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Bayesian filtering

Dardari, Davide · AMS Campus - AlmaDL · 2017

Cited by 0

Bayesian Filtering

Dardari, Davide · AMS Campus - AlmaDL · 2018

Cited by 0

Variational Bayesian Filtering

V. Smidl, Anthony Quinn · IEEE Transactions on Signal Processing · 2008

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The use of the variational Bayes (VB) approximation in Bayesian filtering is studied, both as a means to accelerate marginalized particle filtering and as a deterministic local (one-step) approximation. The VB method of approximation is reviewed, together with restrictions that allow various computational savings to be achieved. These variants provide a range of algorithms that can be used in a principled tradeoff between quality of approximation and computational cost. In combination with marginalized particle filtering, they generalize previously published work on variational filtering and extend currently available methods for speeding up stochastic approximations in Bayesian filtering. In particular, the free-form nature of the VB approximation allows optimal selection of moments which summarize the particles. Other Bayesian filtering schemes are developed by replacing the marginalization operator in Bayesian filtering with VB-marginals. This leads to further computational savings at the cost of quality of approximation. The performance of the various VB filtering schemes is illustrated in the context of a Gaussian model with a nonlinear substate, and a hidden Markov model. </para>

Cited by 137

Bayesian Filtering Module

Virtanen, Ilkka I · Zenodo (CERN European Organization for Nuclear Research) · 2024

Added support from the Flipchem (IDC) chemistry model in ion composition fits. See the README file for instructions. Full Changelog: https://github.com/ilkkavir/BAFIM/compare/v0.1...v0.2

Cited by 1Open access

Bayesian filtering with wavefunctions

Lachlan McCalman, Hugh Durrant‐Whyte · 2010

This paper describes a general framework for performing Bayesian filtering on probability density functions represented by the modulus squared of a wavefunction in an orthogonal function basis. The objective of this work is to find a sparse representation for high-dimensional non-Gaussian density functions enabling tractable implementations of the general Bayesian filtering problem. The general form of the Bayesian filtering algorithms employing the modulus squared of a wavefunction is presented without specification of a particular basis. A simple 0-th order implementation of this formulation for a bearing only sensor is also demonstrated.

Cited by 1

Robotics - Localization & Bayesian Filtering

Simone Ceriani · 2012

Cited by 0

Naive Bayesian Spam Filtering

Yuhao Zhu · Highlights in Science Engineering and Technology · 2023

The spam filtering system is used to identify which emails in the received emails are completely meaningless to the recipient and perform operations such as interception and deletion. Nowadays, with the rapid development of the Internet, while e-mail provides convenience for people, spam also comes along with it, which brings many troubles to users. According to statistics, 80% of the emails in the world are spam, and e-spam is really annoying. Therefore, how to solve the problem of filtering emails has important practical significance. Spam filtering using Bayesian theory is a statistical technique applied to email filtering. It essentially uses Bayesian classification to discriminate the attributes of emails, including spam and non-spam. Bayesian-based spam filtering is a very effective technique that can modify the model to meet the needs of specific users and give a lower spam detection rate that is acceptable to users. In this experiment, we use Naive Bayes for experiments, and we use Unigram and bigram methods to preprocess the data, respectively. Finally, it is concluded that the data processing accuracy of unigram and bigram is greater than 0.75, and bigram performs better in four different evaluation indicators.

Cited by 1Open access

Bayesian Inference: Particle Filtering

Emin Orhan · 2012

Introduction: Particle filtering is a general Monte Carlo (sampling) method for performing inference in state-space models where the state of a system evolves in time, and information about the state is obtained via noisy measurements made at each time step. In a general discrete-time state-space model, the state of a system evolves according to: xk = fk(xk−1,vk−1) (1)

Cited by 0

Bayesian Conditional Density Filtering

Rajarshi Guhaniyogi, Shaan Qamar, Dunson, David B. · Figshare · 2018

We propose a Conditional Density Filtering (C-DF) algorithm for efficient online Bayesian inference. C-DF adapts MCMC sampling to the online setting, sampling from approximations to conditional posterior distributions obtained by propagating surrogate conditional sufficient statistics (a function of data and parameter estimates) as new data arrive. These quantities eliminate the need to store or process the entire dataset simultaneously and offer a number of desirable features. Often, these include a reduction in memory requirements and runtime and improved mixing, along with state-of-the-art parameter inference and prediction. These improvements are demonstrated through several illustrative examples including an application to high dimensional compressed regression. In the cases where dimension of the model parameter does not grow with time, we also establish sufficient conditions under which C-DF samples converge to the target posterior distribution asymptotically as sampling proceeds and more data arrive. Supplementary materials of C-DF are available online.

Cited by 0Open access

Robotics - Localization & Bayesian Filtering

Matteo Pirotta · 2013

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Bayesian Filtering and Smoothing

Simo Särkkä · Cambridge University Press eBooks · 2013

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include Matlab computations, and the numerous end-of-chapter exercises include computational assignments. Matlab code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

Cited by 1,725

Optimal bayesian feature filtering

Ali Foroughi pour, Lori A. Dalton · 2015

Recent work proposes a Bayesian hierarchical model for feature selection in which a prior describes the identity of feature sets as well as their underlying class-conditional distribution. In this work, we consider this model under an independence assumption on both feature identities, and the underlying class-conditional distribution of each feature. This framework results in optimal Bayesian feature filtering. Closed form solutions, which are applicable to high dimensional data with low computation cost, can be found. In addition, this model may be used to provide feedback on the quality of any feature set via closed-form estimators of the expected number of good features missed and the expected number of bad features selected. Synthetic data simulations depict outstanding performance of the optimal Bayesian feature filter relative to other popular feature selection methods. We also observe robustness with respect to assumptions in the model, particularly the independence assumption, and robustness under non-informative priors on the underlying class-conditional distributions. Furthermore, application of the optimal Bayesian feature filter on gene expression microarray datasets provides a gene list in which markers with known links to the cancer in question are highly ranked.

Cited by 12

Bayesian Filtering and Smoothing

Simo Särkkä, Lennart Svensson · Cambridge University Press eBooks · 2023

Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.

Cited by 232Open access

Bayesian Conditional Density Filtering

Rajarshi Guhaniyogi, Shaan Qamar, Dunson, David B. · Figshare · 2018

We propose a Conditional Density Filtering (C-DF) algorithm for efficient online Bayesian inference. C-DF adapts MCMC sampling to the online setting, sampling from approximations to conditional posterior distributions obtained by propagating surrogate conditional sufficient statistics (a function of data and parameter estimates) as new data arrive. These quantities eliminate the need to store or process the entire dataset simultaneously and offer a number of desirable features. Often, these include a reduction in memory requirements and runtime and improved mixing, along with state-of-the-art parameter inference and prediction. These improvements are demonstrated through several illustrative examples including an application to high dimensional compressed regression. In the cases where dimension of the model parameter does not grow with time, we also establish sufficient conditions under which C-DF samples converge to the target posterior distribution asymptotically as sampling proceeds and more data arrive. Supplementary materials of C-DF are available online.

Cited by 0Open access

CoBaFi: Collaborative Bayesian Filtering

Alex Beutel, Kenton Murray, Christos Faloutsos et al. · 2014

Given a large dataset of users ’ ratings of movies, what is the best model to accurately predict which movies a person will like? And how can we prevent spammers from tricking our algorithms into suggesting a bad movie? Is it possible to infer structure between movies simultaneously? In this paper we describe a unified Bayesian approach to Collaborative Filtering that accomplishes all of these goals. It models the discrete structure of ratings and is flexible to the often non-Gaussian shape of the distribution. Addi-tionally, our method finds a co-clustering of the users and items, which improves the model’s accuracy and makes the model robust to fraud. We offer three main contributions: (1) We provide a novel model and Gibbs sampling algorithm that accurately models the quirks of real world ratings, such as convex ratings distributions. (2) We provide proof of our model’s robustness to spam and anomalous behavior. (3) We use several real world datasets to demonstrate the model’s effectiveness in accurately predicting user’s ratings, avoiding prediction skew in the face of injected spam, and finding interesting patterns in real world ratings data.

Cited by 0

Bayesian Boundary Trend Filtering

Takahiro Onizuka, Fumiya Iwashige, Shintaro Hashimoto · arXiv (Cornell University) · 2023

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This paper develops a Bayesian trend filtering for estimating the boundary trend. To this end, the truncated multivariate normal working likelihood and global-local shrinkage priors based on the scale mixtures of normal distribution are introduced. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, an approximation of truncated multivariate normal distribution is employed. Using the approximation, the proposed models lead to an efficient Gibbs sampling algorithm via the Pólya-Gamma data augmentation. The proposed method is also extended by considering a nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.

Cited by 0Open access

Bayesian boundary trend filtering

Takahiro Onizuka, Fumiya Iwashige, Shintaro Hashimoto · Computational Statistics & Data Analysis · 2023

Cited by 3

Bayesian Filtering on Graphs

Bishwadeep Das, Madeline Navarro, Santiago Segarra et al. · 2025

Graph filters are ubiquitous for processing data over graphs. However, most filters obtained from data are point-estimates and may be sensitive to changes in topology or data distributions. Thus, modeling uncertainty in filters is critical to quantify confidence in analyses or improve downstream tasks in low-data regimes. We introduce a Bayesian framework for graph filter design, termed Bayesian graph filters. Given input-output realizations on a graph, we obtain the posterior filter and prior filter precision hyper-parameters via a constrained EM algorithm. The posterior filter leads to uncertainty in its frequency response, which has implications for stability. We study the stability via the integral Lipschitz (IL) property and derive a lower bound for the probability of Bayesian filters being IL. Results show that Bayesian filters can be more stable across the spectrum and under perturbations, provide uncertainty estimates and can outperform point filters on multiple tasks.

Cited by 0

Bayesian Quadrature in Nonlinear Filtering

Jakub Prüher, Miroslav Ŝimandl · 2015

The paper deals with the state estimation of nonlinear stochastic discrete-time systems by means of quadrature-based filtering algorithms. The algorithms use quadrature to approximate the moments given by integrals. The aim is at evaluation of the integral by Bayesian quadrature. The Bayesian quadrature perceives the integral itself as a random variable, on which inference is to be performed by conditioning on the function evaluations. Advantage of this approach is that in addition to the value of the integral, the variance of the integral is also obtained. In this paper, we improve estimation of covariances in quadrature-based filtering algorithms by taking into account the integral variance. The proposed modifications are applied to the Gauss-Hermite Kalman filter and the unscented Kalman filter algorithms. Finally, the performance of the modified filters is compared with the unmodified versions in numerical simulations. The modified versions of the filters exhibit significantly improved estimate credibility and a comparable root-mean-square error.

Cited by 5Open access

Bayesian Filtering of Myoelectric Signals

Terence D. Sanger · Journal of Neurophysiology · 2006

Surface electromyography is used in research, to estimate the activity of muscle, in prosthetic design, to provide a control signal, and in biofeedback, to provide subjects with a visual or auditory indication of muscle contraction. Unfortunately, successful applications are limited by the variability in the signal and the consequent poor quality of estimates. I propose to use a nonlinear recursive filter based on Bayesian estimation. The desired filtered signal is modeled as a combined diffusion and jump process and the measured electromyographic (EMG) signal is modeled as a random process with a density in the exponential family and rate given by the desired signal. The rate is estimated on-line by calculating the full conditional density given all past measurements from a single electrode. The Bayesian estimate gives the filtered signal that best describes the observed EMG signal. This estimate yields results with very low short-time variability but also with the capability of very rapid response to change. The estimate approximates isometric joint torque with lower error and higher signal-to-noise ratio than current linear methods. Use of the nonlinear filter significantly reduces noise compared with current algorithms, and it may therefore permit more effective use of the EMG signal for prosthetic control, biofeedback, and neurophysiology research.

Cited by 126