An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor classification methods. In the presence of small amounts of training data, kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary. We develop the Tensor Train Multi-way Multi-level Kernel (TT-MMK), which combines the simplicity of the Canonical Polyadic decomposition, the classification power of the Dual Structure-preserving Support Vector Machine, and the reliability of the Tensor Train (TT) approximation. We show by experiments that the TT-MMK method is usually more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques.
We propose a novel technique for faster deep neural network training which systematically applies sample-based approximation to the constituent tensor operations, i.e., matrix multiplications and convolutions. We introduce new sampling techniques, study their theoretical properties, and prove that they provide the same convergence guarantees when applied to SGD training. We apply approximate tensor operations to single and multi-node training of MLP and CNN networks on MNIST, CIFAR-10 and ImageNet datasets. We demonstrate up to 66% reduction in the amount of computations and communication, and…
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann f…
We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This class of tensor network is argued to be a natural choice for classifiers as (i) they map classical data to classical data, and thus preserve the interpretability of data under tensor transformations, (ii) they can be efficiently trained to maximize their scalar product against classical data sets, and (iii) they seem to be as powerful as generic (unrestricted) tensor networks in this task. Our proposal is demonstrated using a variety of benchmark classification…
Emory University（埃默里大学）；UT Health Science Center at Houston（德克萨斯大学休斯顿健康科学中心）
Tensor factorization has been demonstrated as an efficient approach for computational phenotyping, where massive electronic health records (EHRs) are converted to concise and meaningful clinical concepts. While distributing the tensor factorization tasks to local sites can avoid direct data sharing, it still requires the exchange of intermediary results which could reveal sensitive patient information. Therefore, the challenge is how to jointly decompose the tensor under rigorous and principled privacy constraints, while still support the model's interpretability. We propose DPFact, a privacy-…
South China University of Technology（华南理工大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Northwestern University（西北大学）；Guangdong University of Technology（广东工业大学）
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate …
With the widespread use of LBSs (Location-based Services), synthesizing location traces plays an increasingly important role in analyzing spatial big data while protecting user privacy. In particular, a synthetic trace that preserves a feature specific to a cluster of users (e.g., those who commute by train, those who go shopping) is important for various geo-data analysis tasks and for providing a synthetic location dataset. Although location synthesizers have been widely studied, existing synthesizers do not provide sufficient utility, privacy, or scalability, hence are not practical for lar…
Privacy-preserving machine learning with tensor networks
University of Geneva（日内瓦大学）；Constructor Institute（康斯特拉克特研究所）；Instituto de Ciencias Matemáticas（数学科学研究所）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Universidad Politécnica de Madrid（马德里理工大学）
High-order Tensor Completion for Data Recovery via Sparse Tensor-train Optimization
Graduate School of Engineering, Saitama Institute of Technology, Japan（埼玉工科大学工学研究科）；Tensor Learning Unit, RIKEN Center for Advanced Intelligence Project (AIP), Japan（日本先进情报项目（AIP）RIKEN智能学习单元）；School of Automation, Guangdong University of Technology, China（广东技术大学自动化学院）；School of Computer Science and Technology, Hangzhou Dianzi University, China（杭州电子科技大学计算机科学与技术学院）
This work proposes a novel general-purpose estimator for supervised machine learning (ML) based on tensor trains (TT). The estimator uses TTs to parametrize discretized functions, which are then optimized using Riemannian gradient descent under the form of a tensor completion problem. Since this optimization is sensitive to initialization, it turns out that the use of other ML estimators for initialization is crucial. This results in a competitive, fast ML estimator with lower memory usage than many other ML estimators, like the ones used for the initialization.
As a hot research topic, many multi-view clustering approaches are proposed over the past few years. Nevertheless, most existing algorithms merely take the consensus information among different views into consideration for clustering. Actually, it may hinder the multi-view clustering performance in real-life applications, since different views usually contain diverse statistic properties. To address this problem, we propose a novel Tensor-based Intrinsic Subspace Representation Learning (TISRL) for multi-view clustering in this paper. Concretely, the rank preserving decomposition is proposed f…
High-dimension Tensor Completion via Gradient-based Optimization Under Tensor-train Format
Graduate School of Engineering, Saitama Institute of Technology, Japan（日本埼玉科技大学工学研究科）；Tensor Learning Unit, RIKEN Center for Advanced Intelligence Project (AIP), Japan（日本RIKEN先进人工智能项目（AIP）张量学习单元）；School of Automation, Guangdong University of Technology, China（广东技术大学自动化学院）；School of Computer Science and Technology, Hangzhou Dianzi University, China（杭州电子科技大学计算机科学与技术学院）
We implement a Tensor Train layer in the TensorFlow Neural Machine Translation (NMT) model using the t3f library. We perform training runs on the IWSLT English-Vietnamese '15 and WMT German-English '16 datasets with learning rates $\in \{0.0004,0.0008,0.0012\}$, maximum ranks $\in \{2,4,8,16\}$ and a range of core dimensions. We compare against a target BLEU test score of 24.0, obtained by our benchmark run. For the IWSLT English-Vietnamese training, we obtain BLEU test/dev scores of 24.0/21.9 and 24.2/21.9 using core dimensions $(2, 2, 256) \times (2, 2, 512)$ with learning rate 0.0012 and ra…
Seoul National University（首尔国立大学）；Seoul, Korea（韩国首尔（注意：根据要求，地址信息不应提取为机构，此处可能是误判，正确机构应为Seoul National University相关部分））
Adversarial training is a defense technique that improves adversarial robustness of a deep neural network (DNN) by including adversarial examples in the training data. In this paper, we identify an overlooked problem of adversarial training in that these adversarial examples often have different semantics than the original data, introducing unintended biases into the model. We hypothesize that such non-semantics-preserving (and resultingly ambiguous) adversarial data harm the robustness of the target models. To mitigate such unintended semantic changes of adversarial examples, we propose seman…
Duke University（杜克大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Rice University（莱斯大学）
This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy high-order tensor observation. The proposed TTOI consists of initialization via TT-SVD (Oseledets, 2011) and new iterative backward/forward updates. We develop the general upper bound on estimation error for TTOI with the support of several new representation lemmas on tensor matricizations. By developing a matching information-theoretic lower bound, we also prov…
ETH Zurich（苏黎世联邦理工学院）；HSE University（俄罗斯国立高等经济大学）；KU Leuven（鲁汶大学）
We study low-rank parameterizations of weight matrices with embedded spectral properties in the Deep Learning context. The low-rank property leads to parameter efficiency and permits taking computational shortcuts when computing mappings. Spectral properties are often subject to constraints in optimization problems, leading to better models and stability of optimization. We start by looking at the compact SVD parameterization of weight matrices and identifying redundancy sources in the parameterization. We further apply the Tensor Train (TT) decomposition to the compact SVD components, and pro…
Guangdong University of Technology（广东工业大学）；RIKEN（理化学研究所）
Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor recovery tasks. However, due to the large-scale tensor data in real-world applications, previous TRPCA models often suffer from high computational complexity. In this letter, we propose an efficient TRPCA under hybrid model of Tucker and TT. Specifically, in theory we reveal that TT nuclear norm (TTNN) of the original big tensor can be equivalently converted …
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has been a lot of work in the area of tensor decomposition and low-rank tensor approximation, extensions to supervised learning, feature extraction and classification are still limited. Moreover, most of the existing supervised tensor learning approaches are based on the orthogonal Tucker model. However, this model has some limitations for large tensors including h…
The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exaflops also come the extra-large high-dimensional data generated by high-performance computing. High-dimensional data is presented as multidimensional arrays, aka tensors. The presence of latent (not directly observable) structures in the tensor allows a unique representation and compression of the data by classical tensor factorization techniques. However, the classical tensor methods are not always stable or they can be exponential in thei…
Type-based compositional distributional semantic models present an interesting line of research into functional representations of linguistic meaning. One of the drawbacks of such models, however, is the lack of training data required to train each word-type combination. In this paper we address this by introducing training methods that share parameters between similar words. We show that these methods enable zero-shot learning for words that have no training data at all, as well as enabling construction of high-quality tensors from very few training examples per word.
