Related papers: Maximum a Posteriori Inference for Factor Graphs v…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding,…
There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the…
Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…
We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Laplacian constructed from the low-fidelity data is used to…
We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal…
Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper,…
Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…
It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately solved via Gaussian filtering and smoothing, whenever a…
State estimation in robotic systems presents significant challenges, particularly due to the prevalence of multimodal posterior distributions in real-world scenarios. One effective strategy for handling such complexity is to compute maximum…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…
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…
We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…
We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve…
We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
We investigate the geometry of the maximal a posteriori (MAP) partition in the Bayesian Mixture Model where the component and the base distributions are chosen from conjugate exponential families. We prove that in this case the clusters are…
Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…