Recognition of objects with subtle differences has been used in many practical applications, such as car model recognition and maritime vessel identification. For discrimination of the objects in fine-grained detail, we focus on deep embedding learning by using a multi-task learning framework, in which the hierarchical labels (coarse and fine labels) of the samples are utilized both for classification and a quadruplet-based loss function. In order to improve the recognition strength of the learned features, we present a novel feature selection method specifically designed for four training samples of a quadruplet. By experiments, it is observed that the selection of very hard negative samples with relatively easy positive ones from the same coarse and fine classes significantly increases some performance metrics in a fine-grained dataset when compared to selecting the quadruplet samples randomly. The feature embedding learned by the proposed method achieves favorable performance against its state-of-the-art counterparts.
Another approach is to utilize the hierarchical class labels of the training samples @cite_15 . In that method, samples with similar fine labels have the same coarse label, i.e. a sample has more than one label. The cost function is modified by considering both the coarse and fine labels. For this purpose, each quadruplet sample is constructed as follows: (1) Reference sample (anchor sample), @math , (2) Positive positive sample, @math , (3) Positive negative sample, @math , (4) Negative sample, @math . Similar to the triplet selection, the quadruplets are selected such that three constraints should be taken into account. First, both the coarse and fine classes of @math and @math should be the same. Second, although the coarse class of @math is the same as the coarse class of @math , the fine classes are different. Finally, the coarse class of @math and @math should be different.
@cite_15
2964189431
Recent progress of face recognition benefits a lot from large-scale face datasets with deep Convoluitonal Neural Networks(CNN). However, when dataset contains a large number of subjects but with few samples for each subject, conventional CNN with softmax loss is heavily prone to overfitting. To address this issue, we propose a hierarchical training schema to optimize CNN with coarse-to-fine class labels, referred to as Hit-CNN. Firstly trained with coarse class labels and then refined with fine class labels, Hit-CNN is enabled the to capture the distribution of data from major variations to fine variations progressively, which can effectively relieve the overfitting and lead to better generalization. In this work, the hierarchical coarse-to-fine class labels are obtained via hierarchical k-means clustering according to the face identities. Evaluated on two face datasets, the proposed Hit-CNN provides better results compared with the conventional CNN under the circumstances of large-scale data with few samples per subject. Automatic organ segmentation is an important yet challenging problem for medical image analysis. The pancreas is an abdominal organ with very high anatomical variability. This inhibits previous segmentation methods from achieving high accuracies, especially compared to other organs such as the liver, heart or kidneys. In this paper, we present a probabilistic bottom-up approach for pancreas segmentation in abdominal computed tomography (CT) scans, using multi-level deep convolutional networks (ConvNets). We propose and evaluate several variations of deep ConvNets in the context of hierarchical, coarse-to-fine classification on image patches and regions, i.e. superpixels. We first present a dense labeling of local image patches via @math and nearest neighbor fusion. Then we describe a regional ConvNet ( @math ) that samples a set of bounding boxes around each image superpixel at different scales of contexts in a "zoom-out" fashion. Our ConvNets learn to assign class probabilities for each superpixel region of being pancreas. Last, we study a stacked @math leveraging the joint space of CT intensities and the @math dense probability maps. Both 3D Gaussian smoothing and 2D conditional random fields are exploited as structured predictions for post-processing. We evaluate on CT images of 82 patients in 4-fold cross-validation. We achieve a Dice Similarity Coefficient of 83.6 @math 6.3 in training and 71.8 @math 10.7 in testing. Like other machine learning paradigms, multi-label learning also suffers from the curse of dimensionality problem. Multi-label dimensionality reduction can alleviate the problem but they generally ask for sufficient labeled samples. Nevertheless, we often may only have scarce labeled samples and abundant unlabeled samples. In this paper, we propose a @math emi-supervised @math ulti-label @math imensionality @math eduction based on @math ependence @math aximization approach (SMDRdm in short). SDMRdm assumes the semantic similarity and feature similarity of multi-label samples are inter-depended. SMDRdm first applies label propagation on a neighborhood graph composed with labeled and unlabeled samples to obtain the soft labels of unlabeled samples, and then measures the semantic similarity between all the training samples (including unlabeled ones) based on these soft labels and available labels of labeled samples. Next, it measures the feature similarity between samples in the subspace projected by the target projective matrix, instead of the original high-dimensional feature space. After that, it maximizes the dependence between these two types of similarities and incorporates the dependence into linear discriminant analysis to optimize the target projective matrix. Experiments on publicly accessible multi-label data sets demonstrate that SMDRdm achieves more prominent results than other related approaches across various evaluation metrics. In addition, the empirical study also shows the semantic similarity between samples derived from soft labels works better than that derived from scarce available labels. In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by (2006) that ensures that the output of an algorithm leaks little information about the data point provided by any of the participating individuals. Sample complexity of private PAC and agnostic learning was studied in a number of prior works starting with (, 2008) but a number of basic questions still remain open, most notably whether learning with privacy requires more samples than learning without privacy. We show that the sample complexity of learning with (pure) differential privacy can be arbitrarily higher than the sample complexity of learning without the privacy constraint or the sample complexity of learning with approximate differential privacy. Our second contribution and the main tool is an equivalence between the sample complexity of (pure) differentially private learning of a concept class @math (or @math ) and the randomized one-way communication complexity of the evaluation problem for concepts from @math . Using this equivalence we prove the following bounds: 1. @math , where @math is the Littlestone's (1987) dimension characterizing the number of mistakes in the online-mistake-bound learning model. Known bounds on @math then imply that @math can be much higher than the VC-dimension of @math . 2. For any @math , there exists a class @math such that @math but @math . 3. For any @math , there exists a class @math such that the sample complexity of (pure) @math -differentially private PAC learning is @math but the sample complexity of the relaxed @math -differentially private PAC learning is @math . This resolves an open problem of (2013b). In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability @math , and the random label noise can be class-conditional. Here, we address two fundamental problems raised by this scenario. The first is how to best use the abundant surrogate loss functions designed for the traditional classification problem when there is label noise. We prove that any surrogate loss function can be used for classification with noisy labels by using importance reweighting, with consistency assurance that the label noise does not ultimately hinder the search for the optimal classifier of the noise-free sample. The other is the open problem of how to obtain the noise rate @math . We show that the rate is upper bounded by the conditional probability @math of the noisy sample. Consequently, the rate can be estimated, because the upper bound can be easily reached in classification problems. Experimental results on synthetic and real datasets confirm the efficiency of our methods. The paper is concerned with two-class active learning. While the common approach for collecting data in active learning is to select samples close to the classification boundary, better performance can be achieved by taking into account the prior data distribution. The main contribution of the paper is a formal framework that incorporates clustering into active learning. The algorithm first constructs a classifier on the set of the cluster representatives, and then propagates the classification decision to the other samples via a local noise model. The proposed model allows to select the most representative samples as well as to avoid repeatedly labeling samples in the same cluster. During the active learning process, the clustering is adjusted using the coarse-to-fine strategy in order to balance between the advantage of large clusters and the accuracy of the data representation. The results of experiments in image databases show a better performance of our algorithm compared to the current methods. This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function @math in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where labels are known. Our work makes the following assumption: there exists a non-linear transformation between the joint feature label space distributions of the two domain @math and @math . We propose a solution of this problem with optimal transport, that allows to recover an estimated target @math by optimizing simultaneously the optimal coupling and @math . We show that our method corresponds to the minimization of a bound on the target error, and provide an efficient algorithmic solution, for which convergence is proved. The versatility of our approach, both in terms of class of hypothesis or loss functions is demonstrated with real world classification and regression problems, for which we reach or surpass state-of-the-art results. We introduce the notion of a canonical tester for a class of properties on distributions, that is, a tester strong and general enough that “a distribution property in the class is testable if and only if the canonical tester tests it.” We construct a canonical tester for the class of properties of one or two distributions that are symmetric and satisfy a certain weak continuity condition. Analyzing the performance of the canonical tester on specific properties resolves two open problems, establishing lower bounds that match known upper bounds: we show that distinguishing between entropy @math on distributions over @math requires @math samples, and distinguishing whether a pair of distributions has statistical distance @math requires @math samples. Our techniques also resolve a conjecture about a property that our canonical tester does not apply to: distinguishing identical distributions from those with statistical distance @math requires @math samples. In stochastic convex optimization the goal is to minimize a convex function @math over a convex set @math where @math is some unknown distribution and each @math in the support of @math is convex over @math . The optimization is commonly based on i.i.d. samples @math from @math . A standard approach to such problems is empirical risk minimization (ERM) that optimizes @math . Here we consider the question of how many samples are necessary for ERM to succeed and the closely related question of uniform convergence of @math to @math over @math . We demonstrate that in the standard @math setting of Lipschitz-bounded functions over a @math of bounded radius, ERM requires sample size that scales linearly with the dimension @math . This nearly matches standard upper bounds and improves on @math dependence proved for @math setting by Shalev- (2009). In stark contrast, these problems can be solved using dimension-independent number of samples for @math setting and @math dependence for @math setting using other approaches. We further show that our lower bound applies even if the functions in the support of @math are smooth and efficiently computable and even if an @math regularization term is added. Finally, we demonstrate that for a more general class of bounded-range (but not Lipschitz-bounded) stochastic convex programs an infinite gap appears already in dimension 2. This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples at the low end of the spectrum. Suppose we have many point sources at unknown locations in @math and with unknown complex-valued amplitudes. We only observe Fourier samples of this object up until a frequency cut-off @math . We show that one can super-resolve these point sources with infinite precision---i.e. recover the exact locations and amplitudes---by solving a simple convex optimization problem, which can essentially be reformulated as a semidefinite program. This holds provided that the distance between sources is at least @math . This result extends to higher dimensions and other models. In one dimension for instance, it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well. We also show that the theory and methods are robust to noise. In particular, in the discrete setting we develop some theoretical results explaining how the accuracy of the super-resolved signal is expected to degrade when both the noise level and the super-resolution factor vary. We consider the problem of learning a one-hidden-layer neural network: we assume the input @math is from Gaussian distribution and the label @math , where @math is a nonnegative vector in @math with @math , @math is a full-rank weight matrix, and @math is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly attempts to decompose a sequence of low-rank tensors simultaneously. Inspired by the formula, we design a non-convex objective function @math whose landscape is guaranteed to have the following properties: 1. All local minima of @math are also global minima. 2. All global minima of @math correspond to the ground truth parameters. 3. The value and gradient of @math can be estimated using samples. With these properties, stochastic gradient descent on @math provably converges to the global minimum and learn the ground-truth parameters. We also prove finite sample complexity result and validate the results by simulations. We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property @math is called a @math -graph . If @math satisfies certain properties, then an n-node m-edge @math -graph G can be encoded by a binary string X such that (1) G and X can be obtained from each other in O(n log n) time, and (2) X has at most @math bits for any continuous superadditive function @math so that there are at most @math distinct @math -node @math -graphs. The methodology is applicable to general classes of graphs; this paper focuses on planar graphs. Examples of such @math include all conjunctions over the following groups of properties: (1) G is a planar graph or a plane graph; (2) @math is directed or undirected; (3) @math is triangulated, triconnected, biconnected, merely connected, or not required to be connected; (4) the nodes of G are labeled with labels from @math for @math ; (5) the edges of G are labeled with labels from @math for @math ; and (6) each node (respectively, edge) of G has at most @math self-loops (respectively, @math multiple edges). Moreover, @math and @math are not required to be O(1) for the cases of @math being a plane triangulation. These examples are novel applications of small cycle separators of planar graphs and are the only nontrivial classes of graphs, other than rooted trees, with known polynomial-time information-theoretically optimal coding schemes. The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a 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 natural supervised learning problem --- we consider agnostic PAC learning of halfspaces over @math -sparse vectors in @math . This class is inefficiently learnable using @math 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 @math formulas is hard, it is impossible to efficiently learn this class using only @math examples. We further show that under stronger hardness assumptions, even @math examples do not suffice. On the other hand, we show a new algorithm that learns this class efficiently using @math examples. This formally establishes the tradeoff between sample and computational complexity for a natural supervised learning problem. Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of full volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of seven abdominal structures (artery, vein, liver, spleen, stomach, gallbladder, and pancreas) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training organ-specific models. To this end, we propose a two-stage, coarse-to-fine approach that trains an FCN model to roughly delineate the organs of interest in the first stage (seeing @math 40 of the voxels within a simple, automatically generated binary mask of the patient's body). We then use these predictions of the first-stage FCN to define a candidate region that will be used to train a second FCN. This step reduces the number of voxels the FCN has to classify to @math 10 while maintaining a recall high of @math 99 . This second-stage FCN can now focus on more detailed segmentation of the organs. We respectively utilize training and validation sets consisting of 281 and 50 clinical CT images. Our hierarchical approach provides an improved Dice score of 7.5 percentage points per organ on average in our validation set. We furthermore test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans with three anatomical labels (liver, spleen, and pancreas). In such challenging organs as the pancreas, our hierarchical approach improves the mean Dice score from 68.5 to 82.2 , achieving the highest reported average score on this dataset. We study the problem of sampling from a distribution where the negative logarithm of the target density is @math -smooth everywhere and @math -strongly convex outside a ball of radius @math , but potentially non-convex inside this ball. We study both overdamped and underdamped Langevin MCMC and prove upper bounds on the time required to obtain a sample from a distribution that is within @math of the target distribution in @math -Wasserstein distance. For the first-order method (overdamped Langevin MCMC), the time complexity is @math , where @math is the dimension of the underlying space. For the second-order method (underdamped Langevin MCMC), the time complexity is @math for some explicit positive constant @math . Surprisingly, the convergence rate is only polynomial in the dimension @math and the target accuracy @math . It is however exponential in the problem parameter @math , which is a measure of non-logconcavity of the target distribution. We propose a general methodology for the construction and analysis of essentially minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the support size @math is unknown and may be comparable with or even much larger than the number of observations @math . We treat the respective regions where the functional is nonsmooth and smooth separately. In the nonsmooth regime, we apply an unbiased estimator for the best polynomial approximation of the functional whereas, in the smooth regime, we apply a bias-corrected version of the maximum likelihood estimator (MLE). We illustrate the merit of this approach by thoroughly analyzing the performance of the resulting schemes for estimating two important information measures: 1) the entropy @math and 2) @math . We obtain the minimax @math rates for estimating these functionals. In particular, we demonstrate that our estimator achieves the optimal sample complexity @math for entropy estimation. We also demonstrate that the sample complexity for estimating @math n S^ 1 S @math 1 , we show the minimax @math rate for estimating @math is @math for infinite support size, while the maximum @math rate for the MLE is @math . For all the above cases, the behavior of the minimax rate-optimal estimators with @math samples is essentially that of the MLE (plug-in rule) with @math samples, which we term “effective sample size enlargement.” We highlight the practical advantages of our schemes for the estimation of entropy and mutual information. We compare our performance with various existing approaches, and demonstrate that our approach reduces running time and boosts the accuracy. Moreover, we show that the minimax rate-optimal mutual information estimator yielded by our framework leads to significant performance boosts over the Chow–Liu algorithm in learning graphical models. The wide use of information measure estimation suggests that the insights and estimators obtained in this paper could be broadly applicable. We give efficient algorithms for volume sampling, i.e., for picking @math -subsets of the rows of any given matrix with probabilities proportional to the squared volumes of the simplices defined by them and the origin (or the squared volumes of the parallelepipeds defined by these subsets of rows). In other words, we can efficiently sample @math -subsets of @math with probabilities proportional to the corresponding @math by @math principal minors of any given @math by @math positive semi definite matrix. This solves an open problem from the monograph on spectral algorithms by Kannan and Vempala (see Section @math of KV , also implicit in BDM, DRVW ). Our first algorithm for volume sampling @math -subsets of rows from an @math -by- @math matrix runs in @math arithmetic operations (where @math is the exponent of matrix multiplication) and a second variant of it for @math -approximate volume sampling runs in @math arithmetic operations, which is almost linear in the size of the input (i.e., the number of entries) for small @math . Our efficient volume sampling algorithms imply the following results for low-rank matrix approximation: (1) Given @math , in @math arithmetic operations we can find @math of its rows such that projecting onto their span gives a @math -approximation to the matrix of rank @math closest to @math under the Frobenius norm. This improves the @math -approximation of Boutsidis, Drineas and Mahoney BDM and matches the lower bound shown in DRVW . The method of conditional expectations gives a algorithm with the same complexity. The running time can be improved to @math at the cost of losing an extra @math in the approximation factor. (2) The same rows and projection as in the previous point give a @math -approximation to the matrix of rank @math closest to @math under the spectral norm. In this paper, we show an almost matching lower bound of @math , even for @math . By transferring knowledge from the abundant labeled samples of known source classes, zero-shot learning (ZSL) makes it possible to train recognition models for novel target classes that have no labeled samples. Conventional ZSL approaches usually adopt a two-step recognition strategy, in which the test sample is projected into an intermediary space in the first step, and then the recognition is carried out by considering the similarity between the sample and target classes in the intermediary space. Due to this redundant intermediate transformation, information loss is unavoidable, thus degrading the performance of overall system. Rather than adopting this two-step strategy, in this paper, we propose a novel one-step recognition framework that is able to perform recognition in the original feature space by using directly trained classifiers. To address the lack of labeled samples for training supervised classifiers for the target classes, we propose to transfer samples from source classes with pseudo labels assigned, in which the transferred samples are selected based on their transferability and diversity. Moreover, to account for the unreliability of pseudo labels of transferred samples, we modify the standard support vector machine formulation such that the unreliable positive samples can be recognized and suppressed in the training phase. The entire framework is fairly general with the possibility of further extensions to several common ZSL settings. Extensive experiments on four benchmark data sets demonstrate the superiority of the proposed framework, compared with the state-of-the-art approaches, in various settings. We present Epoch-Greedy, an algorithm for multi-armed bandits with observable side information. Epoch-Greedy has the following properties: No knowledge of a time horizon @math is necessary. The regret incurred by Epoch-Greedy is controlled by a sample complexity bound for a hypothesis class. The regret scales as @math or better (sometimes, much better). Here @math is the complexity term in a sample complexity bound for standard supervised learning. Automated computer-aided detection (CADe) has been an important tool in clinical practice and research. State-of-the-art methods often show high sensitivities at the cost of high false-positives (FP) per patient rates. We design a two-tiered coarse-to-fine cascade framework that first operates a candidate generation system at sensitivities @math of but at high FP levels. By leveraging existing CADe systems, coordinates of regions or volumes of interest (ROI or VOI) are generated and function as input for a second tier, which is our focus in this study. In this second stage, we generate 2D (two-dimensional) or 2.5D views via sampling through scale transformations, random translations and rotations. These random views are used to train deep convolutional neural network (ConvNet) classifiers. In testing, the ConvNets assign class (e.g., lesion, pathology) probabilities for a new set of random views that are then averaged to compute a final per-candidate classification probability. This second tier behaves as a highly selective process to reject difficult false positives while preserving high sensitivities. The methods are evaluated on three data sets: 59 patients for sclerotic metastasis detection, 176 patients for lymph node detection, and 1,186 patients for colonic polyp detection. Experimental results show the ability of ConvNets to generalize well to different medical imaging CADe applications and scale elegantly to various data sets. Our proposed methods improve performance markedly in all cases. Sensitivities improved from 57 to 70 , 43 to 77 , and 58 to 75 at 3 FPs per patient for sclerotic metastases, lymph nodes and colonic polyps, respectively.