Gaussian mixtures are widely used for approximating density functions in various applications such as density estimation, belief propagation, and Bayesian filtering. These applications often utilize Gaussian mixtures as initial approximations that are updated recursively. A key challenge in these recursive processes stems from the exponential increase in the mixture's order, resulting in intractable inference. To overcome the difficulty, the Gaussian mixture reduction (GMR), which approximates a high order Gaussian mixture by one with a lower order, can be used. Although existing clustering-based methods are known for their satisfactory performance and computational efficiency, their convergence properties and optimal targets remain unknown. In this paper, we propose a novel optimization-based GMR method based on composite transportation divergence (CTD). We develop a majorization-minimization algorithm for computing the reduced mixture and establish its theoretical convergence under general conditions. Furthermore, we demonstrate that many existing clustering-based methods are special cases of ours, effectively bridging the gap between optimization-based and clustering-based techniques. Our unified framework empowers users to select the most appropriate cost function in CTD to achieve superior performance in their specific applications. Through extensive empirical experiments, we demonstrate the efficiency and effectiveness of our proposed method, showcasing its potential in various domains.
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Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, allowing not only the mean function but the entire density of the output to change with the inputs. Sparse Gaussian processes (GP) have shown promise as a leading candidate for the experts in such models, and in this article, we propose to design the gating network for selecting the experts from such mixtures of sparse GPs using a deep neural network (DNN). Furthermore, a fast one pass algorithm called Cluster-Classify-Regress (CCR) is leveraged to approximate the maximum a posteriori (MAP) estimator extremely quickly. This powerful combination of model and algorithm together delivers a novel method which is flexible, robust, and extremely efficient. In particular, the method is able to outperform competing methods in terms of accuracy and uncertainty quantification. The cost is competitive on low-dimensional and small data sets, but is significantly lower for higher-dimensional and big data sets. Iteratively maximizing the distribution of experts given allocations and allocations given experts does not provide significant improvement, which indicates that the algorithm achieves a good approximation to the local MAP estimator very fast. This insight can be useful also in the context of other mixture of experts models.
Deep convolutional neural networks have been widely applied in salient object detection and have achieved remarkable results in this field. However, existing models suffer from information distortion caused by interpolation during up-sampling and down-sampling. In response to this drawback, this article starts from two directions in the network: feature and label. On the one hand, a novel cascaded interaction network with a guidance module named global-local aligned attention (GAA) is designed to reduce the negative impact of interpolation on the feature side. On the other hand, a deep supervision strategy based on edge erosion is proposed to reduce the negative guidance of label interpolation on lateral output. Extensive experiments on five popular datasets demonstrate the superiority of our method.
Semantic part segmentation provides an intricate and interpretable understanding of an object, thereby benefiting numerous downstream tasks. However, the need for exhaustive annotations impedes its usage across diverse object types. This paper focuses on learning part segmentation from synthetic animals, leveraging the Skinned Multi-Animal Linear (SMAL) models to scale up existing synthetic data generated by computer-aided design (CAD) animal models. Compared to CAD models, SMAL models generate data with a wider range of poses observed in real-world scenarios. As a result, our first contribution is to construct a synthetic animal dataset of tigers and horses with more pose diversity, termed Synthetic Animal Parts (SAP). We then benchmark Syn-to-Real animal part segmentation from SAP to PartImageNet, namely SynRealPart, with existing semantic segmentation domain adaptation methods and further improve them as our second contribution. Concretely, we examine three Syn-to-Real adaptation methods but observe relative performance drop due to the innate difference between the two tasks. To address this, we propose a simple yet effective method called Class-Balanced Fourier Data Mixing (CB-FDM). Fourier Data Mixing aligns the spectral amplitudes of synthetic images with real images, thereby making the mixed images have more similar frequency content to real images. We further use Class-Balanced Pseudo-Label Re-Weighting to alleviate the imbalanced class distribution. We demonstrate the efficacy of CB-FDM on SynRealPart over previous methods with significant performance improvements. Remarkably, our third contribution is to reveal that the learned parts from synthetic tiger and horse are transferable across all quadrupeds in PartImageNet, further underscoring the utility and potential applications of animal part segmentation.
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence analysis of fractional gradient descent is currently limited both in the methods analyzed and the settings analyzed. This paper aims to fill in these gaps by analyzing variations of fractional gradient descent in smooth and convex, smooth and strongly convex, and smooth and non-convex settings. First, novel bounds will be established bridging fractional and integer derivatives. Then, these bounds will be applied to the aforementioned settings to prove $O(1/T)$ convergence for smooth and convex functions and linear convergence for smooth and strongly convex functions. Additionally, we prove $O(1/T)$ convergence for smooth and non-convex functions using an extended notion of smoothness that is more natural for fractional derivatives. Finally, empirical results will be presented on the potential speed up of fractional gradient descent over standard gradient descent as well as the challenges of predicting which will be faster in general.
The variability in EEG signals between different individuals poses a significant challenge when implementing brain-computer interfaces (BCI). Commonly proposed solutions to this problem include deep learning models, due to their increased capacity and generalization, as well as explicit domain adaptation techniques. Here, we introduce the Latent Alignment method that won the Benchmarks for EEG Transfer Learning (BEETL) competition and present its formulation as a deep set applied on the set of trials from a given subject. Its performance is compared to recent statistical domain adaptation techniques under various conditions. The experimental paradigms include motor imagery (MI), oddball event-related potentials (ERP) and sleep stage classification, where different well-established deep learning models are applied on each task. Our experimental results show that performing statistical distribution alignment at later stages in a deep learning model is beneficial to the classification accuracy, yielding the highest performance for our proposed method. We further investigate practical considerations that arise in the context of using deep learning and statistical alignment for EEG decoding. In this regard, we study class-discriminative artifacts that can spuriously improve results for deep learning models, as well as the impact of class-imbalance on alignment. We delineate a trade-off relationship between increased classification accuracy when alignment is performed at later modeling stages, and susceptibility to class-imbalance in the set of trials that the statistics are computed on.
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.
Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.
Aspect based sentiment analysis (ABSA) can provide more detailed information than general sentiment analysis, because it aims to predict the sentiment polarities of the given aspects or entities in text. We summarize previous approaches into two subtasks: aspect-category sentiment analysis (ACSA) and aspect-term sentiment analysis (ATSA). Most previous approaches employ long short-term memory and attention mechanisms to predict the sentiment polarity of the concerned targets, which are often complicated and need more training time. We propose a model based on convolutional neural networks and gating mechanisms, which is more accurate and efficient. First, the novel Gated Tanh-ReLU Units can selectively output the sentiment features according to the given aspect or entity. The architecture is much simpler than attention layer used in the existing models. Second, the computations of our model could be easily parallelized during training, because convolutional layers do not have time dependency as in LSTM layers, and gating units also work independently. The experiments on SemEval datasets demonstrate the efficiency and effectiveness of our models.
Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.
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