Related papers: On the identification of ARMA graphical models

This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…

We propose a new model-based computer-aided diagnosis (CAD) system for tumor detection and classification (cancerous v.s. benign) in breast images. Specifically, we show that (x-ray, ultrasound and MRI) images can be accurately modeled by…

The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector…

In many machine learning tasks, models are trained to predict structure data such as graphs. For example, in natural language processing, it is very common to parse texts into dependency trees or abstract meaning representation (AMR)…

This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…

The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is…

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…

The autoregressive (AR) models are used to represent the time-varying random process in which output depends linearly on previous terms and a stochastic term (the innovation). In the classical version, the AR models are based on normal…

We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…

We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…

Global information is essential for dense prediction problems, whose goal is to compute a discrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image…

This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary…

This paper deals with the dynamic factor analysis problem for an ARMA process. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model which contains the true…

A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…

We address the problem to estimate a Kronecker graphical model corresponding to an autoregressive Gaussian stochastic process. The latter is completely described by the power spectral density function whose inverse has support which admits…

We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…

We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that,…

In this article, we consider the problem of reconstructing networks for continuous, binary, count and discrete ordinal variables by estimating sparse precision matrix in Gaussian copula graphical models. We propose two approaches: $\ell_1$…

The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…