Related papers: Invariant Bayesian estimation on manifolds
The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…
Sinopoli et al. (TAC, 2004) considered the problem of optimal estimation for linear systems with Gaussian noise and intermittent observations, available according to a Bernoulli arrival process. They showed that there is a "critical"…
MAP is the problem of finding a most probable instantiation of a set of nvariables in a Bayesian network, given some evidence. MAP appears to be a significantly harder problem than the related problems of computing the probability of…
In this article we introduce a diffeomorphism-invariant Riemannian metric on the space of vector valued one-forms. The particular choice of metric is motivated by potential future applications in the field of functional data and shape…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…
We introduce multi-scale energy models to learn the prior distribution of images, which can be used in inverse problems to derive the Maximum A Posteriori (MAP) estimate and to sample from the posterior distribution. Compared to the…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy…
Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and…
Gauss's Lemma is revised by showing that the point set association of the double tangential space with the tangential space of a Riemannian manifold is not the identity. The latter point set association is called a metrical distortion, an…
Recent studies on deep neural networks show that flat minima of the loss landscape correlate with improved generalization. Sharpness-aware minimization (SAM) efficiently finds flat regions by updating the parameters according to the…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein-Hilbert functional. This article highlights the manner in which one compelling open problem regarding the Yamabe…
Let \Theta be a smooth compact oriented manifold without boundary, embedded in a euclidean space and let \gamma be a smooth map \Theta into a riemannian manifold \Lambda. An unknown state \theta \in \Theta is observed via X=\theta+\epsilon…
Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. AMP only applies to independent identically distributed (IID) transform…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
We describe a general approach for maximum a posteriori (MAP) inference in a class of discrete-continuous factor graphs commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…