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Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…

Water quality monitoring is a core component of ecological environmental protection. However, due to sensor failure or other inevitable factors, data missing often exists in long-term monitoring, posing great challenges in water quality…

This paper presents an innovative approach, called credal wrapper, to formulating a credal set representation of model averaging for Bayesian neural networks (BNNs) and deep ensembles (DEs), capable of improving uncertainty estimation in…

We investigate a correspondence between two formalisms for discrete probabilistic modeling: probabilistic graphical models (PGMs) and tensor networks (TNs), a powerful modeling framework for simulating complex quantum systems. The graphical…

CNNs achieve remarkable performance by leveraging deep, over-parametrized architectures, trained on large datasets. However, they have limited generalization ability to data outside the training domain, and a lack of robustness to noise and…

Deep neural networks are known to be vulnerable to well-designed adversarial attacks. Although numerous defense strategies have been proposed, many are tailored to the specific attacks or tasks and often fail to generalize across diverse…

Statistically consistent methods based on the noise transition matrix ($T$) offer a theoretically grounded solution to Learning with Noisy Labels (LNL), with guarantees of convergence to the optimal clean-data classifier. In practice,…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

When designing new materials, it is often necessary to tailor the material design (with respect to its design parameters) to have some desired properties (e.g. Young's modulus). As the set of design parameters grow, the search space grows…

Tensors have broad applications in neuroimaging, data mining, digital marketing, etc. CANDECOMP/PARAFAC (CP) tensor decomposition can effectively reduce the number of parameters to gain dimensionality-reduction and thus plays a key role in…

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…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…

To collect large scale annotated data, it is inevitable to introduce label noise, i.e., incorrect class labels. To be robust against label noise, many successful methods rely on the noisy classifiers (i.e., models trained on the noisy…

Tensor (multidimensional array) classification problem has become very popular in modern applications such as image recognition and high dimensional spatio-temporal data analysis. Support Tensor Machine (STM) classifier, which is extended…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a…