Related papers: Tensor Regression
Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
Large tensor (multi-dimensional array) data are now routinely collected in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this paper we…
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…
A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between…
We propose a novel framework in high-dimensional factor models to simultaneously analyse multiple tensor time series, each with potentially different tensor orders and dimensionality. The connection between different tensor time series is…
Tensors (also commonly seen as multi-linear operators or as multi-dimensional arrays) are ubiquitous in scientific computing and in data science, and so are the software efforts for tensor operations. Particularly in recent years, we have…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
Recent years have been marked with the fast-pace diversification and increasing ubiquity of machine learning applications. Yet, a firm theoretical understanding of the surprising efficiency of neural networks to learn from high-dimensional…
This article presents a generic approach to convolution that significantly differs from conventional methodologies in the current Machine Learning literature. The approach, in its mathematical aspects, proved to be clear and concise,…
This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic…
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…
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…
This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven…
Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies. At the heart of this is non-commutativity, in the sense that reordering the elements of a…
Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…
Time Series Classification and Extrinsic Regression are important and challenging machine learning tasks. Deep learning has revolutionized natural language processing and computer vision and holds great promise in other fields such as time…