Related papers: Bayesian Functional Principal Components Analysis …
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…
We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given…
Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted…
Undirected graphical models are a widely used class of probabilistic models in machine learning that capture prior knowledge or putative pairwise interactions between variables. Those interactions are encoded in a graph for pairwise…
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction…
In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian framework. Here, the focus is on…
Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…
We propose a new iterative optimization method for the {\bf Data-Fitting} (DF) problem in Machine Learning, e.g. Neural Network (NN) training. The approach relies on {\bf Graphical Model} (GM) representation of the DF problem, where…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…
Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…
A characteristic feature of functional data is the presence of phase variability in addition to amplitude variability. Existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we…
Artificial Neural Networks are connectionist systems that perform a given task by learning on examples without having prior knowledge about the task. This is done by finding an optimal point estimate for the weights in every node.…
While loopy belief propagation (LBP) performs reasonably well for inference in some Gaussian graphical models with cycles, its performance is unsatisfactory for many others. In particular for some models LBP does not converge, and in…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
For spatially dependent functional data, a generalized Karhunen-Lo\`{e}ve expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient…