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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…

Deep neural networks are powerful learning models that achieve state-of-the-art performance on many computer vision, speech, and language processing tasks. In this paper, we study a fundamental question that arises when designing deep…

The computationally cheap machine learning architecture of random feature maps can be viewed as a single-layer feedforward network in which the weights of the hidden layer are random but fixed and only the outer weights are learned via…

We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…

Recent non-linear feature selection approaches employing greedy optimisation of Centred Kernel Target Alignment(KTA) exhibit strong results in terms of generalisation accuracy and sparsity. However, they are computationally prohibitive for…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

Embedding molecular symmetries into machine-learning models is key for efficient learning of chemico-physical scalar properties, but little evidence on how to extend the same strategy to tensorial quantities exists. Here we formulate a…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…

Genetic pathways usually encode molecular mechanisms that can inform targeted interventions. It is often challenging for existing machine learning approaches to jointly model genetic pathways (higher-order features) and variants (atomic…

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…

Few-shot classification addresses the challenge of classifying examples given only limited labeled data. A powerful approach is to go beyond data augmentation, towards data synthesis. However, most of data augmentation/synthesis methods for…

As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…

Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…

Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We…

Most representation learning algorithms for language and image processing are local, in that they identify features for a data point based on surrounding points. Yet in language processing, the correct meaning of a word often depends on its…

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

The presence of irrelevant features in the input dataset tends to reduce the interpretability and predictive quality of machine learning models. Therefore, the development of feature selection methods to recognize irrelevant features is a…