Sharing Features among Dynamical Systems with Beta Processes

By Emily B. Fox, Erik B. Sudderth, Michael I. Jordan, Alan S. Willsky. 2009

162 citations recorded by the source corpus.

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Citations in the corpus

Effective Bayesian Modeling of Groups of Related Count Time Series (2014, methodology): “In the remainder of this paper, we call this model the hierarchical negative-binomial state space (H-NBSS) model.”
An Algorithmic Perspective on Imitation Learning (2018, methodology): “Niekum et al. [2014] segment the demonstrated task using a Beta Process Autoregressive Hidden Markov Model (BPAR-HMM) [Fox et al., 2009], and model the transition between discrete primitives as a finite-state automaton (FSA).”
Spectral Methods for Indian Buffet Process Inference (2014, methodology): “This is a very useful strategy and it has led to many applications including structuring Markov transition matrices [15], learning hidden causes with a bipartite graph [30] and finding latent features in link prediction [26].”
Human Action Segmentation and Recognition Using Discriminative Semi-Markov Models (2011, background): “dataset. In particular, we are investigating the performance of our approach on more complex action sequences including for example Fox et al. (2009) .”
Incremental Semantically Grounded Learning from Demonstration (2013, methodology): “The generative model for the BP-AR-HMM can be summarized as follows [6]: B|B0 ∼ BP(1, B0) Xi|B ∼ BeP(B) π (i) j |fi, γ,κ ∼ Dir([γ, ..., γ + κ, γ, ...]⊗ fi) z (i) t ∼ π (i) z(i)t−1 y(i)t = r j=1 A j,z(i)t y(i)t−j + e (i) t (z (i) t ) First, a draw B from a Beta Process (BP) provides a set of global w”
A Non-parametric Learning Method for Confidently Estimating Patient's Clinical State and Dynamics (2016, methodology): “Additionally, applying fully Bayesian methods [9] for clinical state estimation are computationally prohibitive as the computational complexity of constructing the stochastic model of all patients grows polynomially with the number of samples and maximum number of possible states of all patients.”
Streaming dynamic and distributed inference of latent geometric structures (2018, methodology): “d on Proposition 1. Streaming Dynamic Matching (SDM) is summarized in Algorithm 1. Additional related literature We note some prior work using similar technical building blocks in different contexts. Fox et al. (2009) utilized Beta-Bernoulli process in time series modeling to capture switching regim”
A Tutorial on Bayesian Nonparametric Models (2011, methodology): “Models that are built on BNP mixtures or latent factor models include those tailored for sequential data (Beal et al., 2002; Paisley and Carin, 2009; Fox et al., 2008, 2009), grouped data (Teh et al., 2006; Navarro et al., 2006), data in a tree (Johnson et al., 2007; Liang et al., 2007), relational…”
The IBP Compound Dirichlet Process and its Application to Focused Topic Modeling (2010, methodology): “Recent work by Fox et al. (2009) uses draws from an IBP to select subsets of an infinite set of states, to model multiple dynamic systems with shared states.”
Statistical Model Aggregation via Parameter Matching (2019, unknown): “Hierarchical Bayesian models [3, 12, 29] are widely used for performing such analyses, as they are able to both naturally model heterogeneity in data and share statistical strength across heterogeneous groups.”
Stochastic Variational Inference for Bayesian Time Series Models (2014, methodology): “Bayesian time series models can be applied to complex data in many domains, including data arising from behavior and motion (Fox et al., 2010; 2011), home energy consumption (Johnson & Willsky, 2013), physiological signals (Lehman et al.”
Scalable inference of topic evolution via models for latent geometric structures (2018, methodology): “[8] utilized Beta-Bernoulli process in time series modeling to capture switching regimes of an autoregressive process, where the corresponding Indian Buffet Process was used to select subsets of the latent states of the Hidden Markov Model.”
Learning grounded finite-state representations from unstructured demonstrations (2015, methodology): “The Beta Process Autoregressive HMM (BP-AR-HMM) [Fox et al., 2009], shown in Figure 1, is a recent model that integrates many of the advantages of the aforementioned models, while extending them and providing principled solutions to some of their shortcomings .”
Hierarchical Aligned Cluster Analysis for Temporal Clustering of Human Motion (2013, methodology): “…a nonparametric Bayesian method that utilizes the hierarchical Dirichlet process (HDP) as a prior on the parameters of SLDSs. Recently, Fox et al. [36] further extended this work by adding the beta process prior to discover and model dynamical behaviors that are shared among multiple related time…”