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Long-term time series forecasting is a vital task and has a wide range of real applications. Recent methods focus on capturing the underlying patterns from one single domain (e.g. the time domain or the frequency domain), and have not taken…
For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…
Deep neural networks perform remarkably well on image classification tasks but remain vulnerable to carefully crafted adversarial perturbations. This work revisits linear dimensionality reduction as a simple, data-adapted defense. We…
We study the high-dimensional dynamics of online stochastic gradient descent (SGD) for the multi-spiked tensor model. This multi-index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the…
In a longitudinal metabolomics study, multiple metabolites are measured from several observations at many time points. Interest lies in reducing the dimensionality of such data and in highlighting influential metabolites which change over…
As a network-based functional approximator, we have proposed a "Lagrangian Density Space-Time Deep Neural Networks" (LDDNN) topology. It is qualified for unsupervised training and learning to predict the dynamics of underlying physical…
This paper proposes a tree-based convolutional neural network (TBCNN) for discriminative sentence modeling. Our models leverage either constituency trees or dependency trees of sentences. The tree-based convolution process extracts…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
A dynamic graph (DG) is frequently encountered in numerous real-world scenarios. Consequently, A dynamic graph convolutional network (DGCN) has been successfully applied to perform precise representation learning on a DG. However,…
In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…
In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…
Data augmentation in deep neural networks is the process of generating artificial data in order to reduce the variance of the classifier with the goal to reduce the number of errors. This idea has been shown to improve deep neural network's…
This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…
Time Series Classification (TSC) is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed. Among these methods, only a few have considered Deep…
Time Series Classification (TSC) has drawn a lot of attention in literature because of its broad range of applications for different domains, such as medical data mining, weather forecasting. Although TSC algorithms are designed for…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
Convolutional architectures have recently been shown to be competitive on many sequence modelling tasks when compared to the de-facto standard of recurrent neural networks (RNNs), while providing computational and modeling advantages due to…
This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…