Parallelizable sparse inverse formulation Gaussian processes (SpInGP)

稀疏贝叶斯多维项目反应理论

Sparse Bayesian Multidimensional Item Response Theory

本文提出一种可扩展的贝叶斯EM算法，用于从混合数据中估计稀疏因子载荷并自动确定潜在因子维度，有效解决了传统MCMC方法在MIRT模型中速度慢且难以实现精确稀疏恢复的问题。

The Sparse Principal Component of a Constant-rank Matrix

The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem ${\mathcal{NP}}$-hard. In this work, we prove that, if the matrix is positive semidefinite and its rank is constant, then its sparse principal component is polynomially computable. Our proof utilizes the auxiliary unit vector technique that has been recently developed to identify problems that are polynomially solvable. Moreover, we use this technique to design an algorithm wh…

Efficient variational inference in large-scale Bayesian compressed sensing

We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing framework shifts towards capturing the full posterior distribution on the latent variables, which allows quantifying the estimation uncertainty and learning model parameters using maximum likelihood. The exact posterior distribution under the sparse linear model is intractable and we concentrate on variational Bayesian techniques to approximate it. Repeatedly compu…

A simple and provable algorithm for sparse diagonal CCA

Given two sets of variables, derived from a common set of samples, sparse Canonical Correlation Analysis (CCA) seeks linear combinations of a small number of variables in each set, such that the induced canonical variables are maximally correlated. Sparse CCA is NP-hard. We propose a novel combinatorial algorithm for sparse diagonal CCA, i.e., sparse CCA under the additional assumption that variables within each set are standardized and uncorrelated. Our algorithm operates on a low rank approximation of the input data and its computational complexity scales linearly with the number of input va…

A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models

Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large $K$) under a high-dimensional (large $p$) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs rely on penalized log-likelihood estimators that involve expensive and difficult non-smooth optimizations. We propose a novel approach, FASJEM for \underline{fa}st and \underline{s}calable \underline{j}oint structure-\underline{e}stimation of \underline{m}ultiple sGGMs at a large scale. As the first study of joint sGGM using the Elementary Estimator framework,…

A Fast and Scalable Joint Estimator for Integrating Additional Knowledge in Learning Multiple Related Sparse Gaussian Graphical Models

We consider the problem of including additional knowledge in estimating sparse Gaussian graphical models (sGGMs) from aggregated samples, arising often in bioinformatics and neuroimaging applications. Previous joint sGGM estimators either fail to use existing knowledge or cannot scale-up to many tasks (large $K$) under a high-dimensional (large $p$) situation. In this paper, we propose a novel \underline{J}oint \underline{E}lementary \underline{E}stimator incorporating additional \underline{K}nowledge (JEEK) to infer multiple related sparse Gaussian Graphical models from large-scale heterogene…