相关论文: Probabilistic Simplex Component Analysis

We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…

Identifying pure components in mixtures is a common yet challenging problem. The associated unmixing process requires the pure components, also known as endmembers, to be sufficiently spectrally distinct. Even with this requirement met,…

Simplex identification via split augmented Lagrangian (SISAL) is a popularly-used algorithm in blind unmixing of hyperspectral images. Developed by Jos\'{e} M. Bioucas-Dias in 2009, the algorithm is fundamentally relevant to tackling…

The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…

Diffusion models are now commonly used to solve inverse problems in computational imaging. However, most diffusion-based inverse solvers require complete knowledge of the forward operator to be used. In this work, we introduce a novel…

We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research…

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…

Large Language Models (LLMs), constrained by their auto-regressive nature, suffer from slow decoding. Speculative decoding methods have emerged as a promising solution to accelerate LLM decoding, attracting attention from both systems and…

We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…

Undersampling is a common method in Magnetic Resonance Imaging (MRI) to subsample the number of data points in k-space, reducing acquisition times at the cost of decreased image quality. A popular approach is to employ undersampling…

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…

The problem of infering the top component of a noisy sample covariance matrix with prior information about the distribution of its entries is considered, in the framework of the spiked covariance model. Using the replica method of…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…

Sparse Blind Source Separation (sparse BSS) is a key method to analyze multichannel data in fields ranging from medical imaging to astrophysics. However, since it relies on seeking the solution of a non-convex penalized matrix factorization…