Related papers: Provable Tensor Methods for Learning Mixtures of G…

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…

Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves…

We present an approach for continual learning (CL) that is based on fully probabilistic (or generative) models of machine learning. In contrast to, e.g., GANs that are "generative" in the sense that they can generate samples, fully…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Ensemble algorithms offer state of the art performance in many machine learning applications. A common explanation for their excellent performance is due to the bias-variance decomposition of the mean squared error which shows that the…

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…

We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…

Large language models (LLMs) demonstrate outstanding performance in various tasks in machine learning and have thus become one of the most important workloads in today's computing landscape. However, deploying LLM inference poses challenges…

Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…

Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…

Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its…

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…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor…