Related papers: A Solution for Large Scale Nonlinear Regression wi…
Deep Reinforcement Learning has enabled the learning of policies for complex tasks in partially observable environments, without explicitly learning the underlying model of the tasks. While such model-free methods achieve considerable…
Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…
Deep regression models typically learn in an end-to-end fashion without explicitly emphasizing a regression-aware representation. Consequently, the learned representations exhibit fragmentation and fail to capture the continuous nature of…
We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given…
Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…
We present a simple linear regression based approach for learning the weights and biases of a neural network, as an alternative to standard gradient based backpropagation. The present work is exploratory in nature, and we restrict the…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…
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…
Value-function (VF) approximation is a central problem in Reinforcement Learning (RL). Classical non-parametric VF estimation suffers from the curse of dimensionality. As a result, parsimonious parametric models have been adopted to…
Long Short-Term Memory (LSTM) is a popular approach to boosting the ability of Recurrent Neural Networks to store longer term temporal information. The capacity of an LSTM network can be increased by widening and adding layers. However,…
Traditional algorithms for compressive sensing recovery are computationally expensive and are ineffective at low measurement rates. In this work, we propose a data driven non-iterative algorithm to overcome the shortcomings of earlier…