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## Modeling the Complex Dynamics and Changing Correlations of Epileptic Events

### Citations

1342 | Reversible jump Markov chain Monte Carlo computation and Bayesian model determination - Green - 1995 |

940 | Dirichlet Processes
- Teh, Jordan
- 2004
(Show Context)
Citation Context ...states in the HDPHMM. The weak limit approximation still encourages using a subset of these L states. Based on the weak limit approximation, we first sample the parent transition distribution β as in =-=[22, 18]-=-, followed by sampling each φl from its Dirichlet posterior, p (φl | Z1:T ,β) ∝ Dir(αeβ + elκe + nl), (16) where nl is a vector of transition counts of Z1:T from state l to the L different states. Usi... |

646 | On bayesian analysis of mixtures with an unknown number of components - Richardson, Green - 1997 |

272 | Infinite latent feature models and the Indian buffet process.
- Griffiths, Ghahramani
- 2005
(Show Context)
Citation Context ...e f (i) marginalizing z (i) 1:T and then sample z (i) 1:T given the sampled f (i). Sampling the active features f (i) for channel i follows as in Fox et al. [5], using the Indian buffet process (IBP) =-=[19]-=- predictive representation associated with the beta process, but using a likelihood term that conditions on neighboring channel state sequences z (i′) 1:T and observations y (i′) 1:T . We additionally... |

183 |
Hyper Markov laws in the statistical analysis of decomposable graphical models
- Dawid, Lauritzen
- 1993
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Citation Context ...with sparse precisions ∆ −1 l determined by the graph G, we specify a hyper-inverse Wishart (HIW) prior, ∆l ∼ HIWG(b0, D0), (5) where b0 denotes the degrees of freedom and D0 the scale. The HIW prior =-=[15]-=- enforces hyper-Markov conditions specified by G. Feature constrained channel transition distributions. A natural question is how many AR states are the channels switching between? Likewise, which are... |

131 | Hierarchical beta processes and the Indian buffet process
- Thibaux, Jordan
- 2007
(Show Context)
Citation Context ...ever get excited into a certain state. To capture this structure, we take a Bayesian nonparametric approach building on the beta process (BP) AR-HMM of Fox et al. [16]. Through the beta process prior =-=[17]-=-, the BP-AR-HMM defines a shared library of infinitely many AR coefficients {ak}, but encourages each channel to only use a sparse subset of them. 7 The BP-AR-HMM specifically defines a featural model... |

74 |
Exact and approximate sum representations for the Dirichlet process.
- Ishwaran, Zarepour
- 2002
(Show Context)
Citation Context ...d to allow block-sampling of z1:T , we consider a weak limit approximation of the sticky HDP-HMM as in [18]. The top-level Dirichlet process is approximated by an L-dimensional Dirichlet distribution =-=[21]-=-, inducing a finite Dirichlet for φl: β ∼ Dir(γe/L, . . . , γe/L), φl ∼ Dir(αeβ + κeel). (15) Here, L provides an upper bound on the number of states in the HDPHMM. The weak limit approximation still ... |

52 | Beam sampling for the infinite hidden markov model,”
- Gael, Saatci, et al.
- 2007
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Citation Context ... numbers of channels between patients to share dynamics between event recordings. Other work has explored nonparametric modeling of multiple time series. The infinite factorial HMM of Van Gael et al. =-=[9]-=- considers an infinite collection of chains each with a binary state space. The infinite hierarchical HMM [10] also involves infinitely many chains with finite state spaces, but with constrained trans... |

44 |
Epileptic seizures may begin hours in advance of clinical onset: A report of five patients,
- Litt, Esteller, et al.
- 2001
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Citation Context ...g various types of abnormal activity. Recent evidence shows that the range of epileptic events extends beyond clinical seizures to include shorter, sub-clinical “bursts” lasting fewer than 10 seconds =-=[3]-=-. What is the relationship between these shorter bursts and the longer seizures? In this work, we demonstrate that machine learning techniques can have substantial impact in this domain by unpacking h... |

44 |
A sticky HDP-HMM with application to speaker diarization.
- Fox, Sudderth, et al.
- 2011
(Show Context)
Citation Context ...here K(i) = ∑ k f (i) k represents the number of states channel i uses. For convenience, we sometimes denote the set of transition variables {η(i)jk }j as η(i). As in the sticky HDP-HMM of Fox et al. =-=[18]-=-, the parameter κc encourages self-transitions (i.e., state j at time t− 1 to state j at time t). Unconstrained event transition distributions. We again take a Bayesian nonparametric approach to defin... |

37 | Sharing features among dynamical systems with beta processes.
- Fox, Sudderth, et al.
- 2009
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Citation Context ...multaneous recordings, as is almost always the case in EEG, we wish to share AR states between the channels while allowing for asynchronous switches. The recent beta process (BP) AR-HMM of Fox et al. =-=[5]-=- provides a flexible model of such dynamics: a shared library of infinitely many possible AR states is defined and each time series uses a finite subset of the states. The process encourages sharing o... |

31 | Simulation of hyperinverse Wishart distributions in graphical models.
- Carvalho, Massam, et al.
- 2007
(Show Context)
Citation Context ...z1:T , Z1:T , {ak}) ∝ HIWG(bl, Dl), (17) where bl = b0 + |{t | Zt = l, t = 1, . . . , T}|, Dl = D0 + ∑ t|Zt=l t T t . 12 Details on how to efficiently sample from a HIW distribution are provided in =-=[23]-=-. Conditioned on the truncated HDP-HMM event transition distributions {φl} and emission parameters {∆l}, we use a standard backward filtering forward sampling scheme to block sample Z1:T . AR coeffici... |

29 | Bayesian Nonparametric Learning of Complex Dynamical Phenomena - Fox - 2009 |

25 | Assessing seizure dynamics by analysing the correlation structure of multichannel intracranial - Schindler, Leung, et al. - 2007 |

25 | Bayesian Nonparametric Inference of Switching Dynamic Linear Models.
- Fox, Sudderth, et al.
- 2011
(Show Context)
Citation Context ...lations, we additionally compare to two alternatives where channels evolve independently: the BP-AR-HMM of Fox et al. [5] and an AR-HMM without the feature-based modeling provided by the beta process =-=[24]-=-. Both of these models use inverse gamma (IG) priors on the individual channel innovation variances. We inferred a set of AR coefficients {ak} and event covariances {∆l} on one seizure and then comput... |

19 | Classification of patterns of EEG synchronization for seizure prediction,” - Mirowski, Madhavan, et al. - 2009 |

19 | Line length: an efficient feature of seizure onset detection
- Estellar, Echauz, et al.
- 2001
(Show Context)
Citation Context ...contain information about the seizure-generation process. The events were automatically extracted from the patient’s continuous iEEG record by taking sections of iEEG whose median line-length feature =-=[25]-=- crossed a preset threshold, also including 10 seconds before and after each event. The iEEG was preprocessed in the same way as in the previous section. The six channels studied came from a depth ele... |

13 | A multi-feature and multi-channel univariate selection process for seizure prediction. Clin Neurophysiol 2005;116:506–16 - D'Alessandro, Vachtsevanos, et al. |

12 | Neuronal spatiotemporal pattern discrimination: the dynamical evolution of seizures., NeuroImage 28
- Schiff, Sauer, et al.
- 2005
(Show Context)
Citation Context ...se of alternative spatial and multivariate time series modeling techniques. It is well-known that the correlations between EEG channels usually vary during the beginning, middle, and end of a seizure =-=[6, 7]-=-. Prado et al. [8] employ a mixture-of-expert vector autoregressive (VAR) model to describe the different dynamics present in seven channels of scalp EEG. We take a similar approach by allowing for a ... |

11 | New methods of time series analysis of non-stationary EEG data: eigenstructure decompositions of time-varying autoregressions.
- Krystal, Prado, et al.
- 1999
(Show Context)
Citation Context ... EEG voltage traces. EEG signals exhibit nonstationary behavior during a variety of neurological events, and time-varying autoregressive (AR) processes have been proposed to model single channel data =-=[4]-=-. Here we aim to parse the recordings into interpretable regions of activity and thus propose to use autoregressive hidden Markov models (AR-HMMs) to define locally stationary processes. In the presen... |

10 | Infinite dynamic Bayesian networks.
- Doshi, Wingate, et al.
- 2011
(Show Context)
Citation Context ... hierarchical HMM [10] also involves infinitely many chains with finite state spaces, but with constrained transitions between the chains in a top down fashion. The infinite DBN of Doshi-Velez et al. =-=[11]-=- considers more general connection structures and arbitrary state spaces. Alternatively, the graph-coupled HMM of Dong et al. [12] allows graph-structured dependencies in the underlying states of some... |

7 |
Infinite hierarchical hidden Markov models.
- Heller, Teh, et al.
- 2009
(Show Context)
Citation Context ...parametric modeling of multiple time series. The infinite factorial HMM of Van Gael et al. [9] considers an infinite collection of chains each with a binary state space. The infinite hierarchical HMM =-=[10]-=- also involves infinitely many chains with finite state spaces, but with constrained transitions between the chains in a top down fashion. The infinite DBN of Doshi-Velez et al. [11] considers more ge... |

7 | Graph-coupled hmms for modeling the spread of infection
- Dong, Pentland, et al.
- 2012
(Show Context)
Citation Context ... chains in a top down fashion. The infinite DBN of Doshi-Velez et al. [11] considers more general connection structures and arbitrary state spaces. Alternatively, the graph-coupled HMM of Dong et al. =-=[12]-=- allows graph-structured dependencies in the underlying states of some N Markov chains. Here, we consider a finite set of chains with infinite state spaces that evolve independently. The factorial str... |

7 | Joint modeling of multiple related time series via the beta process with application to motion capture segmentation
- Fox, Hughes, et al.
(Show Context)
Citation Context ...ple, maybe only some of the channels ever get excited into a certain state. To capture this structure, we take a Bayesian nonparametric approach building on the beta process (BP) AR-HMM of Fox et al. =-=[16]-=-. Through the beta process prior [17], the BP-AR-HMM defines a shared library of infinitely many AR coefficients {ak}, but encourages each channel to only use a sparse subset of them. 7 The BP-AR-HMM ... |

5 |
Multivariate time series modeling and classification via hierarchical VAR mixtures
- Prado, Molina, et al.
- 2006
(Show Context)
Citation Context ...tial and multivariate time series modeling techniques. It is well-known that the correlations between EEG channels usually vary during the beginning, middle, and end of a seizure [6, 7]. Prado et al. =-=[8]-=- employ a mixture-of-expert vector autoregressive (VAR) model to describe the different dynamics present in seven channels of scalp EEG. We take a similar approach by allowing for a Markov evolution t... |

4 | Effective split-merge monte carlo methods for nonparametric models of sequential data - Hughes, Fox, et al. - 2012 |

2 | Bayesian Nonparametric Modeling of Epileptic Events - Wulsin - 2013 |

1 | Parsing Epileptic Events Using a Markov Switching Process for Correlated Time Series
- Wulsin, Fox, et al.
- 2013
(Show Context)
Citation Context ...factorial structure combines the chain-specific AR dynamic states and the graph-structured innovations to generate the multivariate observations with sparse dependencies. Expanding upon previous work =-=[13]-=-, we show that our model for correlated time series has better out-of-sample predictions of iEEG data than standard AR- and BP-AR-HMMs and demonstrate the utility of our model in comparing short, sub-... |