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## A monte carlo sequential estimation for point process optimum filtering (2006)

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Venue: | Neural Networks, 2006. IJCNN ’06. International Joint Conference on, pp. 1846 – 1850 |

Citations: | 6 - 2 self |

### Citations

2004 | A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
- Arulampalam, Maskell, et al.
- 2002
(Show Context)
Citation Context ...cursive approach the algorithm not only depend on the previous observation, but also depend on the whole path of the spike observation events. i i N S Let { x 0 : k , wk} i= 1 denote a Random Measure =-=[13]-=- in the i posterior density p( x 0: k | N1: k ) , where { x 0: k , i = 1, L, NS } is the set of all state samples up to time k with associated i normalized weights { wk , i = 1, L, NS } , and N S is t... |

1733 |
Novel approach to nonlinear/non-Gaussian Bayesian state estimation
- Gordon, Salmond, et al.
- 1993
(Show Context)
Citation Context ...is applied to eliminate the samples with small weight and to concentrate on samples with large weights. In our Monte Carlo sequential estimation of the point process, Sequential Importance Resampling =-=[9]-=- is applied at every time index, so that the samples are i.i.d. and uniform distributed with weights w i k−1 . The weights then change proportionally given by = 1 NS w i k ∝ p(∆Nk|x i k) (10) where p(... |

1225 |
On Estimation of a Probability Density Function and Mode
- Parzen
- 1962
(Show Context)
Citation Context ... is assumed known. Random state samples are generated using Monte Carlo simulations [11] in the neighborhood of the previous state according to x k = Fk xk −1 + ηk (3) Then, weighted Parzen windowing =-=[12]-=- was used with a Gaussian kernel to estimate the posterior density. The process is recursively repeated for each time instant propagating the estimate of the posterior density, and the state itself, b... |

1051 | On sequential Monte Carlo sampling methods for Bayesian filtering
- Doucet, Godsill, et al.
- 2000
(Show Context)
Citation Context ...II-A, and k(x − x,σ) is the Gaussian kernel in term of x with mean x and covariance σ. By generating samples from a proposed density q(x0:k|N1:k) according to the principle of Importance Sampling [7] =-=[8]-=-, which usually assumes dependence on xk−1 and Nk only, the weights can be derived by Bayes’ rule and Markov Chain property (see Arulampalam et al. [6] for details on a similar derivation, for the con... |

720 |
The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely moving rat.
- O’Keefe, Dostrovsky
- 1971
(Show Context)
Citation Context ... responses. In the rat hippocampus, for example, information about the spatial movement can be extracted from neural decoding, i.e. from the activity of simultaneously recorded noisy place cells [11] =-=[12]-=- representing the spikeobserved events. In a conceptually simplified motor cortical neural model [13], the one-dimensional velocity can also be reconstructed from the neuron spiking events by Monte Ca... |

346 |
Neuronal population coding of movement direction.
- Georgopoulos, Schwartz, et al.
- 1986
(Show Context)
Citation Context ...the predicted movements, and control a prosthetic robot arm to coordinate the intended movements. One of the best well known methods is the population vector algorithm proposed by Georgopoulos et al. =-=[3]-=-. In this method the movement direction is predicted from all cells preferred direction vectors appropriately weighted according This work was supported by NSF grants ECS-0422718, CISE-0541241 and CNS... |

271 |
Real-time prediction of hand trajectory by ensembles of cortical neurons in primates
- Wessberg, Stambaugh, et al.
- 2000
(Show Context)
Citation Context ...face (BMI) is a framework in which the understanding of the spatial and temporal structure of neural activity is used to control a prosthetic device with the intention of movement. In the experiments =-=[1]-=-[2], the microelectrode arrays were implanted into multiple cortical areas of a primate’s brain to collect different signals of neural activity, such as local field potentials and single unit activiti... |

267 | An improved particle filter for non-linear problems
- Carpenter, Clifford, et al.
- 1999
(Show Context)
Citation Context ...e need is the estimation of the state from the conditional intensity function (1), since the nonlinear relation f(·) is assumed known. Random state samples are generated using Monte Carlo simulations =-=[4]-=- in the neighborhood of the previous state according to (6). Then, weighted Parzen windowing [5] was used with a Gaussian kernel to estimate the posterior density. Due to the linearity of the integral... |

192 | Learning to control a brain-machine interface for reaching and grasping by primates,”
- Carmena, Lebedev, et al.
- 2003
(Show Context)
Citation Context ... cursor intersected the target. The corresponding position of the manipulandum was recorded continuously for an initial 30-min period at a 50Hz sampling rate, referred to as the “pole control” period =-=[16]-=- . BMI data provides us with 185 neural spike train channels and 2-dimensional movement trajectories for about 30 minutes. Compared to the one-neuron decoding simulation in [10], there are big differe... |

148 | Recursive Bayesian Estimation: Navigation and Tracking Applications. Linkoping studies in science and technology. thesis no 579,
- Bergman
- 1999
(Show Context)
Citation Context ...ion II-A, and k(x − x,σ) is the Gaussian kernel in term of x with mean x and covariance σ. By generating samples from a proposed density q(x0:k|N1:k) according to the principle of Importance Sampling =-=[7]-=- [8], which usually assumes dependence on xk−1 and Nk only, the weights can be derived by Bayes’ rule and Markov Chain property (see Arulampalam et al. [6] for details on a similar derivation, for the... |

143 |
Using Kernel Density Estimates to Investigate Multimodality,”
- Silverman
- 1981
(Show Context)
Citation Context ...terior density for each neuron by weighted Parzon window. The posterior density was smoothed by convolving with a Gaussian kernel, where the kernel size was designed according to the Silverman’s rule =-=[21]-=-. The kinematics vector was estimated and compared by both Maximum Likelihood Estimation and the expectation by collapse. Figure 2 shows the reconstructed kinematics from all 185 neuron spike trains f... |

131 | The time-rescaling theorem and its application to neural spike train data analysis.
- Brown, Barbieri, et al.
- 2002
(Show Context)
Citation Context ...lation parameter βk are set to be 1 and 3 respectively for the whole simulation time, 200s. A neuron spike is drawn as a Bernoulli random variable with probability λ(tk)∆t within each 1ms time window =-=[15]-=-.velocity reconstruction 1.5 1 desired velocity velocity by seq. estimation (MLE) velocity by seq. estimation (collapse) velocity by adaptive filtering 0.5 velocity 0 −0.5 −1 −1.5 2 3 4 5 6 7 8 9 10 ... |

111 | Motor cortical representation of speed and direction during reaching.
- Moran, Schwartz
- 1999
(Show Context)
Citation Context ...movement to neural activities. Most were linear weight combinations of the projection on 2 or 3 dimensions of kinematic vectors and bias, including the direction angle information. Moran and Schwartz =-=[17]-=- introduced an exponential velocity and direction tuned motor cortical model. Emery Brown used a Gaussian tuning function for the hippocampal pyramidal neurons [9]. These nonlinear mathematical models... |

86 |
Brain-machine interface: instant neural control of a movement signal.
- Serruya, Hatsopoulos, et al.
- 2002
(Show Context)
Citation Context ...e (BMI) is a framework in which the understanding of the spatial and temporal structure of neural activity is used to control a prosthetic device with the intention of movement. In the experiments [1]=-=[2]-=-, the microelectrode arrays were implanted into multiple cortical areas of a primate’s brain to collect different signals of neural activity, such as local field potentials and single unit activities,... |

86 | Recursive Bayesian decoding of motor cortical signals by particle filtering
- Brockwell, Rojas, et al.
- 2004
(Show Context)
Citation Context ...mptions may be too restrictive for BMI applications. The particle filter algorithm, generalizes the Kalman filter, and was also investigated to recover movement velocities from binned neural activity =-=[7]-=- [8]. The above algorithms are coarse approaches that lose spike timing resolution due to binning and may exclude rich neural dynamics due to single spikes. The primary reason for this limitation is t... |

82 | Bayesian population decoding of motor cortical activity using a Kalman filter,”
- Wu, Gao, et al.
- 2006
(Show Context)
Citation Context ...l neural recordings by estimating the expectation of the posterior density or by maximum likelihood estimation. The Kalman filter is a special case of this framework and was previously applied to BMI =-=[6]-=-. Two strong assumptions of the Kalman filter are that time-series neural activities are generated from the stimulus through a linear system and that, given the neural spiking activities at every time... |

72 | Characterization of neural responses with stochastic stimuli.
- Simoncelli, Pillow, et al.
- 2004
(Show Context)
Citation Context ...relis and Naka [18] developed a statistical method, called white noise analysis, to model the neural responses with stochastic stimuli. This method was improved by Simoncelli, Paninski and colleagues =-=[19]-=- . By parametric model identification, the nonlinear property between the neural spikes and the stimuli was directly estimated from data, which is more reliable than just assuming a linear or Gaussian... |

65 | Modeling and decoding motor cortical activity using a switching kalman filter
- Wu, Black, et al.
- 2004
(Show Context)
Citation Context ...he posterior density as the state estimation. As we smooth the posterior density by convolving with a Gaussian kernel, we can easily obtain the expectation ˜xk and its error covariance Vk by collapse =-=[10]-=-: NS ∑ ˜xk = p(∆Nk|x i k) · x i k (12) NS ∑ Vk = i=1 i=1 p(∆Nk|x i k ) · (σ +(xi k − ˜xk)(x i k − ˜xk) T ) (13) From (12) and (13), we can see that without complex computation we can easily estimate t... |

63 |
Dynamic analysis of neural encoding by point process adaptive filtering,”
- Eden, Frank, et al.
- 2004
(Show Context)
Citation Context ...Processes with Gaussian Assumption One can model a point process using a Bayesian approach to estimate the system state by evaluating the posterior density of the state given the discrete observation =-=[2]-=-. This framework provides a nonlinear time-series probabilistic model between the state and the spiking event [3]. Given an observation interval (0,T], the number N(t) of events (e.g. spikes) can be m... |

60 |
Reconstructing the engram: simultaneous, multisite, many single neuron recordings
- Nicolelis
- 1997
(Show Context)
Citation Context ...fied and band pass filtered from 500 Hz to 5KHz.The spikes of a single neuron from each microwire were discriminated based on time-amplitude discriminators and a principal component (PC) algorithm [1]=-=[15]-=- . The firing times of each spike were stored. The monkey performed a two-dimensional target-reaching task to move the cursor on a computer screen by controlling a hand-held manipulandum in order to r... |

60 | Experience-dependent asymmetric shape of hippocampal receptive fields,
- Mehta, Quirk, et al.
- 2000
(Show Context)
Citation Context ...ronal responses. In the rat hippocampus, for example, information about the spatial movement can be extracted from neural decoding, i.e. from the activity of simultaneously recorded noisy place cells =-=[11]-=- [12] representing the spikeobserved events. In a conceptually simplified motor cortical neural model [13], the one-dimensional velocity can also be reconstructed from the neuron spiking events by Mon... |

57 | Motor cortical activity during drawing movements: Population representation during sinusoidal tracing.
- Schwartz
- 1993
(Show Context)
Citation Context ...ons may be too restrictive for BMI applications. The particle filter algorithm, generalizes the Kalman filter, and was also investigated to recover movement velocities from binned neural activity [7] =-=[8]-=-. The above algorithms are coarse approaches that lose spike timing resolution due to binning and may exclude rich neural dynamics due to single spikes. The primary reason for this limitation is that ... |

37 |
An analysis of neural receptive field plasticity by point process adaptive filtering.
- Brown, Nguyen, et al.
- 2001
(Show Context)
Citation Context ...annot be applied directly to point processes. Indeed, a spike train point process is completely specified by the spike times. A general point process adaptive filtering paradigm wasrecently proposed =-=[9]-=- to probabilistically reconstruct a freely running rat’s position from the discrete observation of the neural firing. This algorithm modeled the neural spike train as an inhomogeneous Poisson process ... |

32 | Input-Output Mapping Performance of Linear and Nonlinear Models for Estimating Hand Trajectories from Cortical Neuronal Firing Patterns,
- Sanchez, Kim, et al.
- 2002
(Show Context)
Citation Context ...ct the 3D hand using neuronal binned spike rates embedded by a 10-tap delay line [1]. In addition to this forward model, a recursive multilayer perceptrons (RMLP) model was proposed by Sanchez et al. =-=[4]-=-. Subsequently, Kim et al. [5] proposed the development of switching multiple linear models combined with a nonlinear network to increase prediction performance in food reaching. Yet another methodolo... |

27 |
White-noise analysis of a neuron chain: an application of the Wiener theory
- Marmarelis, Naka
- 1972
(Show Context)
Citation Context ...e over time. The accuracy of the tuning function estimation can directly affect the pre-knowledge of the Bayesian approach and, therefore, the results of the kinematic estimation. Marmarelis and Naka =-=[18]-=- developed a statistical method, called white noise analysis, to model the neural responses with stochastic stimuli. This method was improved by Simoncelli, Paninski and colleagues [19] . By parametri... |

20 | From cortical neural spike trains to behavior: Modeling and analysis. Unpublished doctoral dissertation
- Sanchez
- 2004
(Show Context)
Citation Context ...a 16×8 matrix. Each recording site occupied a total area of 15.7 k k k k mm 2 (5.6×2.8 mm) and was capable of recording up to four single cells from each microwire for a total of 512 neurons (4 ×128) =-=[14]-=-. After the surgical procedure, a multi-channel acquisition processor (MAP, Plexon, Dallas, TX) cluster was used in the experiments to record the neuronal action potentials simultaneously. Analog wave... |

17 |
Divide-and-Conquer Approach for Brain Machine Interfaces:
- Kim, Sanchez, et al.
- 2003
(Show Context)
Citation Context ...binned spike rates embedded by a 10-tap delay line [1]. In addition to this forward model, a recursive multilayer perceptrons (RMLP) model was proposed by Sanchez et al. [4]. Subsequently, Kim et al. =-=[5]-=- proposed the development of switching multiple linear models combined with a nonlinear network to increase prediction performance in food reaching. Yet another methodology can be derived probabilisti... |

8 |
On Estimation of a Probability Function and Mode
- Parzen
- 1962
(Show Context)
Citation Context ...linear relation f(·) is assumed known. Random state samples are generated using Monte Carlo simulations [4] in the neighborhood of the previous state according to (6). Then, weighted Parzen windowing =-=[5]-=- was used with a Gaussian kernel to estimate the posterior density. Due to the linearity of the integral in the Chapman-Kolmogorov equation and the weighted sum of Gaussians centered at the samples we... |

6 |
y P. Fearnhead, «An Improved Particle Filter for Non-linear Problems
- Carpenter, Clifford
- 2004
(Show Context)
Citation Context ... need is the estimation of the state from the conditional intensity function (1), since the nonlinear relation f (⋅) is assumed known. Random state samples are generated using Monte Carlo simulations =-=[11]-=- in the neighborhood of the previous state according to x k = Fk xk −1 + ηk (3) Then, weighted Parzen windowing [12] was used with a Gaussian kernel to estimate the posterior density. The process is r... |

2 |
Statistical approaches to place field estimation and neuronal population decoding
- Brown, Frank, et al.
- 1996
(Show Context)
Citation Context ... state by evaluating the posterior density of the state given the discrete observation [2]. This framework provides a nonlinear time-series probabilistic model between the state and the spiking event =-=[3]-=-. Given an observation interval (0,T], the number N(t) of events (e.g. spikes) can be modeled as a stochastic inho-mogeneous Poisson process characterized by its conditional intensity function λ(t|x(... |

1 |
A Monte Carlo Sequential Estimation for
- Paiva, Principe
- 2006
(Show Context)
Citation Context ...n distributed. Recently, we proposed a Monte Carlo sequential estimation algorithm on point process as a probabilistic approach to infer the kinematic information directly from the neural spike train =-=[10]-=-. The posterior density of the kinematic stimulus, given the neural spike train was estimated at each time step non-parametrically. The preliminary simulations showed a better velocity reconstruction ... |

1 |
Information theoretical tuning depth and time delay estimators of motor cortex neuron
- Wang, Sanchez, et al.
- 2007
(Show Context)
Citation Context ...r, which contains all the relevant information of position, velocity and r r r r r r T acceleration [ p x v x a x p y v y a y ] t , with the causal time delay estimated for the motor cortical neurons =-=[20]-=- . D. Monte Carlo Sequential Estimation Framework for BMI Decoding We have thus far presented background on the difference between simulation and BMI real data, and have elaborated on the Monte Carlo ... |