Related papers: Nonlinear Inductive Matrix Completion based on One…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample…
We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We first prove that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set, where simple…
Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive…
We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
Matrix completion is widely used in machine learning, engineering control, image processing, and recommendation systems. Currently, a popular algorithm for matrix completion is Singular Value Threshold (SVT). In this algorithm, the singular…
Matrix completion problem has been investigated under many different conditions since Netflix announced the Netflix Prize problem. Many research work has been done in the field once it has been discovered that many real life dataset could…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…
In this paper, we study the following nonlinear matrix decomposition (NMD) problem: given a sparse nonnegative matrix $X$, find a low-rank matrix $\Theta$ such that $X \approx f(\Theta)$, where $f$ is an element-wise nonlinear function. We…
Collaborative filtering is one of the most common scenarios and popular research topics in recommender systems. Among existing methods, latent factor models, i.e., learning a specific embedding for each user/item by reconstructing the…
The success of nonlinear noise reduction applied to a single channel recording of human voice is measured in terms of the recognition rate of a commercial speech recognition program in comparison to the optimal linear filter. The overall…
Port-Hamiltonian neural networks have shown promising results in the identification of nonlinear dynamics of complex systems, as their combination of physical principles with data-driven learning allows for accurate modelling. However, due…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…
We consider training over-parameterized two-layer neural networks with Rectified Linear Unit (ReLU) using gradient descent (GD) method. Inspired by a recent line of work, we study the evolutions of network prediction errors across GD…
The two main tasks in the Recommender Systems domain are the ranking and rating prediction tasks. The rating prediction task aims at predicting to what extent a user would like any given item, which would enable to recommend the items with…
Design of recommender systems aimed at achieving high prediction accuracy is a widely researched area. However, several studies have suggested the need for diversified recommendations, with acceptable level of accuracy, to avoid monotony…
In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…