Related papers: Bayesian Nonlinear Principal Component Analysis Us…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…
This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion:…
Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in inference on the relationship structure and…
We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…
Composition of low-dimensional distributions, whose foundations were laid in the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In…
Reduced-Rank (RR) regression is a powerful dimensionality reduction technique but it overlooks any possible group configuration among the responses by assuming a low-rank structure on the entire coefficient matrix. Moreover, the temporal…
Compositional data, also referred to as simplicial data, naturally arise in many scientific domains such as geochemistry, microbiology, and economics. In such domains, obtaining sensible lower-dimensional representations and modes of…
We perform approximate inference in state-space models with nonlinear state transitions. Without parameterizing a generative model, we apply Bayesian update formulas using a local linearity approximation parameterized by neural networks.…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix…
The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the…
Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the…