This paper considers the sparse generalized eigenvalue problem (SGEP), which aims to find the leading eigenvector with at most $k$ nonzero entries. SGEP naturally arises in many applications in machine learning, statistics, and scientific computing, for example, the sparse principal component analysis (SPCA), the sparse discriminant analysis (SDA), and the sparse canonical correlation analysis (SCCA). In this paper, we focus on the development of a three-stage algorithm named {\em inverse-free truncated Rayleigh-Ritz method} ({\em IFTRR}) to efficiently solve SGEP. In each iteration of IFTRR, only a small number of matrix-vector products is required. This makes IFTRR well-suited for large scale problems. Particularly, a new truncation strategy is proposed, which is able to find the support set of the leading eigenvector effectively. Theoretical results are developed to explain why IFTRR works well. Numerical simulations demonstrate the merits of IFTRR.
Neural networks of ads systems usually take input from multiple resources, e.g., query-ad relevance, ad features and user portraits. These inputs are encoded into one-hot or multi-hot binary features, with typically only a tiny fraction of nonzero feature values per example. Deep learning models in online advertising industries can have terabyte-scale parameters that do not fit in the GPU memory nor the CPU main memory on a computing node. For example, a sponsored online advertising system can contain more than $10^{11}$ sparse features, making the neural network a massive model with around 10 TB parameters. In this paper, we introduce a distributed GPU hierarchical parameter server for massive scale deep learning ads systems. We propose a hierarchical workflow that utilizes GPU High-Bandwidth Memory, CPU main memory and SSD as 3-layer hierarchical storage. All the neural network training computations are contained in GPUs. Extensive experiments on real-world data confirm the effectiveness and the scalability of the proposed system. A 4-node hierarchical GPU parameter server can train a model more than 2X faster than a 150-node in-memory distributed parameter server in an MPI cluster. In addition, the price-performance ratio of our proposed system is 4-9 times better than an MPI-cluster solution.
Training generative models that can generate high-quality text with sufficient diversity is an important open problem for Natural Language Generation (NLG) community. Recently, generative adversarial models have been applied extensively on text generation tasks, where the adversarially trained generators alleviate the exposure bias experienced by conventional maximum likelihood approaches and result in promising generation quality. However, due to the notorious defect of mode collapse for adversarial training, the adversarially trained generators face a quality-diversity trade-off, i.e., the generator models tend to sacrifice generation diversity severely for increasing generation quality. In this paper, we propose a novel approach which aims to improve the performance of adversarial text generation via efficiently decelerating mode collapse of the adversarial training. To this end, we introduce a cooperative training paradigm, where a language model is cooperatively trained with the generator and we utilize the language model to efficiently shape the data distribution of the generator against mode collapse. Moreover, instead of engaging the cooperative update for the generator in a principled way, we formulate a meta learning mechanism, where the cooperative update to the generator serves as a high level meta task, with an intuition of ensuring the parameters of the generator after the adversarial update would stay resistant against mode collapse. In the experiment, we demonstrate our proposed approach can efficiently slow down the pace of mode collapse for the adversarial text generators. Overall, our proposed method is able to outperform the baseline approaches with significant margins in terms of both generation quality and diversity in the testified domains.
It is well known that attention mechanisms can effectively improve the performance of many CNNs including object detectors. Instead of refining feature maps prevalently, we reduce the prohibitive computational complexity by a novel attempt at attention. Therefore, we introduce an efficient object detector called Selective Convolutional Network (SCN), which selectively calculates only on the locations that contain meaningful and conducive information. The basic idea is to exclude the insignificant background areas, which effectively reduces the computational cost especially during the feature extraction. To solve it, we design an elaborate structure with negligible overheads to guide the network where to look next. It's end-to-end trainable and easy-embedding. Without additional segmentation datasets, we explores two different train strategies including direct supervision and indirect supervision. Extensive experiments assess the performance on PASCAL VOC2007 and MS COCO detection datasets. Results show that SSD and Pelee integrated with our method averagely reduce the calculations in a range of 1/5 and 1/3 with slight loss of accuracy, demonstrating the feasibility of SCN.
Various methods to deal with graph data have been proposed in recent years. However, most of these methods focus on graph feature aggregation rather than graph pooling. Besides, the existing top-k selection graph pooling methods have a few problems. First, to construct the pooled graph topology, current top-k selection methods evaluate the importance of the node from a single perspective only, which is simplistic and unobjective. Second, the feature information of unselected nodes is directly lost during the pooling process, which inevitably leads to a massive loss of graph feature information. To solve these problems mentioned above, we propose a novel graph self-adaptive pooling method with the following objectives: (1) to construct a reasonable pooled graph topology, structure and feature information of the graph are considered simultaneously, which provide additional veracity and objectivity in node selection; and (2) to make the pooled nodes contain sufficiently effective graph information, node feature information is aggregated before discarding the unimportant nodes; thus, the selected nodes contain information from neighbor nodes, which can enhance the use of features of the unselected nodes. Experimental results on four different datasets demonstrate that our method is effective in graph classification and outperforms state-of-the-art graph pooling methods.
The idea of Innovation Search was proposed as a data clustering method in which the directions of innovation were utilized to compute the adjacency matrix and it was shown that Innovation Pursuit can notably outperform the self representation based subspace clustering methods. In this paper, we present a new discovery that the directions of innovation can be used to design a provable and strong robust (to outlier) PCA method. The proposed approach, dubbed iSearch, uses the direction search optimization problem to compute an optimal direction corresponding to each data point. iSearch utilizes the directions of innovation to measure the innovation of the data points and it identifies the outliers as the most innovative data points. Analytical performance guarantees are derived for the proposed robust PCA method under different models for the distribution of the outliers including randomly distributed outliers, clustered outliers, and linearly dependent outliers. In addition, we study the problem of outlier detection in a union of subspaces and it is shown that iSearch provably recovers the span of the inliers when the inliers lie in a union of subspaces. Moreover, we present theoretical studies which show that the proposed measure of innovation remains stable in the presence of noise and the performance of iSearch is robust to noisy data. In the challenging scenarios in which the outliers are close to each other or they are close to the span of the inliers, iSearch is shown to remarkably outperform most of the existing methods. The presented method shows that the directions of innovation are useful representation of the data which can be used to perform both data clustering and outlier detection.
We study the estimation of $f(\btheta)$ under Gaussian shift model $\bx = \btheta+\bxi$, where $\btheta \in \RR^d$ is an unknown parameter, $\bxi \sim \mathcal{N}(\mathbf{0},\bSigma)$ is the random noise with covariance matrix $\bSigma$, and $f$ is a given function which belongs to certain Besov space with smoothness index $s>1$. Let $\sigma^2 = \|\bSigma\|_{op}$ be the operator norm of $\bSigma$ and $\sigma^{-2\alpha} = \br(\bSigma)$ be its effective rank with some $0<\alpha<1$ and $\sigma>0$. We develop a new estimator $g(\bx)$ based on a Fourier analytical approach that achieves effective bias reduction. We show that when the intrinsic dimension of the problem is large enough such that nontrivial bias reduction is needed, the mean square error (MSE) rate of $g(\bx)$ is $O\big(\sigma^2 \vee \sigma^{2(1-\alpha)s}\big)$ as $\sigma\rightarrow 0$. By developing new methods to establish the minimax lower bounds under standard Gaussian shift model, we show that this rate is indeed minimax optimal and so is $g(\bx)$. The minimax rate implies a sharp threshold on the smoothness $s$ such that for only $f$ with smoothness above the threshold, $f(\btheta)$ can be estimated efficiently with an MSE rate of the order $O(\sigma^2)$. Normal approximation and asymptotic efficiency were proved for $g(\bx)$ under mild restrictions. Furthermore, we propose a data-driven procedure to develop an adaptive estimator when the covariance matrix $\bSigma$ is unknown. Numerical simulations are presented to validate our analysis. The simplicity of implementation and its superiority over the plug-in approach indicate the new estimator can be applied to a broad range of real world applications.
The spatial convolution layer which is widely used in the Graph Neural Networks (GNNs) aggregates the feature vector of each node with the feature vectors of its neighboring nodes. The GNN is not aware of the locations of the nodes in the global structure of the graph and when the local structures corresponding to different nodes are similar to each other, the convolution layer maps all those nodes to similar or same feature vectors in the continuous feature space. Therefore, the GNN cannot distinguish two graphs if their difference is not in their local structures. In addition, when the nodes are not labeled/attributed the convolution layers can fail to distinguish even different local structures. In this paper, we propose an effective solution to address this problem of the GNNs. The proposed approach leverages a spatial representation of the graph which makes the neural network aware of the differences between the nodes and also their locations in the graph. The spatial representation which is equivalent to a point-cloud representation of the graph is obtained by a graph embedding method. Using the proposed approach, the local feature extractor of the GNN distinguishes similar local structures in different locations of the graph and the GNN infers the topological structure of the graph from the spatial distribution of the locally extracted feature vectors. Moreover, the spatial representation is utilized to simplify the graph down-sampling problem. A new graph pooling method is proposed and it is shown that the proposed pooling method achieves competitive or better results in comparison with the state-of-the-art methods.
In "Unlabeled Sensing", one observes a set of linear measurements of an underlying signal with incomplete or missing information about their ordering, which can be modeled in terms of an unknown permutation. Previous work on the case of a single noisy measurement vector has exposed two main challenges: 1) a high requirement concerning the \emph{signal-to-noise ratio} (snr), i.e., approximately of the order of $n^{5}$, and 2) a massive computational burden in light of NP-hardness in general. In this paper, we study the case of \emph{multiple} noisy measurement vectors (MMVs) resulting from a \emph{common} permutation and investigate to what extent the number of MMVs $m$ facilitates permutation recovery by "borrowing strength". The above two challenges have at least partially been resolved within our work. First, we show that a large stable rank of the signal significantly reduces the required snr which can drop from a polynomial in $n$ for $m = 1$ to a constant for $m = \Omega(\log n)$, where $m$ denotes the number of MMVs and $n$ denotes the number of measurements per MV. This bound is shown to be sharp and is associated with a phase transition phenomenon. Second, we propose computational schemes for recovering the unknown permutation in practice. For the "oracle case" with the known signal, the maximum likelihood (ML) estimator reduces to a linear assignment problem whose global optimum can be obtained efficiently. For the case in which both the signal and permutation are unknown, the problem is reformulated as a bi-convex optimization problem with an auxiliary variable, which can be solved by the Alternating Direction Method of Multipliers (ADMM). Numerical experiments based on the proposed computational schemes confirm the tightness of our theoretical analysis.
Multi-spectral sensors consisting of a standard (visible-light) camera and a long-wave infrared camera can simultaneously provide both visible and thermal images. Since thermal images are independent from environmental illumination, they can help to overcome certain limitations of standard cameras under complicated illumination conditions. However, due to the difference in the information source of the two types of cameras, their images usually share very low texture similarity. Hence, traditional texture-based feature matching methods cannot be directly applied to obtain stereo correspondences. To tackle this problem, a multi-spectral visual odometry method without explicit stereo matching is proposed in this paper. Bundle adjustment of multi-view stereo is performed on the visible and the thermal images using direct image alignment. Scale drift can be avoided by additional temporal observations of map points with the fixed-baseline stereo. Experimental results indicate that the proposed method can provide accurate visual odometry results with recovered metric scale. Moreover, the proposed method can also provide a metric 3D reconstruction in semi-dense density with multi-spectral information, which is not available from existing multi-spectral methods.