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Knowledge graph embedding research has mainly focused on learning continuous representations of entities and relations tailored towards the link prediction problem. Recent results indicate an ever increasing predictive ability of current…
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…
We present Sketch 'n Solve, an open-source Python package that implements efficient randomized numerical linear algebra (RandNLA) techniques for solving large-scale least squares problems. While sketch-and-solve algorithms have demonstrated…
We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor networks. For tensor train decomposition, we give a bicriteria…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
For polynomial representations of $GL_n$ of a fixed degree, H. Krause defined a new internal tensor product using the language of strict polynomial functors. We show that over an arbitrary commutative base ring $k$, the Schur functor…
In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem…
Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction or network inference problems. During the last decade kernel…
We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…
Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…
Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation…
We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats. We use alternating projections between the nonnegative orthant and the set of low-rank tensors, using STHOSVD and TTSVD…
Running machine learning analytics over geographically distributed datasets is a rapidly arising problem in the world of data management policies ensuring privacy and data security. Visualizing high dimensional data using tools such as…
A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al.…
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in…
Rotation equivariant graph neural networks, i.e. networks designed to guarantee certain geometric relations between their inputs and outputs, yield state of the art performance on spatial deep learning tasks. They exhibit high data…
We consider the problem of recovering an $n_1 \times n_2$ low-rank matrix with $k$-sparse singular vectors from a small number of linear measurements (sketch). We propose a sketching scheme and an algorithm that can recover the singular…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with…
Computing low-rank approximations of kernel matrices is an important problem with many applications in scientific computing and data science. We propose methods to efficiently approximate and store low-rank approximations to kernel matrices…