Bayesian Filtering and Smoothing

By Simo Särkkä. 2013

1,934 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Ocean Engineering, Probabilistic & Bayesian Methods

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Citations in the corpus

Time-series forecasting with deep learning: a survey (2020, methodology): “nh(W c 1 ht 1 + W 2 x~t+ bc); (2.14) Where is the element-wise (Hadamard) product, and tanh(:) is the tanh activation function. Relationship to Bayesian Filtering As examined in [30], Bayesian ﬁlters [35] and RNNs are both similar in their maintenance of a hidden state which is recursively updated o”
Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction (2019, methodology): “Performing inference via a series of prediction and update steps (Sarkka, 2013), Bayes ﬁlters recursively update the posterior distribution of predictions – or the belief state (Thrun et al., 2005) – with the arrival of new data.”
Generative Temporal Models with Memory (2017, background): “Generative temporal models (GTMs), such as Kalman filters, non-linear dynamical systems, hidden Markov models, switching state-space models, and change-point models (Särkkä, 2013) are a popular choice for modeling temporal and sequential data using latent variables.”
Multivariate covariance generalized linear models (2015, methodology): “Based on the results from Särkkä (2013) the partial derivative of Σ̃r with respect to pr and τrd are given by ∂Σ̃r ∂pr = Σ̃rΦ ( Σ̃ −1 r ∂Σr ∂pr Σ̃ −1 r ) , and ∂Σ̃r ∂τrd = Σ̃rΦ ( Σ̃ −1 r ∂Σr ∂τrd Σ̃ −1 r ) , respectively, where the function Φ returns the lower triangular part of the argument and…”
Applied Stochastic Differential Equations (2019, methodology): “These kinds of methods are particularly commonly used in Bayesian analysis (Gelman et al., 2013; Särkkä, 2013), but MCMC methods have a multitude of other applications as well (Liu, 2001; Brooks et al.”
A comprehensive review of digital twin — part 1: modeling and twinning enabling technologies (2022, methodology): “Table 4 compares four (recursive) Bayesian filters regarding system nonlinearity, state distribution constraints, and computational efficiency (Särkkä, 2013).”
A framework for quantifying the value of vibration-based structural health monitoring (2022, methodology): “For w∗ 1 = [p I∗ th = 5 · 10−4, pR∗ th = 1 · 10,∆tI = 5], a visual inspection is performed at tinsp = [5, 10, 15, 20, 25, 30, 35, 40, 45] years, as dictated by ∆tI = 5.”
Probabilistic Line Searches for Stochastic Optimization (2015, background): “We note in passing that regression on f and f ′ from N observations of pairs (yt, y′ t) can be formulated as a filter [26] and thus performed in O(N) time.”
Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling (2018, background): “Bayesian state space models and inference algorithms enable posterior inference of the latent states of a system and the parameters that govern their dynamics (Särkkä, 2013; Barber et al., 2011; Doucet et al., 2001).”
MCMC for Variationally Sparse Gaussian Processes (2015, background): “Other authors have introduced approximations based on the spectrum of the GP [5, 6], or which exploit specific structures within the covariance matrix [7, 8], or by making unbiased stochastic estimates of key computations [9].”