A Unifying Review of Linear Gaussian Models

By Sam T. Roweis, Zoubin Ghahramani. 1999

Subfields: Probabilistic & Bayesian Methods, Statistical Learning Theory

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Citations in the corpus

Generative and Latent Mean Map Kernels (2010, methodology): “3Note that we can use identity covariance (I) without loss of generality (as per footnote 4 of [17]).”
High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes (2019, methodology): “We also lags values as input L according to the time-frequency, [1, 24, 168] for hourly data, [1, 7, 14] for daily, and [1, 2, 4, 12, 24, 48] for 30 minutes data.”
A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning (2017, methodology): “While the LGSSM’s process and measurement noise in (1) are typically formulated with full covariance matrices [26], we will consider them as isotropic in a KVAE, as at act as a prior in a generative model that includes these extra degrees of freedom.”
Lifelong Generative Modeling (2017, background): “The idea of learning in a continual manner has been explored extensively in machine learning, seeded by the seminal works of lifelong-learning [126, 125, 117], online-learning [32, 9, 11, 12] and sequential linear gaussian models [105, 36] such as the Kalman Filter [56] and its non-linear counterpar”
Sequential Neural Models with Stochastic Layers (2016, background): “Although SSMs have an illustrious history [24], their stochasticity has limited their widespread use in the deep learning community, as inference can only be exact for two relatively simple classes of SSMs, namely hidden Markov models and linear Gaussian models, neither of which are well-suited to m”
Exploiting compositionality to explore a large space of model structures (2012, background): “Roweis and Ghahramani (1999)’s “generative model for generative models” presents a lattice showing relationships between different models.”
AMICA : An Adaptive Mixture of Independent Component Analyzers with Shared Components (2011, methodology): “Related Work The Gaussian liner model approach is described [1]–[3].”
Learning to Filter with Predictive State Inference Machines (2015, methodology): “Following Hefny et al. (2015), we define the predictive state at time step t as E[φ(ft)|ht−1] where φ is some feature function that is sufficient for the distribution P (ft|ht−1).”
Predictive State Recurrent Neural Networks (2017, background): “Bayes Filters (BFs) [1] focus on modeling and maintaining a belief state: a set of statistics, which, if known at time t, are sufficient to predict all future observations as accurately as if we know the full history.”
Fields of Experts (2009, background): “For example, Principal Component Analysis (PCA) (Roweis and Ghahramani, 1999) of image patches yields visually intuitive components, some of which resemble derivative filters of various orders and orientations.”
A free energy principle for a particular physics (2019, methodology): “s driven to minimise a variational bound on surprisal. From the perspective of an engineer, this is exactly the form of a Kalman-Bucy filter (a.k.a. predictive coding in neuroscience) (Dauwels, 2007; Roweis and Ghahramani, 1999). In short, the divergence free flows – that attend dissipative structur”
Estimating a State-Space Model from Point Process Observations (2003, background): “Several approaches have been taken to the problem of simultaneous state estimation and model parameter estimation, the latter being termed system identi(cid:142)cation (Roweis & Ghahramani, 1999).”
Hierarchical Aligned Cluster Analysis for Temporal Clustering of Human Motion (2013, unknown): “This section proposes an efficient coordinate-descent scheme that alternates between computing s using dynamic programming and G with a winner-take-all strategy [52].”