Parameter estimation for linear dynamical systems

By Zoubin Ghahramani, Geoffrey E. Hinton. 1996

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Citations in the corpus

Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data (2016, background): “M L ] 2 0 M ay images, audio or other sensory inputs and (iii) scales to large data due to optimization of parameters based on stochastic gradient descent [2].”
Markovian Models for Sequential Data (2004, methodology): “For o -line applications, the EM algorithm can also be used [130], with a backward pass that is equivalent to the Rauch equations.”
Generative Temporal Models with Memory (2017, background): “Examples of such models include Hidden Markov Models (Rabiner, 1989), and linear dynamical systems such as Kalman ﬁlters and their non-linear extensions (Kalman, 1960; Ghahramani and Hinton, 1996; Krishnan et al., 2015).”
Temporal Models for Predicting Student Dropout in Massive Open Online Courses (2015, methodology): “For both formulations of IOHMM, we train the models using an expectation-maximization (EM) algorithm similar to that for linear dynamical systems as described in [30].”
Bayesian Temporal Factorization for Multidimensional Time Series Prediction (2019, methodology): “A classical approach is to consider the observations collected at a time point as a vector and model temporal dynamics using VAR process [23] and linear dynamical systems (LDS) [24].”
A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models (2012, unknown): “(10)A detailed derivation of the EM algorithm for dynamic factor model is provided by Ghahramani and Hinton (1996).”
Machine Recognition of Human Activities: A Survey (2008, background): “Advances in system identification theory for learning LDS model parameters from data [77]–[79] and distance metrics on”
Deep learning helicopter dynamics models (2015, methodology): “Together, the target trajectory and time-varying dynamics around that trajectory allow for successful control of the helicopter through advanced aerobatics, using Model Predictive Control (MPC).”
Variational Learning for Switching State-Space Models (2000, methodology): “…regard to the literature on neural computation, the model presented in this article is a generalization of both the mixture-of-experts neural network (Jacobs et al., 1991; Jordan & Jacobs, 1994) and the related mixture of factor analyzers (Hinton, Dayan, & Revow, 1997; Ghahramani & Hinton , 1996b).”
An Introduction to Hidden Markov Models and Bayesian Networks (2001, methodology): “The expected value of (20) can be expressed as a function of 〈St〉 and 〈StS> t−1〉.”
A Unifying Review of Linear Gaussian Models (1999, methodology): “…made by previous authors (Rubin & Thayer, 1982; Delyon, 1993; Digalakis et al., 1993; Hinton et al., 1995; Elliott, Aggoun, & Moore, 1995; Ghahramani & Hinton, 1996a,b, 1997; Hinton & Ghahramani, 1997) and present a review of all these algorithms as instances of a single basic generative…”
A Constraint Generation Approach to Learning Stable Linear Dynamical Systems (2007, methodology): “Standard algorithms for learning LDS parameters do not enforce this stability criterion, learning locally optimal values for LDS parameters by gradient descent [4], Expectation Maximization (EM) [5] or least squares on a state sequence estimate obtained by subspace identification methods, as describ”
A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis (2015, methodology): “, rLDSG and rLDSR to the following LDS learning baselines: • LDS learned using the standard EM learning algorithm (EM) (Ghahramani and Hinton 1996) that iteratively finds the maximum likelihood solution.”
Pattern Recognition and Machine Learning (2006, unknown): “Next, we consider the determination of these parameters using maximum likelihood (Ghahramani and Hinton, 1996b).”
Layered Dynamic Textures (2005, result): “The M-step of LDT learning is similar to that of LDS learning [41], [ 47 ], with two significant differences: 1) Each rowC ðjÞ i of”