Related papers: Fisher Vectors Derived from Hybrid Gaussian-Laplac…
Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to…
We study the problem of estimating the magnitude of a Gaussian beam displacement using a two pixel or 'split' detector. We calculate the maximum likelihood estimator, and compute its asymptotic mean-squared-error via the Fisher information.…
We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation…
The goal of this paper is to provide a new perspective on speech modeling by incorporating perceptual invariances such as amplitude scaling and temporal shifts. Conventional generative formulations often treat each dataset sample as a fixed…
In object recognition, Fisher vector (FV) representation is one of the state-of-art image representations ways at the expense of dense, high dimensional features and increased computation time. A simplification of FV is attractive, so we…
The Fisher information is a fundamental concept for characterizing the sensitivity of parameters in neural networks. However, leveraging the full observed Fisher information is too expensive for large models, so most methods rely on simple…
In this paper, we provide a novel method for the estimation of unknown parameters of the Gaussian Mixture Model (GMM) in Positron Emission Tomography (PET). A vast majority of PET imaging methods are based on reconstruction model that is…
The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…
Point estimators may not exist, need not be unique, and their distributions are not parameter invariant. Generalized estimators provide distributions that are parameter invariant, unique, and exist when point estimates do not. Comparing…
Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically…
The extraction of keypoints in images is at the basis of many computer vision applications, from localization to 3D reconstruction. Keypoints come with a score permitting to rank them according to their quality. While learned keypoints…
Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The…
Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…
In this paper, we model a pixel as a linear combination of endmembers sampled from probability distributions of Gaussian mixture models (GMM). The parameters of the GMM distributions are estimated using spectral libraries. Abundances are…
In this paper, a new probability distribution, referred to as the matrix Fisher-Gaussian (MFG) distribution, is proposed on the nonlinear manifold $\mathrm{SO}(3)\times\mathbb{R}^n$. It is constructed by conditioning a (9+n)-variate…
This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao…
The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…
A fast forward feature selection algorithm is presented in this paper. It is based on a Gaussian mixture model (GMM) classifier. GMM are used for classifying hyperspectral images. The algorithm selects iteratively spectral features that…
This work focuses on the critical aspect of accurate weight computation during the measurement incorporation phase of Gaussian mixture filters. The proposed novel approach computes weights by linearizing the measurement model about each…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…