Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large inputs, and computational tasks in this area tend to be expensive. We propose two compression methods for chain complexes of free 2-parameter persistence modules. The first method extends the multi-chunk algorithm for one-parameter persistent homology, returning the smallest chain complex among all the ones quasi-isomorphic to the input. The second method produces minimal presentations of the homology of the input; it is based on an algorithm of Lesnick and Wright, but incorporates several improvements that lead to dramatic performance gains. The two methods are complementary, and can be combined to compute minimal presentations for complexes with millions of generators in a few seconds. The methods have been implemented, and the software is publicly available. We report on experimental evaluations, which demonstrate substantial improvements in performance compared to previously available compression strategies.
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This paper proposes a stable volume and its variant, a stable sub-volume for more reliable data analysis using persistent homology. In the previous research, an optimal cycle and similar ideas are proposed to identify the homological structure corresponding to each birth-death pair in a persistence diagram. It is helpful for data analysis using persistent homology. However, the result is unstable against noises. Stable volumes and stable sub-volumes are proposed to solve the problem. In a special case, we prove that a stable volume is the robust part of an optimal volume against noises. We implement stable volumes and sub-volumes on HomCloud, persistent homology based data analysis software. This paper also shows some examples of stable volumes and sub-volumes.
A recently proposed SLOPE estimator (arXiv:1407.3824) has been shown to adaptively achieve the minimax $\ell_2$ estimation rate under high-dimensional sparse linear regression models (arXiv:1503.08393). Such minimax optimality holds in the regime where the sparsity level $k$, sample size $n$, and dimension $p$ satisfy $k/p \rightarrow 0$, $k\log p/n \rightarrow 0$. In this paper, we characterize the estimation error of SLOPE under the complementary regime where both $k$ and $n$ scale linearly with $p$, and provide new insights into the performance of SLOPE estimators. We first derive a concentration inequality for the finite sample mean square error (MSE) of SLOPE. The quantity that MSE concentrates around takes a complicated and implicit form. With delicate analysis of the quantity, we prove that among all SLOPE estimators, LASSO is optimal for estimating $k$-sparse parameter vectors that do not have tied non-zero components in the low noise scenario. On the other hand, in the large noise scenario, the family of SLOPE estimators are sub-optimal compared with bridge regression such as the Ridge estimator.
Previous AutoML pruning works utilized individual layer features to automatically prune filters. We analyze the correlation for two layers from the different blocks which have a short-cut structure. It shows that, in one block, the deeper layer has many redundant filters which can be represented by filters in the former layer. So, it is necessary to take information from other layers into consideration in pruning. In this paper, a novel pruning method, named GraphPruning, is proposed. Any series of the network is viewed as a graph. To automatically aggregate neighboring features for each node, a graph aggregator based on graph convolution networks(GCN) is designed. In the training stage, a PruningNet that is given aggregated node features generates reasonable weights for any size of the sub-network. Subsequently, the best configuration of the Pruned Network is searched by reinforcement learning. Different from previous work, we take the node features from a well-trained graph aggregator instead of the hand-craft features, as the states in reinforcement learning. Compared with other AutoML pruning works, our method has achieved the state-of-the-art under the same conditions on ImageNet-2012.
Automated Machine Learning(Auto-ML) pruning methods aim at searching a pruning strategy automatically to reduce the computational complexity of deep Convolutional Neural Networks(deep CNNs). However, some previous work found that the results of many Auto-ML pruning methods cannot even surpass the results of the uniformly pruning method. In this paper, the ineffectiveness of Auto-ML pruning which is caused by unfull and unfair training of the supernet is shown. A deep supernet suffers from unfull training because it contains too many candidates. To overcome the unfull training, a stage-wise pruning(SWP) method is proposed, which splits a deep supernet into several stage-wise supernets to reduce the candidate number and utilize inplace distillation to supervise the stage training. Besides, A wide supernet is hit by unfair training since the sampling probability of each channel is unequal. Therefore, the fullnet and the tinynet are sampled in each training iteration to ensure each channel can be overtrained. Remarkably, the proxy performance of the subnets trained with SWP is closer to the actual performance than that of most of the previous Auto-ML pruning work. Experiments show that SWP achieves the state-of-the-art on both CIFAR-10 and ImageNet under the mobile setting.
Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success and become a milestone in the field of artificial intelligence (AI). Owing to sophisticated pre-training objectives and huge model parameters, large-scale PTMs can effectively capture knowledge from massive labeled and unlabeled data. By storing knowledge into huge parameters and fine-tuning on specific tasks, the rich knowledge implicitly encoded in huge parameters can benefit a variety of downstream tasks, which has been extensively demonstrated via experimental verification and empirical analysis. It is now the consensus of the AI community to adopt PTMs as backbone for downstream tasks rather than learning models from scratch. In this paper, we take a deep look into the history of pre-training, especially its special relation with transfer learning and self-supervised learning, to reveal the crucial position of PTMs in the AI development spectrum. Further, we comprehensively review the latest breakthroughs of PTMs. These breakthroughs are driven by the surge of computational power and the increasing availability of data, towards four important directions: designing effective architectures, utilizing rich contexts, improving computational efficiency, and conducting interpretation and theoretical analysis. Finally, we discuss a series of open problems and research directions of PTMs, and hope our view can inspire and advance the future study of PTMs.
Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.
Estimating post-click conversion rate (CVR) accurately is crucial for ranking systems in industrial applications such as recommendation and advertising. Conventional CVR modeling applies popular deep learning methods and achieves state-of-the-art performance. However it encounters several task-specific problems in practice, making CVR modeling challenging. For example, conventional CVR models are trained with samples of clicked impressions while utilized to make inference on the entire space with samples of all impressions. This causes a sample selection bias problem. Besides, there exists an extreme data sparsity problem, making the model fitting rather difficult. In this paper, we model CVR in a brand-new perspective by making good use of sequential pattern of user actions, i.e., impression -> click -> conversion. The proposed Entire Space Multi-task Model (ESMM) can eliminate the two problems simultaneously by i) modeling CVR directly over the entire space, ii) employing a feature representation transfer learning strategy. Experiments on dataset gathered from Taobao's recommender system demonstrate that ESMM significantly outperforms competitive methods. We also release a sampling version of this dataset to enable future research. To the best of our knowledge, this is the first public dataset which contains samples with sequential dependence of click and conversion labels for CVR modeling.
Recently, caption generation with an encoder-decoder framework has been extensively studied and applied in different domains, such as image captioning, code captioning, and so on. In this paper, we propose a novel architecture, namely Auto-Reconstructor Network (ARNet), which, coupling with the conventional encoder-decoder framework, works in an end-to-end fashion to generate captions. ARNet aims at reconstructing the previous hidden state with the present one, besides behaving as the input-dependent transition operator. Therefore, ARNet encourages the current hidden state to embed more information from the previous one, which can help regularize the transition dynamics of recurrent neural networks (RNNs). Extensive experimental results show that our proposed ARNet boosts the performance over the existing encoder-decoder models on both image captioning and source code captioning tasks. Additionally, ARNet remarkably reduces the discrepancy between training and inference processes for caption generation. Furthermore, the performance on permuted sequential MNIST demonstrates that ARNet can effectively regularize RNN, especially on modeling long-term dependencies. Our code is available at: //github.com/chenxinpeng/ARNet
Image segmentation is the process of partitioning the image into significant regions easier to analyze. Nowadays, segmentation has become a necessity in many practical medical imaging methods as locating tumors and diseases. Hidden Markov Random Field model is one of several techniques used in image segmentation. It provides an elegant way to model the segmentation process. This modeling leads to the minimization of an objective function. Conjugate Gradient algorithm (CG) is one of the best known optimization techniques. This paper proposes the use of the Conjugate Gradient algorithm (CG) for image segmentation, based on the Hidden Markov Random Field. Since derivatives are not available for this expression, finite differences are used in the CG algorithm to approximate the first derivative. The approach is evaluated using a number of publicly available images, where ground truth is known. The Dice Coefficient is used as an objective criterion to measure the quality of segmentation. The results show that the proposed CG approach compares favorably with other variants of Hidden Markov Random Field segmentation algorithms.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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