Related papers: Identifying Sparse Low-Dimensional Structures in M…
It is common to address the curse of dimensionality in Markov decision processes (MDPs) by exploiting low-rank representations. This motivates much of the recent theoretical study on linear MDPs. However, most approaches require a given…
Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and…
Contrastive learning is a powerful framework for learning self-supervised representations that generalize well to downstream supervised tasks. We show that multiple existing contrastive learning methods can be reinterpreted as learning…
In this paper, we propose a simple, versatile model for learning the structure and parameters of multivariate distributions from a data set. Learning a Markov network from a given data set is not a simple problem, because Markov networks…
Hierarchical reinforcement learning methods offer a powerful means of planning flexible behavior in complicated domains. However, learning an appropriate hierarchical decomposition of a domain into subtasks remains a substantial challenge.…
Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best…
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…
A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…
We propose a two-step algorithm for the construction of a Hidden Markov Model (HMM) of assigned size, i.e. cardinality of the state space of the underlying Markov chain, whose $n$-dimensional distribution is closest in divergence to a given…
This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…
We study stochastic optimization algorithms for constrained nonconvex stochastic optimization problems with Markovian data. In particular, we focus on the case when the transition kernel of the Markov chain is state-dependent. Such…
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
Representation learning aims to extract meaningful lower-dimensional embeddings from data, known as representations. Despite its widespread application, there is no established definition of a ``good'' representation. Typically, the…
Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…