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Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…
Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects'…
Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…
We introduce a new global sensitivity measure, the global activity scores. The measure is based on finite differences of the underlying function, in contrast to several sensitivity measures in the literature that are based on derivatives of…
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…
New global sensitivity measures based on quantiles of the output are introduced. Such measures can be used for global sensitivity analysis of problems in which quantiles are explicitly the functions of interest and for identification of…
The optimization algorithms for solving multi-parameter inverse problem for the mathematical model of parabolic equations arising in social networks, epidemiology and economy are investigated. The data fitting is formulated as optimization…
Temporal graph signals are multivariate time series with individual components associated with nodes of a fixed graph structure. Data of this kind arises in many domains including activity of social network users, sensor network readings…
Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…
Temporal Graph Learning, which aims to model the time-evolving nature of graphs, has gained increasing attention and achieved remarkable performance recently. However, in reality, graph structures are often incomplete and noisy, which…
Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…
Modern enterprises generate vast streams of time series metrics when monitoring complex systems, known as observability data. Unlike conventional time series from domains such as climate, observability data are zero-inflated, highly…
We propose a new statistical estimation framework for a large family of global sensitivity analysis methods. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Sourav Chatterjee. We…
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…
Global Sensitivity Analysis (GSA) is the study of the influence of any given inputs on the outputs of a model. In the context of engineering design, GSA has been widely used to understand both individual and collective contributions of…
Crystal plasticity models are a powerful tool for predicting the deformation behaviour of polycrystalline materials accounting for the underlying grain morphology and texture. These models typically have a large number of parameters, an…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
Problem decomposition plays a vital role when applying cooperative coevolution (CC) to large scale global optimization problems. However, most learning-based decomposition algorithms either only apply to additively separable problems or…