Related papers: Optimal Matrix-Mimetic Tensor Algebras via Variabl…

Time series classification (TSC) performance depends not only on architectural design but also on the diversity of input representations. In this work, we propose a scalable multi-scale convolutional framework that systematically integrates…

We present a new inverse optimization methodology for multi-objective convex optimization that accommodates an input solution that may not be Pareto optimal and determines a weight vector that produces a Pareto optimal solution that…

Non-negative matrix and tensor factorisations are a classical tool for finding low-dimensional representations of high-dimensional datasets. In applications such as imaging, datasets can be regarded as distributions supported on a space…

With the advancement of the data acquisition techniques, multi-view learning has become a hot topic. Some multi-view learning methods assume that the multi-view data is complete, which means that all instances are present, but this too…

We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…

Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…

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…

In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent…

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…

It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…

Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators and apply it to problems closely related to classifying…

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…

Tensor processing is the cornerstone of modern technological advancements, powering critical applications in data analytics and artificial intelligence. While optical computing offers exceptional advantages in bandwidth, parallelism, and…

Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…

The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a…

Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…

We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…

Multiplication is a fundamental operation in many applications, and multipliers are widely adopted in various circuits. However, optimizing multipliers is challenging due to the extensive design space. In this paper, we propose a multiplier…