Related papers: Bayesian Matrix Decomposition and Applications

Bayesian component separation techniques have played a central role in the data reduction process of Planck. The most important strength of this approach is its global nature, in which a parametric and physical model is fitted to the data.…

Educational guide focused on the statistical treatment of measurement uncertainties. The conditions of application of current practices are detailed and precised: mean values, central limit theorem, linear regression. The last two chapters…

Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…

Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian data analysis, like all data analysis, is an iterative process…

The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…

This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to…

The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and…

Bayesian optimization has emerged at the forefront of expensive black-box optimization due to its data efficiency. Recent years have witnessed a proliferation of studies on the development of new Bayesian optimization algorithms and their…

Neural network architectures are achieving superhuman performance on an expanding range of tasks. To effectively and safely deploy these systems, their decision-making must be understandable to a wide range of stakeholders. Methods to…

Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

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…

High-dimensional data are crucial in biomedical research. Integrating such data from multiple studies is a critical process that relies on the choice of advanced statistical models, enhancing statistical power, reproducibility, and…