Related papers: A Support Tensor Train Machine
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
Recurrent Neural Networks (RNNs) with Long Short-Term Memory units (LSTM) are widely used because they are expressive and are easy to train. Our interest lies in empirically evaluating the expressiveness and the learnability of LSTMs in the…
The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper,…
Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
We introduce a new nearest-prototype classifier, the prototype vector machine (PVM). It arises from a combinatorial optimization problem which we cast as a variant of the set cover problem. We propose two algorithms for approximating its…
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…
Long Short-Term Memory Recurrent Neural Networks (LSTM-RNN) are one of the most powerful dynamic classifiers publicly known. The network itself and the related learning algorithms are reasonably well documented to get an idea how it works.…
In this paper, we introduce novel Twin Parametric Margin Support Vector Machine (TPMSVM) models designed to address multiclass classification tasks under feature uncertainty. To handle data perturbations, we construct bounded-by-norm…
We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs,…
The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through…
Neural Networks and related Deep Learning methods are currently at the leading edge of technologies used for classifying objects. However, they generally demand large amounts of time and data for model training; and their learned models can…
Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…
Marginal Structural Models (MSM) are the most popular models for causal inference from time-series observational data. However, they have two main drawbacks: (a) they do not capture subject heterogeneity, and (b) they only consider fixed…
Modeling spatiotemporal dynamical systems is a fundamental challenge in machine learning. Transformer models have been very successful in NLP and computer vision where they provide interpretable representations of data. However, a…
The computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced…
In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…
Spatiotemporal and motion features are two complementary and crucial information for video action recognition. Recent state-of-the-art methods adopt a 3D CNN stream to learn spatiotemporal features and another flow stream to learn motion…