and ILSVRC 2013 detection challenge. On VOC 2007, the proposed method yields the annotation accuracy of 48 , which outperforms previous results by 10 . More importantly, we achieve the detection average precision of 30.9 , which improves previous results by 8 and can be competitive with the supervised deformable part model (DPM) 5.0 baseline 33.7 . On ILSVRC 2013 detection, the method yields the precision of 6.0 , which is also competitive with the DPM 5.0. This paper describes a novel approach of packing sparse convolutional neural networks for their efficient systolic array implementations. By combining subsets of columns in the original filter matrix associated with a convolutional layer, we increase the utilization efficiency of the systolic array substantially (e.g., 4x) due to the increased density of nonzeros in the resulting packed filter matrix. In combining columns, for each row, all filter weights but one with the largest magnitude are pruned. We retrain the remaining weights to preserve high accuracy. We demonstrate that in mitigating data privacy concerns the retraining can be accomplished with only fractions of the original dataset (e.g., 10 for CIFAR-10). We study the effectiveness of this joint optimization for both high utilization and classification accuracy with ASIC and FPGA designs based on efficient bit-serial implementations of multiplier-accumulators. We present analysis and empirical evidence on the superior performance of our column combining approach against prior arts under metrics such as energy efficiency (3x) and inference latency (12x). Recent advances in Convolutional Neural Networks (CNNs) have obtained promising results in difficult deep learning tasks. However, the success of a CNN depends on finding an architecture to fit a given problem. A hand-crafted architecture is a challenging, time-consuming process that requires expert knowledge and effort, due to a large number of architectural design choices. In this article, we present an efficient framework that automatically designs a high-performing CNN architecture for a given problem. In this framework, we introduce a new optimization objective function that combines the error rate and the information learnt by a set of feature maps using deconvolutional networks (deconvnet). The new objective function allows the hyperparameters of the CNN architecture to be optimized in a way that enhances the performance by guiding the CNN through better visualization of learnt features via deconvnet. The actual optimization of the objective function is carried out via the Nelder-Mead Method (NMM). Further, our new objective function results in much faster convergence towards a better architecture. The proposed framework has the ability to explore a CNN architecture’s numerous design choices in an efficient way and also allows effective, distributed execution and synchronization via web services. Empirically, we demonstrate that the CNN architecture designed with our approach outperforms several existing approaches in terms of its error rate. Our results are also competitive with state-of-the-art results on the MNIST dataset and perform reasonably against the state-of-the-art results on CIFAR-10 and CIFAR-100 datasets. Our approach has a significant role in increasing the depth, reducing the size of strides, and constraining some convolutional layers not followed by pooling layers in order to find a CNN architecture that produces a high recognition performance. To reliably determine the camera pose of an image relative to a 3D point cloud of a scene, correspondences between 2D features and 3D points are needed. Recent work has demonstrated that directly matching the features against the points outperforms methods that take an intermediate image retrieval step in terms of the number of images that can be localized successfully. Yet, direct matching is inherently less scalable than retrievalbased approaches. In this paper, we therefore analyze the algorithmic factors that cause the performance gap and identify false positive votes as the main source of the gap. Based on a detailed experimental evaluation, we show that retrieval methods using a selective voting scheme are able to outperform state-of-the-art direct matching methods. We explore how both selective voting and correspondence computation can be accelerated by using a Hamming embedding of feature descriptors. Furthermore, we introduce a new dataset with challenging query images for the evaluation of image-based localization. We consider the task of learning a classifier for semantic segmentation using weak supervision in the form of image labels which specify the object classes present in the image. Our method uses deep convolutional neural networks (CNNs) and adopts an Expectation-Maximization (EM) based approach. We focus on the following three aspects of EM: (i) initialization; (ii) latent posterior estimation (E-step) and (iii) the parameter update (M-step). We show that saliency and attention maps, our bottom-up and top-down cues respectively, of simple images provide very good cues to learn an initialization for the EM-based algorithm. Intuitively, we show that before trying to learn to segment complex images, it is much easier and highly effective to first learn to segment a set of simple images and then move towards the complex ones. Next, in order to update the parameters, we propose minimizing the combination of the standard softmax loss and the KL divergence between the true latent posterior and the likelihood given by the CNN. We argue that this combination is more robust to wrong predictions made by the expectation step of the EM method. We support this argument with empirical and visual results. Extensive experiments and discussions show that: (i) our method is very simple and intuitive; (ii) requires only image-level labels; and (iii) consistently outperforms other weakly-supervised state-of-the-art methods with a very high margin on the PASCAL VOC 2012 dataset. This paper focuses on predicting a single step of streamline tractography from diffusion magnetic resonance imaging data by using different predictors based on neural networks. We train 18 different classifiers in order to assess the effect of including neighbourhood information in the learning step or as a post processing step. Moreover, the performance using four different post processing approaches as well as the variation of the number of classes resulting in a total of 60 experimental configurations are assessed. Further, a comparison to 12 regression-based networks is performed and the effect of including several streamline steps in the network input is investigated. All networks are trained and tested on the ISMRM 2015 tractography challenge data. Our results do not indicate a clear improvement when using neighbouring data (regardless if it used as an input or as a post processing). Also, the linear interpolation of the diffusion data does not outperform the less expensive nearest neighbour approach. As opposed to that, using a linear model on top of the output of the classifiers is beneficial and—in combination with at least 200 classes—resulted in a similar performance as the regression approach. Finally, providing the networks with additional curvature information led to a clear improvement of prediction performance. Our analysis of accuracy based on average angular errors suggests that also considering spatial location in the learning step might further improve machine learning-based streamline tractography algorithms. Visual search and image retrieval underpin numerous applications, however the task is still challenging predominantly due to the variability of object appearance and ever increasing size of the databases, often exceeding billions of images. Prior art methods rely on aggregation of local scale-invariant descriptors, such as SIFT, via mechanisms including Bag of Visual Words (BoW), Vector of Locally Aggregated Descriptors (VLAD) and Fisher Vectors (FV). However, their performance is still short of what is required. This paper presents a novel method for deriving a compact and distinctive representation of image content called Robust Visual Descriptor with Whitening (RVD-W). It significantly advances the state of the art and delivers world-class performance. In our approach local descriptors are rank-assigned to multiple clusters. Residual vectors are then computed in each cluster, normalized using a direction-preserving normalization function and aggregated based on the neighborhood rank. Importantly, the residual vectors are de-correlated and whitened in each cluster before aggregation, leading to a balanced energy distribution in each dimension and significantly improved performance. We also propose a new post-PCA normalization approach which improves separability between the matching and non-matching global descriptors. This new normalization benefits not only our RVD-W descriptor but also improves existing approaches based on FV and VLAD aggregation. Furthermore, we show that the aggregation framework developed using hand-crafted SIFT features also performs exceptionally well with Convolutional Neural Network (CNN) based features. The RVD-W pipeline outperforms state-of-the-art global descriptors on both the Holidays and Oxford datasets. On the large scale datasets, Holidays1M and Oxford1M, SIFT-based RVD-W representation obtains a mAP of 45.1 and 35.1 percent, while CNN-based RVD-W achieve a mAP of 63.5 and 44.8 percent, all yielding superior performance to the state-of-the-art. 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. This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho's basis pursuit (BP) paradigm can recover the optimal representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasi-incoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function is introduced to quantify the level of incoherence. This analysis unifies all the recent results on BP and extends them to OMP. Furthermore, the paper develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal. From there, it argues that OMP is an approximation algorithm for the sparse problem over a quasi-incoherent dictionary. That is, for every input signal, OMP calculates a sparse approximant whose error is only a small factor worse than the minimal error that can be attained with the same number of terms. Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to minimize an objective function that includes a quadratic (lscr 2) error term added to a sparsity-inducing (usually lscr1) regularizater. We present an algorithmic framework for the more general problem of minimizing the sum of a smooth convex function and a nonsmooth, possibly nonconvex regularizer. We propose iterative methods in which each step is obtained by solving an optimization subproblem involving a quadratic term with diagonal Hessian (i.e., separable in the unknowns) plus the original sparsity-inducing regularizer; our approach is suitable for cases in which this subproblem can be solved much more rapidly than the original problem. Under mild conditions (namely convexity of the regularizer), we prove convergence of the proposed iterative algorithm to a minimum of the objective function. In addition to solving the standard lscr2-lscr1 case, our framework yields efficient solution techniques for other regularizers, such as an lscrinfin norm and group-separable regularizers. It also generalizes immediately to the case in which the data is complex rather than real. Experiments with CS problems show that our approach is competitive with the fastest known methods for the standard lscr2-lscr1 problem, as well as being efficient on problems with other separable regularization terms. In this work, we present a SIFT-Bag based generative-to-discriminative framework for addressing the problem of video event recognition in unconstrained news videos. In the generative stage, each video clip is encoded as a bag of SIFT feature vectors, the distribution of which is described by a Gaussian Mixture Models (GMM). In the discriminative stage, the SIFT-Bag Kernel is designed for characterizing the property of Kullback-Leibler divergence between the specialized GMMs of any two video clips, and then this kernel is utilized for supervised learning in two ways. On one hand, this kernel is further refined in discriminating power for centroid-based video event classification by using the Within-Class Covariance Normalization approach, which depresses the kernel components with high-variability for video clips of the same event. On the other hand, the SIFT-Bag Kernel is used in a Support Vector Machine for margin-based video event classification. Finally, the outputs from these two classifiers are fused together for final decision. The experiments on the TRECVID 2005 corpus demonstrate that the mean average precision is boosted from the best reported 38.2 in [36] to 60.4 based on our new framework. Suppose an n x d design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number k << n of the responses, and then produce a weight vector whose sum of squares loss over all points is at most 1+epsilon times the minimum. When k is very small (e.g., k=d), jointly sampling diverse subsets of points is crucial. One such method called "volume sampling" has a unique and desirable property that the weight vector it produces is an unbiased estimate of the optimum. It is therefore natural to ask if this method offers the optimal unbiased estimate in terms of the number of responses k needed to achieve a 1+epsilon loss approximation. Surprisingly we show that volume sampling can have poor behavior when we require a very accurate approximation -- indeed worse than some i.i.d. sampling techniques whose estimates are biased, such as leverage score sampling. We then develop a new rescaled variant of volume sampling that produces an unbiased estimate which avoids this bad behavior and has at least as good a tail bound as leverage score sampling: sample size k=O(d log d + d epsilon) suffices to guarantee total loss at most 1+epsilon times the minimum with high probability. Thus, we improve on the best previously known sample size for an unbiased estimator, k=O(d^2 epsilon). Our rescaling procedure leads to a new efficient algorithm for volume sampling which is based on a "determinantal rejection sampling" technique with potentially broader applications to determinantal point processes. Other contributions include introducing the combinatorics needed for rescaled volume sampling and developing tail bounds for sums of dependent random matrices which arise in the process.