Related papers: Identifying Sparse Low-Dimensional Structures in M…

A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…

We analytically derive the geometrical structure of the weight space in multilayer neural networks (MLN), in terms of the volumes of couplings associated to the internal representations of the training set. Focusing on the parity and…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

Large kernel convolutions offer a scalable alternative to vision transformers for high-resolution 3D volumetric analysis, yet naively increasing kernel size often leads to optimization instability. Motivated by the spatial bias inherent in…

As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization…

The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are…

We investigate neural network image reconstruction for magnetic particle imaging. The network performance depends strongly on the convolution effects of the spectrum input data. The larger convolution effect appearing at a relatively…

This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite…

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…

In this paper, we propose an extremely simple deep model for the unsupervised nonlinear dimensionality reduction -- deep distributed random samplings, which performs like a stack of unsupervised bootstrap aggregating. First, its network…

We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable…

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…

In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…

Inferring the sequence of states from observations is one of the most fundamental problems in Hidden Markov Models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a…

Despite their attractiveness, popular perception is that techniques for nonparametric function approximation do not scale to streaming data due to an intractable growth in the amount of storage they require. To solve this problem in a…

Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…

Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques,…