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This paper investigates a general family of models that stratifies the space of covariance matrices by eigenvalue multiplicity. This family, coined Stratified Principal Component Analysis (SPCA), includes in particular Probabilistic PCA (PPCA) models, where the noise component is assumed to be isotropic. We provide an explicit maximum likelihood and a geometric characterization relying on flag manifolds. A key outcome of this analysis is that PPCA's parsimony (with respect to the full covariance model) is due to the eigenvalue-equality constraint in the noise space and the subsequent inference of a multidimensional eigenspace. The sequential nature of flag manifolds enables to extend this constraint to the signal space and bring more parsimonious models. Moreover, the stratification and the induced partial order on SPCA yield efficient model selection heuristics. Experiments on simulated and real datasets substantiate the interest of equalising adjacent sample eigenvalues when the gaps are small and the number of samples is limited. They notably demonstrate that SPCA models achieve a better complexity/goodness-of-fit tradeoff than PPCA.

Few-shot classification aims to adapt to new tasks with limited labeled examples. To fully use the accessible data, recent methods explore suitable measures for the similarity between the query and support images and better high-dimensional features with meta-training and pre-training strategies. However, the potential of multi-modality information has barely been explored, which may bring promising improvement for few-shot classification. In this paper, we propose a Language-guided Prototypical Network (LPN) for few-shot classification, which leverages the complementarity of vision and language modalities via two parallel branches. Concretely, to introduce language modality with limited samples in the visual task, we leverage a pre-trained text encoder to extract class-level text features directly from class names while processing images with a conventional image encoder. Then, a language-guided decoder is introduced to obtain text features corresponding to each image by aligning class-level features with visual features. In addition, to take advantage of class-level features and prototypes, we build a refined prototypical head that generates robust prototypes in the text branch for follow-up measurement. Finally, we aggregate the visual and text logits to calibrate the deviation of a single modality. Extensive experiments demonstrate the competitiveness of LPN against state-of-the-art methods on benchmark datasets.

The complexity of learning problems, such as Generative Adversarial Network (GAN) and its variants, multi-task and meta-learning, hyper-parameter learning, and a variety of real-world vision applications, demands a deeper understanding of their underlying coupling mechanisms. Existing approaches often address these problems in isolation, lacking a unified perspective that can reveal commonalities and enable effective solutions. Therefore, in this work, we proposed a new framework, named Learning with Constraint Learning (LwCL), that can holistically examine challenges and provide a unified methodology to tackle all the above-mentioned complex learning and vision problems. Specifically, LwCL is designed as a general hierarchical optimization model that captures the essence of these diverse learning and vision problems. Furthermore, we develop a gradient-response based fast solution strategy to overcome optimization challenges of the LwCL framework. Our proposed framework efficiently addresses a wide range of applications in learning and vision, encompassing three categories and nine different problem types. Extensive experiments on synthetic tasks and real-world applications verify the effectiveness of our approach. The LwCL framework offers a comprehensive solution for tackling complex machine learning and computer vision problems, bridging the gap between theory and practice.

Data augmentation is a powerful technique to improve performance in applications such as image and text classification tasks. Yet, there is little rigorous understanding of why and how various augmentations work. In this work, we consider a family of linear transformations and study their effects on the ridge estimator in an over-parametrized linear regression setting. First, we show that transformations that preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations that mix data can improve estimation by playing a regularization effect. Finally, we validate our theoretical insights on MNIST. Based on the insights, we propose an augmentation scheme that searches over the space of transformations by how uncertain the model is about the transformed data. We validate our proposed scheme on image and text datasets. For example, our method outperforms random sampling methods by 1.24% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR-10, CIFAR-100, SVHN, and ImageNet datasets.

Recent advances in event camera research emphasize processing data in its original sparse form, which allows the use of its unique features such as high temporal resolution, high dynamic range, low latency, and resistance to image blur. One promising approach for analyzing event data is through graph convolutional networks (GCNs). However, current research in this domain primarily focuses on optimizing computational costs, neglecting the associated memory costs. In this paper, we consider both factors together in order to achieve satisfying results and relatively low model complexity. For this purpose, we performed a comparative analysis of different graph convolution operations, considering factors such as execution time, the number of trainable model parameters, data format requirements, and training outcomes. Our results show a 450-fold reduction in the number of parameters for the feature extraction module and a 4.5-fold reduction in the size of the data representation while maintaining a classification accuracy of 52.3%, which is 6.3% higher compared to the operation used in state-of-the-art approaches. To further evaluate performance, we implemented the object detection architecture and evaluated its performance on the N-Caltech101 dataset. The results showed an accuracy of 53.7 % [email protected] and reached an execution rate of 82 graphs per second.

Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word ambiguity, (2) word synonymity, and (3) dynamic contextual dependency. To address these challenges, we propose a novel GNN-based sparse structure learning model for inductive document classification. Specifically, a document-level graph is initially generated by a disjoint union of sentence-level word co-occurrence graphs. Our model collects a set of trainable edges connecting disjoint words between sentences and employs structure learning to sparsely select edges with dynamic contextual dependencies. Graphs with sparse structures can jointly exploit local and global contextual information in documents through GNNs. For inductive learning, the refined document graph is further fed into a general readout function for graph-level classification and optimization in an end-to-end manner. Extensive experiments on several real-world datasets demonstrate that the proposed model outperforms most state-of-the-art results, and reveal the necessity to learn sparse structures for each document.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned is receiving an increasing amount of attention. However, this increased focus has led to considerable confusion about the notion of interpretability. In particular, it is unclear how the wide array of proposed interpretation methods are related, and what common concepts can be used to evaluate them. We aim to address these concerns by defining interpretability in the context of machine learning and introducing the Predictive, Descriptive, Relevant (PDR) framework for discussing interpretations. The PDR framework provides three overarching desiderata for evaluation: predictive accuracy, descriptive accuracy and relevancy, with relevancy judged relative to a human audience. Moreover, to help manage the deluge of interpretation methods, we introduce a categorization of existing techniques into model-based and post-hoc categories, with sub-groups including sparsity, modularity and simulatability. To demonstrate how practitioners can use the PDR framework to evaluate and understand interpretations, we provide numerous real-world examples. These examples highlight the often under-appreciated role played by human audiences in discussions of interpretability. Finally, based on our framework, we discuss limitations of existing methods and directions for future work. We hope that this work will provide a common vocabulary that will make it easier for both practitioners and researchers to discuss and choose from the full range of interpretation methods.

Text classification is an important and classical problem in natural language processing. There have been a number of studies that applied convolutional neural networks (convolution on regular grid, e.g., sequence) to classification. However, only a limited number of studies have explored the more flexible graph convolutional neural networks (convolution on non-grid, e.g., arbitrary graph) for the task. In this work, we propose to use graph convolutional networks for text classification. We build a single text graph for a corpus based on word co-occurrence and document word relations, then learn a Text Graph Convolutional Network (Text GCN) for the corpus. Our Text GCN is initialized with one-hot representation for word and document, it then jointly learns the embeddings for both words and documents, as supervised by the known class labels for documents. Our experimental results on multiple benchmark datasets demonstrate that a vanilla Text GCN without any external word embeddings or knowledge outperforms state-of-the-art methods for text classification. On the other hand, Text GCN also learns predictive word and document embeddings. In addition, experimental results show that the improvement of Text GCN over state-of-the-art comparison methods become more prominent as we lower the percentage of training data, suggesting the robustness of Text GCN to less training data in text classification.