Related papers: Maximum entropy low-rank matrix recovery
Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
The macro-to-micro transition in a heterogeneous material is envisaged as the selection of a probability distribution by the Principle of Maximum Entropy (MAXENT). The material is made of constituents, e.g. given crystal orientations. Each…
In this paper, we consider the matrix recovery from rank-one projection measurements proposed in [Cai and Zhang, Ann. Statist., 43(2015), 102-138], via nonconvex minimization. We establish a sufficient identifiability condition, which can…
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix…
We propose an end-to-end trainable image compression framework with a multi-scale and context-adaptive entropy model, especially for low bitrate compression. Due to the success of autoregressive priors in probabilistic generative model, the…
This article provides a new type of analysis of a compressed-sensing based technique for recovering column-sparse matrices, namely minimization of the $\ell_{1,2}$-norm. Rather than providing conditions on the measurement matrix which…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
Objective:Optoacoustic (photoacoustic) tomography is aimed at reconstructing maps of the initial pressure rise induced by the absorption of light pulses in tissue. In practice, due to inaccurate assumptions in the forward model, noise and…
Maximum likelihood estimation is a valuable tool often applied to inverse problems in quantum theory. Estimation from small data sets can, however, have non unique solutions. We discuss this problem and propose to use Jaynes maximum entropy…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…
The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-$s$ principle submatrix of a given order $n$ covariance matrix $C$. Exact algorithms are based on a branch-and-bound framework. The…
The rapid expansion of citizen science initiatives has led to a significant growth of biodiversity databases, and particularly presence-only (PO) observations. PO data are invaluable for understanding species distributions and their…
The asymptotic convergence of probability density function (pdf) and convergence of differential entropy are examined for the non-stationary processes that follow the maximum entropy principle (MaxEnt) and maximum entropy production…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
We propose a context-adaptive entropy model for use in end-to-end optimized image compression. Our model exploits two types of contexts, bit-consuming contexts and bit-free contexts, distinguished based upon whether additional bit…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
Matrix recovery is the problem of recovering a low-rank matrix from a few linear measurements. Recently, this problem has gained a lot of attention as it is employed in many applications such as Netflix prize problem, seismic data…