nips nips2010 nips2010-167 knowledge-graph by maker-knowledge-mining

167 nips-2010-Mixture of time-warped trajectory models for movement decoding

Source: pdf

Author: Elaine Corbett, Eric Perreault, Konrad Koerding

Abstract: Applications of Brain-Machine-Interfaces typically estimate user intent based on biological signals that are under voluntary control. For example, we might want to estimate how a patient with a paralyzed arm wants to move based on residual muscle activity. To solve such problems it is necessary to integrate obtained information over time. To do so, state of the art approaches typically use a probabilistic model of how the state, e.g. position and velocity of the arm, evolves over time – a so-called trajectory model. We wanted to further develop this approach using two intuitive insights: (1) At any given point of time there may be a small set of likely movement targets, potentially identified by the location of objects in the workspace or by gaze information from the user. (2) The user may want to produce movements at varying speeds. We thus use a generative model with a trajectory model incorporating these insights. Approximate inference on that generative model is implemented using a mixture of extended Kalman filters. We find that the resulting algorithm allows us to decode arm movements dramatically better than when we use a trajectory model with linear dynamics. 1 In trod u cti on When patients have lost a limb or the ability to communicate with the outside world, brain machine interfaces (BMIs) are often used to enable robotic prostheses or restore communication. To achieve this, the user's intended state of the device must be decoded from biological signals. In the context of Bayesian statistics, two aspects are important for the design of an estimator of a temporally evolving state: the observation model, which describes how measured variables relate to the system’s state and the trajectory model which describes how the state changes over time in a probabilistic manner. Following this logic many recent BMI applications have relied on Bayesian estimation for a wide range of problems including the decoding of intended human [1] and animal [2] movements. In the context of BMIs, Bayesian approaches offer a principled way of formalizing the uncertainty about signals and thus often result in improvements over other signal processing techniques [1]-[3]. Most work on state estimation in dynamical systems has assumed linear dynamics and Gaussian noise. Under these circumstances, efficient algorithms result from belief propagation. The most frequent application uses the Kalman filter (KF), which recursively combines noisy state observations with the probabilistic evolution of state defined by the trajectory model to estimate the marginal distribution over states [4]. Such approaches have been used widely for applications including upper [1] and lower [5] extremity prosthetic 1 devices, functional electric stimulation [6] and human computer interactions [7]. As these algorithms are so commonly used, it seems promising to develop extensions to nonlinear trajectory models that may better describe the probabilistic distribution of movements in everyday life. One salient departure from the standard assumptions is that people tend to produce both slow and fast movements, depending on the situation. Models with linear dynamics only allow such deviation through the noise term, which makes these models poor at describing the natural variation of movement speeds during real world tasks. Explicitly incorporating movement speed into the trajectory model should lead to better movement estimates. Knowledge of the target position should also strongly affect trajectory models. After all , we tend to accelerate our arm early during movement and slow down later on. Target information can be linearly incorporated into the trajectory model, and this has greatly improved predictions [8]-[12]. Alternatively, if there are a small number of potential targets then a mixture of trajectory models approach [13] can be used. Here we are interested in the case where available data provide a prior over potential t argets but where movement targets may be anywhere. We want to incorporate target uncertainty and allow generalization to novel targets. Prior information about potential targets could come from a number of sources but would generally be noisy. For example, activity in the dorsal premotor cortex provides information about intended target location prior to movement and may be used where such recordings are available [14]. Target information may also be found noninvasively by tracking eye movements. However, such data will generally provide non-zero priors for a number of possible target locations as the subject saccades over the scene. While subjects almost always look at a target before reaching for it [15], there may be a delay of up to a second between looking at the target and the reach – a time interval over which up to 3 saccades are typically made. Each of these fixations could be the target. Hence, a probabilistic distribution of targets is appropriate when using either neural recordings or eye tracking to estimate potential reach targets Here we present an algorithm that uses a mixture of extended Kalman Filters (EKFs) to combine our insights related to the variation of movement speed and the availability of probabilistic target knowledge. Each of the mixture component s allows the speed of the movement to vary continuously over time. We tested how well we could use EMGs and eye movements to decode hand position of humans performing a three -dimensional large workspace reaching task. We find that using a trajectory model that allows for probabilistic target information and variation of speed leads to dramatic improvements in decoding quality. 2 Gen e ral Decod i n g S etti n g We wanted to test how well different decoding algorithms can decode human movement, over a wide range of dynamics. While many recent studies have looked at more restrictive, two-dimensional movements, a system to restore arm function should produce a wide range of 3D trajectories. We recorded arm kinematics and EMGs of healthy subjects during unconstrained 3D reaches to targets over a large workspace. Two healthy subjects were asked to reach at slow, normal and fast speeds, as they would in everyday life. Subjects were seated as they reached towards 16 LEDs in blocks of 150s, which were located on two planes positioned such that all targets were just reachable (Fig 1A). The target LED was lit for one second prior to an auditory go cue, at which time the subject would reach to the target at the appropriate speed. Slow, normal and fast reaches were allotted 3 s, 1.5s and 1s respectively; however, subjects determined the speed. An approximate total of 450 reaches were performed per subject. The subjects provided informed consent, and the protocol was approved by the Northwestern University Institutional Review Board. EMG signals were measured from the pectoralis major, and the three deltoid muscles of the shoulder. This represents a small subset of the muscles involved in reaching, and approximates those muscles retaining some voluntary control following mid-level cervical spinal cord injuries. 2 The EMG signals were band-pass filtered between 10 and 1,000 Hz, and subsequently anti aliased filtered. Hand, wrist, shoulder and head positions were tracked using an Optotrak motion analysis system. We simultaneously recorded eye movements with an ASL EYETRAC-6 head mounted eye tracker. Approximately 25% of the reaches were assigned to the test set, and the rest were used for training. Reaches for which either the motion capture data was incomplete, or there was visible motion artifact on the EMG were removed. As the state we used hand positions and joint angles (3 shoulder, 2 elbow, position, velocity and acceleration, 24 dimensions). Joint angles were calculated from the shoulder and wrist marker data using digitized bony landmarks which defined a coordinate system for the upper limb as detailed by Wu et al. [16]. As the motion data were sampled at 60Hz, the mean absolute value o f the EMG in the corresponding 16.7ms windows was used as an observation of the state at each time-step. Algorithm accuracy was quantified by normalizing the root -mean-squared error by the straight line distance between the first and final position of the endpoint for each reach. We compared the algorithms statistically using repeated measures ANOVAs with Tukey post -hoc tests, treating reach and subject as random effects. In the rest of the paper we will ask how well these reaching movements can be decoded from EMG and eye-tracking data. Figure 1: A Experimental setup and B sample kinematics and processed EMGs for one reach 3 Kal man Fi l ters w i th Target i n f ormati on All models that we consider in this paper assume linear observations with Gaussian noise: (1) where x is the state, y is the observation and v is the measurement noise with p(v) ~ N(0,R), and R is the observation covariance matrix. The model fitted the measured EMGs with an average r2 of 0.55. This highlights the need to integrate information over time. The standard approach also assumes linear dynamics and Gaussian process noise: (2) where, x t represents the hand and joint angle positions, w is the process noise with p(w) ~ N(0,Q), and Q is the state covariance matrix. The Kalman filter does optimal inference for this generative model. This model can effectively capture the dynamics of stereotypical reaches to a single target by appropriately tuning its parameters. However, when used to describe reaches to multiple targets, the model cannot describe target dependent aspects of reaching but boils down to a random drift model. Fast velocities are underestimated as they are unlikely under the trajectory model and there is excessive drift close to the target (Fig. 2A). 3 In many decoding applications we may know the subject’s target. A range of recent studies have addressed the issue of incorporating this information into the trajectory model [8, 13], and we might assume the effect of the target on the dynamics to be linear. This naturally suggests adding the target to the state space, which works well in practice [9, 12]. By appending the target to the state vector (KFT), the simple linear format of the KF may be retained: (3) where xTt is the vector of target positions, with dimensionality less than or equal to that of xt. This trajectory model thus allows describing both the rapid acceleration that characterizes the beginning of a reach and the stabilization towards its end. We compared the accuracy of the KF and the KFT to the Single Target Model (STM), a KF trained only on reaches to the target being tested (Fig. 2). The STM represents the best possible prediction that could be obtained with a Kalman filter. Assuming the target is perfectly known, we implemented the KFT by correctly initializing the target state xT at the beginning of the reach. We will relax this assumption below. The initial hand and joint angle positions were also assumed to be known. Figure 2: A Sample reach and predictions and B average accuracies with standard errors for KFT, KF and MTM. Consistent with the recent literature, both methods that incorporated target information produced higher prediction accuracy than the standard KF (both p<0.0001). Interestingly, there was no significant difference between the KFT and the STM (p=0.9). It seems that when we have knowledge of the target, we do not lose much by training a single model over the whole workspace rather than modeling the targets individually. This is encouraging, as we desire a BMI system that can generalize to any target within the workspace, not just specifically to those that are available in the training data. Clearly, adding the target to the state space allows the dynamics of typical movements to be modeled effectively, resulting in dramatic increases in decoding performance. 4 Ti me Warp i n g 4.1 I m p l e m e n t i n g a t i m e - w a r p e d t r a j e c t o r y mo d e l While the KFT above can capture the general reach trajectory profile, it does not allow for natural variability in the speed of movements. Depending on our task objectives, which would not directly be observed by a BMI, we might lazily reach toward a target or move a t maximal speed. We aim to change the trajectory model to explicitly incorporate a warping factor by which the average movement speed is scaled, allowing for such variability. As the movement speed will be positive in all practical cases, we model the logarithm of this factor, 4 and append it to the state vector: (4) We create a time-warped trajectory model by noting that if the average rate of a trajectory is to be scaled by a factor S, the position at time t will equal that of the original trajectory at time St. Differentiating, the velocity will be multiplied by S, and the acceleration by S 2. For simplicity, the trajectory noise is assumed to be additive and Gaussian, and the model is assumed to be stationary: (5) where Ip is the p-dimensional identity matrix and is a p p matrix of zeros. Only the terms used to predict the acceleration states need to be estimated to build the state transition matrix, and they are scaled as a nonlinear function of xs. After adding the variable movement speed to the state space the system is no longer linear. Therefore we need a different solution strategy. Instead of the typical KFT we use the Extended Kalman Filter (EKFT) to implement a nonlinear trajectory model by linearizing the dynamics around the best estimate at each time-step [17]. With this approach we add only small computational overhead to the KFT recursions. 4.2 Tr a i n i n g t h e t i m e w a r p i n g mo d e l The filter parameters were trained using a variant of the Expectation Maximization (EM) algorithm [18]. For extended Kalman filter learning the initialization for the variables may matter. S was initialized with the ground truth average reach speeds for each movement relative to the average speed across all movements. The state transition parameters were estimated using nonlinear least squares regression, while C, Q and R were estimated linearly for the new system, using the maximum likelihood solution [18] (M-step). For the E-step we used a standard extended Kalman smoother. We thus found the expected values for t he states given the current filter parameters. For this computation, and later when testing the algorithm, xs was initialized to its average value across all reaches while the remaining states were initialized to their true values. The smoothed estimate fo r xs was then used, along with the true values for the other states, to re-estimate the filter parameters in the M-step as before. We alternated between the E and M steps until the log likelihood converged (which it did in all cases). Following the training procedure, the diagonal of the state covariance matrix Q corresponding to xs was set to the variance of the smoothed xs over all reaches, according to how much this state should be allowed to change during prediction. This allowed the estimate of xs to develop over the course of the reach due to the evidence provided by the observations, better capturing the dynamics of reaches at different speeds. 4.3 P e r f o r ma n c e o f t h e t i m e - w a r p e d E K F T Incorporating time warping explicitly into the trajectory model pro duced a noticeable increase in decoding performance over the KFT. As the speed state xs is estimated throughout the course of the reach, based on the evidence provided by the observations, the trajectory model has the flexibility to follow the dynamics of the reach more accurately (Fig. 3). While at the normal self-selected speed the difference between the algorithms is small, for the slow and fast speeds, where the dynamics deviate from average, there i s a clear advantage to the time warping model. 5 Figure 3: Hand positions and predictions of the KFT and EKFT for sample reaches at A slow, B normal and C fast speeds. Note the different time scales between reaches. The models were first trained using data from all speeds (Fig. 4A). The EKFT was 1.8% more accurate on average (p<0.01), and the effect was significant at the slow (1.9%, p<0.05) and the fast (2.8%, p<0.01), but not at the normal (p=0.3) speed. We also trained the models from data using only reaches at the self-selected normal speed, as we wanted to see if there was enough variation to effectively train the EKFT (Fig. 4B). Interestingly, the performance of the EKFT was reduced by only 0.6%, and the KFT by 1.1%. The difference in performance between the EKFT and KFT was even more pronounced on aver age (2.3%, p<0.001), and for the slow and fast speeds (3.6 and 4.1%, both p< 0.0001). At the normal speed, the algorithms again were not statistically different (p=0.6). This result demonstrates that the EKFT is a practical option for a real BMI system, as it is not necessary to greatly vary the speeds while collecting training data for the model to be effective over a wide range of intended speeds. Explicitly incorporating speed information into the trajectory model helps decoding, by modeling the natural variation in volitional speed. Figure 4: Mean and standard error of EKFT and KFT accuracy at the different subjectselected speeds. Models were trained on reaches at A all speeds and B just normal speed reaches. Asterisks indicate statistically significant differences between the algorithms. 5 Mi xtu res of Target s So far, we have assumed that the targets of our reaches are perfectly known. In a real-world system, there will be uncertainty about the intended target of the reach. However, in typical applications there are a small number of possible objectives. Here we address this situation. Drawing on the recent literature, we use a mixture model to consider each of the possible targets [11, 13]. We condition the posterior probability for the state on the N possible targets, T: (6) 6 Using Bayes' Rule, this equation becomes: (7) As we are dealing with a mixture model, we perform the Kalman filter recursion for each possible target, xT, and our solution is a weighted sum of the outputs. The weights are proportional to the prior for that target, , and the likelihood of the model given that target . is independent of the target and does not need to be calculated. We tested mixtures of both algorithms, the mKFT and mEKFT, with real uncert ain priors obtained from eye-tracking in the one-second period preceding movement. As the targets were situated on two planes, the three-dimensional location of the eye gaze was found by projecting its direction onto those planes. The first, middle and last eye samples were selected, and all other samples were assigned to a group according to which of the three was closest. The mean and variance of these three groups were used to initialize three Kalman filters in the mixture model. The priors of the three groups were assigned proportional to the number of samples in them. If the subject looks at multiple positions prior to reaching, this method ensures with a high probability that the correct target was accounted for in one of the filters in the mixture. We also compared the MTM approach of Yu et al. [13], where a different KF model was generated for each target, and a mixture is performed over these models. This approach explicitly captures the dynamics of stereotypical reaches to specific targets. Given perfect target information, it would reduce to the STM described above. Priors for the MTM were found by assigning each valid eye sample to its closest two targets, and weighting the models proportional to the number of samples assigned to the corresponding target, divided by its distance from the mean of those samples. We tried other ways of assigning priors and the one presented gave the best results. We calculated the reduction in decoding quality when instead of perfect priors we provide eye-movement based noisy priors (Fig. 5). The accuracies of the mEKFT, the mKFT and the MTM were only degraded by 0.8, 1.9 and 2.1% respectively, compared to the perfect prior situation. The mEKFT was still close to 10% better than the KF. The mixture model framework is effective in accounting for uncertain priors. Figure 5: Mean and standard errors of accuracy for algorithms with perfect priors, and uncertain priors with full and partial training set. The asterisk indicates a statistically significant effects between the two training types, where real priors are used. Here, only reaches at normal speed were used to train the models, as this is a more realistic training set for a BMI application. This accounts for the degraded performance of the MTM with perfect priors relative to the STM from above (Fig. 2). With even more stereotyped training data for each target, the MTM doesn't generalize as well to new speeds. 7 We also wanted to know if the algorithms could generalize to new targets. In a real application, the available training data will generally not span the entire useable worksp ace. We compared the algorithms where reaches to all targets except the one being tested had been used to train the models. The performance of the MTM was significantly de graded unsurprisingly, as it was designed for reaches to a set of known targets. Performance of the mKFT and mEKFT degraded by about 1%, but not significantly (both p>0.7), demonstrating that the continuous approach to target information is preferable when the target could be anywhere in space, not just at locations for which training data is available. 6 Di scu ssi on and concl u si on s The goal of this work was to design a trajectory model that would improve decoding for BMIs with an application to reaching. We incorporated two features that prominently influence the dynamics of natural reach: the movement speed and the target location. Our approach is appropriate where uncertain target information is available. The model generalizes well to new regions of the workspace for which there is no training data, and across a broad range of reaching dynamics to widely spaced targets in three dimensions. The advantages over linear models in decoding precision we report here could be equally obtained using mixtures over many targets and speeds. While mixture models [11, 13] could allow for slow versus fast movements and any number of potential targets, this strategy will generally require many mixture components. Such an approach would require a lot more training data, as we have shown that it does not generalize well. It would also be run-time intensive which is problematic for prosthetic devices that rely on low power controllers. In contrast, the algorithm introduced here only takes a small amount of additional run-time in comparison to the standard KF approach. The EKF is only marginally slower than the standard KF and the algorithm will not generally need to consider more than 3 mixture components assuming the subject fixates the target within the second pre ceding the reach. In this paper we assumed that subjects always would fixate a reach target – along with other non-targets. While this is close to the way humans usually coordinate eyes and reaches [15], there might be cases where people do not fixate a reach target. Our approach could be easily extended to deal with such situations by adding a dummy mixture component that all ows the description of movements to any target. As an alternative to mixture approaches, a system can explicitly estimate the target position in the state vector [9]. This approach, however, would not straightforwardly allow for the rich target information available; we look at the target but also at other locations, strongly suggesting mixture distributions. A combination of the two approaches could further improve decoding quality. We could both estimate speed and target position for the EKFT in a continuous manner while retaining the mixture over target priors. We believe that the issues that we have addressed here are almost universal. Virtually all types of movements are executed at varying speed. A probabilistic distribution for a small number of action candidates may also be expected in most BMI applications – after all there are usually only a small number of actions that make sense in a given environment. While this work is presented in the context of decoding human reaching, it may be applied to a wide range of BMI applications including lower limb prosthetic devices and human computer interactions, as well as different signal sources such as electrode grid recordings and electroencephalograms. The increased user control in conveying their intended movements would significantly improve the functionality of a neuroprosthetic device. A c k n o w l e d g e me n t s T h e a u t h o r s t h a n k T. H a s w e l l , E . K r e p k o v i c h , a n d V. Ravichandran for assistance with experiments. This work was funded by the NSF Program in Cyber-Physical Systems. R e f e re n c e s [1] L.R. Hochberg, M.D. Serruya, G.M. Friehs, J.A. Mukand, M. Saleh, A.H. Caplan, A. Branner, D. 8 [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] Chen, R.D. Penn, and J.P. Donoghue, “Neuronal ensemble control of prosthetic devices by a human with tetraplegia,” Nature, vol. 442, 2006, pp. 164–171. W. Wu, Y. Gao, E. Bienenstock, J.P. Donoghue, and M.J. Black, “Bayesian population decoding of motor cortical activity using a Kalman filter,” Neural Computation, vol. 18, 2006, pp. 80–118. W. Wu, M.J. Black, Y. Gao, E. Bienenstock, M. Serruya, A. Shaikhouni, and J.P. Donoghue, “Neural decoding of cursor motion using a Kalman filter,” Advances in Neural Information Processing Systems 15: Proceedings of the 2002 Conference, 2003, p. 133. R.E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of basic Engineering, vol. 82, 1960, pp. 35–45. G.G. Scandaroli, G.A. Borges, J.Y. Ishihara, M.H. Terra, A.F.D. Rocha, and F.A.D.O. Nascimento, “Estimation of foot orientation with respect to ground for an above knee robotic prosthesis,” Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems, St. Louis, MO, USA: IEEE Press, 2009, pp. 1112-1117. I. Cikajlo, Z. Matjačić, and T. Bajd, “Efficient FES triggering applying Kalman filter during sensory supported treadmill walking,” Journal of Medical Engineering & Technology, vol. 32, 2008, pp. 133144. S. Kim, J.D. Simeral, L.R. Hochberg, J.P. Donoghue, and M.J. Black, “Neural control of computer cursor velocity by decoding motor cortical spiking activity in humans with tetraplegia,” Journal of Neural Engineering, vol. 5, 2008, pp. 455-476. L. Srinivasan, U.T. Eden, A.S. Willsky, and E.N. Brown, “A state-space analysis for reconstruction of goal-directed movements using neural signals,” Neural computation, vol. 18, 2006, pp. 2465–2494. G.H. Mulliken, S. Musallam, and R.A. Andersen, “Decoding trajectories from posterior parietal cortex ensembles,” Journal of Neuroscience, vol. 28, 2008, p. 12913. W. Wu, J.E. Kulkarni, N.G. Hatsopoulos, and L. Paninski, “Neural Decoding of Hand Motion Using a Linear State-Space Model With Hidden States,” IEEE Transactions on neural systems and rehabilitation engineering, vol. 17, 2009, p. 1. J.E. Kulkarni and L. Paninski, “State-space decoding of goal-directed movements,” IEEE Signal Processing Magazine, vol. 25, 2008, p. 78. C. Kemere and T. Meng, “Optimal estimation of feed-forward-controlled linear systems,” IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005. Proceedings.(ICASSP'05), 2005. B.M. Yu, C. Kemere, G. Santhanam, A. Afshar, S.I. Ryu, T.H. Meng, M. Sahani, and K.V. Shenoy, “Mixture of trajectory models for neural decoding of goal-directed movements,” Journal of neurophysiology, vol. 97, 2007, p. 3763. N. Hatsopoulos, J. Joshi, and J.G. O'Leary, “Decoding continuous and discrete motor behaviors using motor and premotor cortical ensembles,” Journal of neurophysiology, vol. 92, 2004, p. 1165. R.S. Johansson, G. Westling, A. Backstrom, and J.R. Flanagan, “Eye-hand coordination in object manipulation,” Journal of Neuroscience, vol. 21, 2001, p. 6917. G. Wu, F.C. van der Helm, H.E.J. Veeger, M. Makhsous, P. Van Roy, C. Anglin, J. Nagels, A.R. Karduna, and K. McQuade, “ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion–Part II: shoulder, elbow, wrist and hand,” Journal of biomechanics, vol. 38, 2005, pp. 981–992. D. Simon, Optimal state estimation: Kalman, H [infinity] and nonlinear approaches, John Wiley and Sons, 2006. Z. Ghahramani and G.E. Hinton, “Parameter estimation for linear dynamical systems,” University of Toronto technical report CRG-TR-96-2, vol. 6, 1996. 9

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Mixture of time -warped trajectory models for movement decoding Elaine A. [sent-1, score-0.656]

2 position and velocity of the arm, evolves over time – a so-called trajectory model. [sent-11, score-0.35]

3 We wanted to further develop this approach using two intuitive insights: (1) At any given point of time there may be a small set of likely movement targets, potentially identified by the location of objects in the workspace or by gaze information from the user. [sent-12, score-0.377]

4 (2) The user may want to produce movements at varying speeds. [sent-13, score-0.232]

5 We thus use a generative model with a trajectory model incorporating these insights. [sent-14, score-0.291]

6 We find that the resulting algorithm allows us to decode arm movements dramatically better than when we use a trajectory model with linear dynamics. [sent-16, score-0.569]

7 Following this logic many recent BMI applications have relied on Bayesian estimation for a wide range of problems including the decoding of intended human [1] and animal [2] movements. [sent-20, score-0.355]

8 The most frequent application uses the Kalman filter (KF), which recursively combines noisy state observations with the probabilistic evolution of state defined by the trajectory model to estimate the marginal distribution over states [4]. [sent-24, score-0.63]

9 As these algorithms are so commonly used, it seems promising to develop extensions to nonlinear trajectory models that may better describe the probabilistic distribution of movements in everyday life. [sent-26, score-0.512]

10 Models with linear dynamics only allow such deviation through the noise term, which makes these models poor at describing the natural variation of movement speeds during real world tasks. [sent-28, score-0.405]

11 Explicitly incorporating movement speed into the trajectory model should lead to better movement estimates. [sent-29, score-0.742]

12 Knowledge of the target position should also strongly affect trajectory models. [sent-30, score-0.575]

13 After all , we tend to accelerate our arm early during movement and slow down later on. [sent-31, score-0.305]

14 Target information can be linearly incorporated into the trajectory model, and this has greatly improved predictions [8]-[12]. [sent-32, score-0.254]

15 Alternatively, if there are a small number of potential targets then a mixture of trajectory models approach [13] can be used. [sent-33, score-0.569]

16 Here we are interested in the case where available data provide a prior over potential t argets but where movement targets may be anywhere. [sent-34, score-0.375]

17 We want to incorporate target uncertainty and allow generalization to novel targets. [sent-35, score-0.274]

18 For example, activity in the dorsal premotor cortex provides information about intended target location prior to movement and may be used where such recordings are available [14]. [sent-37, score-0.585]

19 However, such data will generally provide non-zero priors for a number of possible target locations as the subject saccades over the scene. [sent-39, score-0.379]

20 While subjects almost always look at a target before reaching for it [15], there may be a delay of up to a second between looking at the target and the reach – a time interval over which up to 3 saccades are typically made. [sent-40, score-0.874]

21 Each of the mixture component s allows the speed of the movement to vary continuously over time. [sent-43, score-0.391]

22 We tested how well we could use EMGs and eye movements to decode hand position of humans performing a three -dimensional large workspace reaching task. [sent-44, score-0.627]

23 We find that using a trajectory model that allows for probabilistic target information and variation of speed leads to dramatic improvements in decoding quality. [sent-45, score-0.935]

24 2 Gen e ral Decod i n g S etti n g We wanted to test how well different decoding algorithms can decode human movement, over a wide range of dynamics. [sent-46, score-0.395]

25 We recorded arm kinematics and EMGs of healthy subjects during unconstrained 3D reaches to targets over a large workspace. [sent-48, score-0.591]

26 Two healthy subjects were asked to reach at slow, normal and fast speeds, as they would in everyday life. [sent-49, score-0.337]

27 Subjects were seated as they reached towards 16 LEDs in blocks of 150s, which were located on two planes positioned such that all targets were just reachable (Fig 1A). [sent-50, score-0.237]

28 The target LED was lit for one second prior to an auditory go cue, at which time the subject would reach to the target at the appropriate speed. [sent-51, score-0.675]

29 Slow, normal and fast reaches were allotted 3 s, 1. [sent-52, score-0.255]

30 We simultaneously recorded eye movements with an ASL EYETRAC-6 head mounted eye tracker. [sent-60, score-0.411]

31 Joint angles were calculated from the shoulder and wrist marker data using digitized bony landmarks which defined a coordinate system for the upper limb as detailed by Wu et al. [sent-64, score-0.255]

32 In the rest of the paper we will ask how well these reaching movements can be decoded from EMG and eye-tracking data. [sent-70, score-0.319]

33 This model can effectively capture the dynamics of stereotypical reaches to a single target by appropriately tuning its parameters. [sent-77, score-0.574]

34 However, when used to describe reaches to multiple targets, the model cannot describe target dependent aspects of reaching but boils down to a random drift model. [sent-78, score-0.541]

35 Fast velocities are underestimated as they are unlikely under the trajectory model and there is excessive drift close to the target (Fig. [sent-79, score-0.528]

36 3 In many decoding applications we may know the subject’s target. [sent-81, score-0.232]

37 A range of recent studies have addressed the issue of incorporating this information into the trajectory model [8, 13], and we might assume the effect of the target on the dynamics to be linear. [sent-82, score-0.643]

38 This naturally suggests adding the target to the state space, which works well in practice [9, 12]. [sent-83, score-0.355]

39 By appending the target to the state vector (KFT), the simple linear format of the KF may be retained: (3) where xTt is the vector of target positions, with dimensionality less than or equal to that of xt. [sent-84, score-0.629]

40 This trajectory model thus allows describing both the rapid acceleration that characterizes the beginning of a reach and the stabilization towards its end. [sent-85, score-0.434]

41 We compared the accuracy of the KF and the KFT to the Single Target Model (STM), a KF trained only on reaches to the target being tested (Fig. [sent-86, score-0.451]

42 Assuming the target is perfectly known, we implemented the KFT by correctly initializing the target state xT at the beginning of the reach. [sent-89, score-0.629]

43 Consistent with the recent literature, both methods that incorporated target information produced higher prediction accuracy than the standard KF (both p<0. [sent-93, score-0.274]

44 It seems that when we have knowledge of the target, we do not lose much by training a single model over the whole workspace rather than modeling the targets individually. [sent-97, score-0.317]

45 This is encouraging, as we desire a BMI system that can generalize to any target within the workspace, not just specifically to those that are available in the training data. [sent-98, score-0.306]

46 Clearly, adding the target to the state space allows the dynamics of typical movements to be modeled effectively, resulting in dramatic increases in decoding performance. [sent-99, score-0.862]

47 1 I m p l e m e n t i n g a t i m e - w a r p e d t r a j e c t o r y mo d e l While the KFT above can capture the general reach trajectory profile, it does not allow for natural variability in the speed of movements. [sent-101, score-0.546]

48 Depending on our task objectives, which would not directly be observed by a BMI, we might lazily reach toward a target or move a t maximal speed. [sent-102, score-0.401]

49 We aim to change the trajectory model to explicitly incorporate a warping factor by which the average movement speed is scaled, allowing for such variability. [sent-103, score-0.578]

50 For simplicity, the trajectory noise is assumed to be additive and Gaussian, and the model is assumed to be stationary: (5) where Ip is the p-dimensional identity matrix and is a p p matrix of zeros. [sent-106, score-0.254]

51 After adding the variable movement speed to the state space the system is no longer linear. [sent-108, score-0.394]

52 Instead of the typical KFT we use the Extended Kalman Filter (EKFT) to implement a nonlinear trajectory model by linearizing the dynamics around the best estimate at each time-step [17]. [sent-110, score-0.332]

53 S was initialized with the ground truth average reach speeds for each movement relative to the average speed across all movements. [sent-115, score-0.531]

54 For this computation, and later when testing the algorithm, xs was initialized to its average value across all reaches while the remaining states were initialized to their true values. [sent-119, score-0.247]

55 The smoothed estimate fo r xs was then used, along with the true values for the other states, to re-estimate the filter parameters in the M-step as before. [sent-120, score-0.222]

56 Following the training procedure, the diagonal of the state covariance matrix Q corresponding to xs was set to the variance of the smoothed xs over all reaches, according to how much this state should be allowed to change during prediction. [sent-122, score-0.302]

57 This allowed the estimate of xs to develop over the course of the reach due to the evidence provided by the observations, better capturing the dynamics of reaches at different speeds. [sent-123, score-0.452]

58 3 P e r f o r ma n c e o f t h e t i m e - w a r p e d E K F T Incorporating time warping explicitly into the trajectory model pro duced a noticeable increase in decoding performance over the KFT. [sent-125, score-0.529]

59 As the speed state xs is estimated throughout the course of the reach, based on the evidence provided by the observations, the trajectory model has the flexibility to follow the dynamics of the reach more accurately (Fig. [sent-126, score-0.721]

60 While at the normal self-selected speed the difference between the algorithms is small, for the slow and fast speeds, where the dynamics deviate from average, there i s a clear advantage to the time warping model. [sent-128, score-0.373]

61 5 Figure 3: Hand positions and predictions of the KFT and EKFT for sample reaches at A slow, B normal and C fast speeds. [sent-129, score-0.316]

62 We also trained the models from data using only reaches at the self-selected normal speed, as we wanted to see if there was enough variation to effectively train the EKFT (Fig. [sent-141, score-0.317]

63 Explicitly incorporating speed information into the trajectory model helps decoding, by modeling the natural variation in volitional speed. [sent-155, score-0.436]

64 Models were trained on reaches at A all speeds and B just normal speed reaches. [sent-157, score-0.458]

65 5 Mi xtu res of Target s So far, we have assumed that the targets of our reaches are perfectly known. [sent-159, score-0.382]

66 In a real-world system, there will be uncertainty about the intended target of the reach. [sent-160, score-0.339]

67 Drawing on the recent literature, we use a mixture model to consider each of the possible targets [11, 13]. [sent-163, score-0.315]

68 We condition the posterior probability for the state on the N possible targets, T: (6) 6 Using Bayes' Rule, this equation becomes: (7) As we are dealing with a mixture model, we perform the Kalman filter recursion for each possible target, xT, and our solution is a weighted sum of the outputs. [sent-164, score-0.343]

69 The weights are proportional to the prior for that target, , and the likelihood of the model given that target . [sent-165, score-0.274]

70 is independent of the target and does not need to be calculated. [sent-166, score-0.274]

71 As the targets were situated on two planes, the three-dimensional location of the eye gaze was found by projecting its direction onto those planes. [sent-168, score-0.348]

72 If the subject looks at multiple positions prior to reaching, this method ensures with a high probability that the correct target was accounted for in one of the filters in the mixture. [sent-172, score-0.379]

73 This approach explicitly captures the dynamics of stereotypical reaches to specific targets. [sent-175, score-0.3]

74 Given perfect target information, it would reduce to the STM described above. [sent-176, score-0.318]

75 We calculated the reduction in decoding quality when instead of perfect priors we provide eye-movement based noisy priors (Fig. [sent-179, score-0.414]

76 Here, only reaches at normal speed were used to train the models, as this is a more realistic training set for a BMI application. [sent-189, score-0.335]

77 We compared the algorithms where reaches to all targets except the one being tested had been used to train the models. [sent-195, score-0.382]

78 The performance of the MTM was significantly de graded unsurprisingly, as it was designed for reaches to a set of known targets. [sent-196, score-0.221]

79 7), demonstrating that the continuous approach to target information is preferable when the target could be anywhere in space, not just at locations for which training data is available. [sent-198, score-0.548]

80 6 Di scu ssi on and concl u si on s The goal of this work was to design a trajectory model that would improve decoding for BMIs with an application to reaching. [sent-199, score-0.486]

81 We incorporated two features that prominently influence the dynamics of natural reach: the movement speed and the target location. [sent-200, score-0.633]

82 Our approach is appropriate where uncertain target information is available. [sent-201, score-0.308]

83 The model generalizes well to new regions of the workspace for which there is no training data, and across a broad range of reaching dynamics to widely spaced targets in three dimensions. [sent-202, score-0.485]

84 The advantages over linear models in decoding precision we report here could be equally obtained using mixtures over many targets and speeds. [sent-203, score-0.437]

85 While mixture models [11, 13] could allow for slow versus fast movements and any number of potential targets, this strategy will generally require many mixture components. [sent-204, score-0.511]

86 The EKF is only marginally slower than the standard KF and the algorithm will not generally need to consider more than 3 mixture components assuming the subject fixates the target within the second pre ceding the reach. [sent-208, score-0.384]

87 In this paper we assumed that subjects always would fixate a reach target – along with other non-targets. [sent-209, score-0.519]

88 While this is close to the way humans usually coordinate eyes and reaches [15], there might be cases where people do not fixate a reach target. [sent-210, score-0.377]

89 Our approach could be easily extended to deal with such situations by adding a dummy mixture component that all ows the description of movements to any target. [sent-211, score-0.307]

90 As an alternative to mixture approaches, a system can explicitly estimate the target position in the state vector [9]. [sent-212, score-0.544]

91 This approach, however, would not straightforwardly allow for the rich target information available; we look at the target but also at other locations, strongly suggesting mixture distributions. [sent-213, score-0.658]

92 A combination of the two approaches could further improve decoding quality. [sent-214, score-0.232]

93 We could both estimate speed and target position for the EKFT in a continuous manner while retaining the mixture over target priors. [sent-215, score-0.816]

94 While this work is presented in the context of decoding human reaching, it may be applied to a wide range of BMI applications including lower limb prosthetic devices and human computer interactions, as well as different signal sources such as electrode grid recordings and electroencephalograms. [sent-219, score-0.534]

95 The increased user control in conveying their intended movements would significantly improve the functionality of a neuroprosthetic device. [sent-220, score-0.341]

96 Black, “Bayesian population decoding of motor cortical activity using a Kalman filter,” Neural Computation, vol. [sent-253, score-0.277]

97 Donoghue, “Neural decoding of cursor motion using a Kalman filter,” Advances in Neural Information Processing Systems 15: Proceedings of the 2002 Conference, 2003, p. [sent-265, score-0.329]

98 Black, “Neural control of computer cursor velocity by decoding motor cortical spiking activity in humans with tetraplegia,” Journal of Neural Engineering, vol. [sent-305, score-0.399]

99 Paninski, “State-space decoding of goal-directed movements,” IEEE Signal Processing Magazine, vol. [sent-338, score-0.232]

100 Shenoy, “Mixture of trajectory models for neural decoding of goal-directed movements,” Journal of neurophysiology, vol. [sent-358, score-0.486]

similar papers computed by tfidf model

tfidf for this paper:

wordName wordTfidf (topN-words)

[('target', 0.274), ('kft', 0.27), ('trajectory', 0.254), ('decoding', 0.232), ('kalman', 0.231), ('targets', 0.205), ('ekft', 0.202), ('movements', 0.197), ('reaches', 0.177), ('movement', 0.17), ('kf', 0.163), ('bmi', 0.157), ('filter', 0.152), ('mtm', 0.135), ('reach', 0.127), ('speeds', 0.123), ('stm', 0.112), ('workspace', 0.112), ('speed', 0.111), ('mixture', 0.11), ('eye', 0.107), ('emg', 0.091), ('reaching', 0.09), ('donoghue', 0.09), ('emgs', 0.09), ('mekft', 0.09), ('state', 0.081), ('dynamics', 0.078), ('subjects', 0.073), ('prosthetic', 0.073), ('shoulder', 0.073), ('arm', 0.072), ('xs', 0.07), ('priors', 0.069), ('bmis', 0.067), ('mkft', 0.067), ('wrist', 0.067), ('intended', 0.065), ('significant', 0.064), ('slow', 0.063), ('positions', 0.061), ('muscles', 0.059), ('wanted', 0.059), ('mo', 0.054), ('devices', 0.053), ('acceleration', 0.053), ('motion', 0.052), ('limb', 0.051), ('velocity', 0.049), ('normal', 0.047), ('position', 0.047), ('wu', 0.046), ('decode', 0.046), ('motor', 0.045), ('cursor', 0.045), ('fixate', 0.045), ('meng', 0.045), ('stereotypical', 0.045), ('tetraplegia', 0.045), ('perfect', 0.044), ('degraded', 0.044), ('significantly', 0.044), ('filters', 0.044), ('warping', 0.043), ('hatsopoulos', 0.039), ('premotor', 0.039), ('serruya', 0.039), ('voluntary', 0.039), ('northwestern', 0.039), ('elbow', 0.039), ('kemere', 0.039), ('incorporating', 0.037), ('statistically', 0.037), ('recordings', 0.037), ('paninski', 0.036), ('saccades', 0.036), ('hochberg', 0.036), ('bienenstock', 0.036), ('kinematics', 0.036), ('gaze', 0.036), ('user', 0.035), ('signals', 0.035), ('kulkarni', 0.034), ('efficient', 0.034), ('uncertain', 0.034), ('variation', 0.034), ('planes', 0.032), ('decoded', 0.032), ('restore', 0.032), ('defined', 0.032), ('system', 0.032), ('fast', 0.031), ('everyday', 0.031), ('human', 0.03), ('probabilistic', 0.03), ('humans', 0.028), ('wide', 0.028), ('gao', 0.028), ('healthy', 0.028), ('robotic', 0.028)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 1.0000002 167 nips-2010-Mixture of time-warped trajectory models for movement decoding

Author: Elaine Corbett, Eric Perreault, Konrad Koerding

2 0.16851529 29 nips-2010-An Approximate Inference Approach to Temporal Optimization in Optimal Control

Author: Konrad Rawlik, Marc Toussaint, Sethu Vijayakumar

Abstract: Algorithms based on iterative local approximations present a practical approach to optimal control in robotic systems. However, they generally require the temporal parameters (for e.g. the movement duration or the time point of reaching an intermediate goal) to be speciﬁed a priori. Here, we present a methodology that is capable of jointly optimizing the temporal parameters in addition to the control command proﬁles. The presented approach is based on a Bayesian canonical time formulation of the optimal control problem, with the temporal mapping from canonical to real time parametrised by an additional control variable. An approximate EM algorithm is derived that efﬁciently optimizes both the movement duration and control commands offering, for the ﬁrst time, a practical approach to tackling generic via point problems in a systematic way under the optimal control framework. The proposed approach, which is applicable to plants with non-linear dynamics as well as arbitrary state dependent and quadratic control costs, is evaluated on realistic simulations of a redundant robotic plant.

3 0.16493216 57 nips-2010-Decoding Ipsilateral Finger Movements from ECoG Signals in Humans

Author: Yuzong Liu, Mohit Sharma, Charles Gaona, Jonathan Breshears, Jarod Roland, Zachary Freudenburg, Eric Leuthardt, Kilian Q. Weinberger

Abstract: Several motor related Brain Computer Interfaces (BCIs) have been developed over the years that use activity decoded from the contralateral hemisphere to operate devices. Contralateral primary motor cortex is also the region most severely affected by hemispheric stroke. Recent studies have identiﬁed ipsilateral cortical activity in planning of motor movements and its potential implications for a stroke relevant BCI. The most fundamental functional loss after a hemispheric stroke is the loss of ﬁne motor control of the hand. Thus, whether ipsilateral cortex encodes ﬁnger movements is critical to the potential feasibility of BCI approaches in the future. This study uses ipsilateral cortical signals from humans (using ECoG) to decode ﬁnger movements. We demonstrate, for the ﬁrst time, successful ﬁnger movement detection using machine learning algorithms. Our results show high decoding accuracies in all cases which are always above chance. We also show that signiﬁcant accuracies can be achieved with the use of only a fraction of all the features recorded and that these core features are consistent with previous physiological ﬁndings. The results of this study have substantial implications for advancing neuroprosthetic approaches to stroke populations not currently amenable to existing BCI techniques. 1

4 0.10943649 171 nips-2010-Movement extraction by detecting dynamics switches and repetitions

Author: Silvia Chiappa, Jan R. Peters

Abstract: Many time-series such as human movement data consist of a sequence of basic actions, e.g., forehands and backhands in tennis. Automatically extracting and characterizing such actions is an important problem for a variety of different applications. In this paper, we present a probabilistic segmentation approach in which an observed time-series is modeled as a concatenation of segments corresponding to different basic actions. Each segment is generated through a noisy transformation of one of a few hidden trajectories representing different types of movement, with possible time re-scaling. We analyze three different approximation methods for dealing with model intractability, and demonstrate how the proposed approach can successfully segment table tennis movements recorded using a robot arm as haptic input device. 1

5 0.085533179 47 nips-2010-Co-regularization Based Semi-supervised Domain Adaptation

Author: Abhishek Kumar, Avishek Saha, Hal Daume

Abstract: This paper presents a co-regularization based approach to semi-supervised domain adaptation. Our proposed approach (EA++) builds on the notion of augmented space (introduced in E ASYA DAPT (EA) [1]) and harnesses unlabeled data in target domain to further assist the transfer of information from source to target. This semi-supervised approach to domain adaptation is extremely simple to implement and can be applied as a pre-processing step to any supervised learner. Our theoretical analysis (in terms of Rademacher complexity) of EA and EA++ show that the hypothesis class of EA++ has lower complexity (compared to EA) and hence results in tighter generalization bounds. Experimental results on sentiment analysis tasks reinforce our theoretical ﬁndings and demonstrate the efﬁcacy of the proposed method when compared to EA as well as few other representative baseline approaches.

6 0.0749292 86 nips-2010-Exploiting weakly-labeled Web images to improve object classification: a domain adaptation approach

7 0.070934273 268 nips-2010-The Neural Costs of Optimal Control

8 0.0688117 98 nips-2010-Functional form of motion priors in human motion perception

9 0.06564635 20 nips-2010-A unified model of short-range and long-range motion perception

10 0.059704017 148 nips-2010-Learning Networks of Stochastic Differential Equations

11 0.056385066 261 nips-2010-Supervised Clustering

12 0.055838685 97 nips-2010-Functional Geometry Alignment and Localization of Brain Areas

13 0.054638859 101 nips-2010-Gaussian sampling by local perturbations

14 0.05251785 50 nips-2010-Constructing Skill Trees for Reinforcement Learning Agents from Demonstration Trajectories

15 0.05216122 44 nips-2010-Brain covariance selection: better individual functional connectivity models using population prior

16 0.050168008 239 nips-2010-Sidestepping Intractable Inference with Structured Ensemble Cascades

17 0.048607353 96 nips-2010-Fractionally Predictive Spiking Neurons

18 0.048153605 34 nips-2010-Attractor Dynamics with Synaptic Depression

19 0.047532018 255 nips-2010-Static Analysis of Binary Executables Using Structural SVMs

20 0.045621231 257 nips-2010-Structured Determinantal Point Processes

similar papers computed by lsi model

lsi for this paper:

topicId topicWeight

[(0, 0.149), (1, 0.005), (2, -0.105), (3, 0.069), (4, -0.011), (5, -0.0), (6, -0.031), (7, -0.049), (8, -0.018), (9, 0.023), (10, 0.028), (11, -0.072), (12, 0.049), (13, -0.029), (14, 0.029), (15, 0.087), (16, -0.047), (17, 0.076), (18, -0.009), (19, 0.017), (20, -0.14), (21, 0.087), (22, 0.108), (23, 0.071), (24, 0.021), (25, -0.092), (26, -0.142), (27, 0.067), (28, 0.109), (29, -0.175), (30, 0.117), (31, 0.121), (32, 0.01), (33, -0.08), (34, 0.001), (35, 0.157), (36, -0.039), (37, 0.069), (38, -0.001), (39, 0.068), (40, 0.105), (41, 0.096), (42, -0.03), (43, 0.023), (44, 0.024), (45, -0.019), (46, 0.146), (47, -0.151), (48, 0.059), (49, 0.063)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 0.95419824 167 nips-2010-Mixture of time-warped trajectory models for movement decoding

Author: Elaine Corbett, Eric Perreault, Konrad Koerding

2 0.80710393 29 nips-2010-An Approximate Inference Approach to Temporal Optimization in Optimal Control

Author: Konrad Rawlik, Marc Toussaint, Sethu Vijayakumar

3 0.79866856 57 nips-2010-Decoding Ipsilateral Finger Movements from ECoG Signals in Humans

Author: Yuzong Liu, Mohit Sharma, Charles Gaona, Jonathan Breshears, Jarod Roland, Zachary Freudenburg, Eric Leuthardt, Kilian Q. Weinberger

4 0.69160175 171 nips-2010-Movement extraction by detecting dynamics switches and repetitions

Author: Silvia Chiappa, Jan R. Peters

5 0.50265419 50 nips-2010-Constructing Skill Trees for Reinforcement Learning Agents from Demonstration Trajectories

Author: George Konidaris, Scott Kuindersma, Roderic Grupen, Andre S. Barreto

Abstract: We introduce CST, an algorithm for constructing skill trees from demonstration trajectories in continuous reinforcement learning domains. CST uses a changepoint detection method to segment each trajectory into a skill chain by detecting a change of appropriate abstraction, or that a segment is too complex to model as a single skill. The skill chains from each trajectory are then merged to form a skill tree. We demonstrate that CST constructs an appropriate skill tree that can be further reﬁned through learning in a challenging continuous domain, and that it can be used to segment demonstration trajectories on a mobile manipulator into chains of skills where each skill is assigned an appropriate abstraction. 1

6 0.45165792 19 nips-2010-A rational decision making framework for inhibitory control

7 0.4448747 2 nips-2010-A Bayesian Approach to Concept Drift

8 0.41412824 47 nips-2010-Co-regularization Based Semi-supervised Domain Adaptation

9 0.38037962 95 nips-2010-Feature Transitions with Saccadic Search: Size, Color, and Orientation Are Not Alike

10 0.36414436 34 nips-2010-Attractor Dynamics with Synaptic Depression

11 0.36150527 248 nips-2010-Sparse Inverse Covariance Selection via Alternating Linearization Methods

12 0.33492321 255 nips-2010-Static Analysis of Binary Executables Using Structural SVMs

13 0.33481646 156 nips-2010-Learning to combine foveal glimpses with a third-order Boltzmann machine

14 0.32140532 157 nips-2010-Learning to localise sounds with spiking neural networks

15 0.31087017 121 nips-2010-Improving Human Judgments by Decontaminating Sequential Dependencies

16 0.30772299 244 nips-2010-Sodium entry efficiency during action potentials: A novel single-parameter family of Hodgkin-Huxley models

17 0.30207428 86 nips-2010-Exploiting weakly-labeled Web images to improve object classification: a domain adaptation approach

18 0.29893887 120 nips-2010-Improvements to the Sequence Memoizer

19 0.29228219 154 nips-2010-Learning sparse dynamic linear systems using stable spline kernels and exponential hyperpriors

20 0.28623179 148 nips-2010-Learning Networks of Stochastic Differential Equations

similar papers computed by lda model

lda for this paper:

topicId topicWeight

[(13, 0.016), (27, 0.048), (30, 0.025), (45, 0.736), (50, 0.037), (52, 0.012), (77, 0.024), (90, 0.013)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 0.99873328 167 nips-2010-Mixture of time-warped trajectory models for movement decoding

Author: Elaine Corbett, Eric Perreault, Konrad Koerding

2 0.99841595 235 nips-2010-Self-Paced Learning for Latent Variable Models

Author: M. P. Kumar, Benjamin Packer, Daphne Koller

Abstract: Latent variable models are a powerful tool for addressing several tasks in machine learning. However, the algorithms for learning the parameters of latent variable models are prone to getting stuck in a bad local optimum. To alleviate this problem, we build on the intuition that, rather than considering all samples simultaneously, the algorithm should be presented with the training data in a meaningful order that facilitates learning. The order of the samples is determined by how easy they are. The main challenge is that often we are not provided with a readily computable measure of the easiness of samples. We address this issue by proposing a novel, iterative self-paced learning algorithm where each iteration simultaneously selects easy samples and learns a new parameter vector. The number of samples selected is governed by a weight that is annealed until the entire training data has been considered. We empirically demonstrate that the self-paced learning algorithm outperforms the state of the art method for learning a latent structural SVM on four applications: object localization, noun phrase coreference, motif ﬁnding and handwritten digit recognition. 1

3 0.99763286 32 nips-2010-Approximate Inference by Compilation to Arithmetic Circuits

Author: Daniel Lowd, Pedro Domingos

Abstract: Arithmetic circuits (ACs) exploit context-speciﬁc independence and determinism to allow exact inference even in networks with high treewidth. In this paper, we introduce the ﬁrst ever approximate inference methods using ACs, for domains where exact inference remains intractable. We propose and evaluate a variety of techniques based on exact compilation, forward sampling, AC structure learning, Markov network parameter learning, variational inference, and Gibbs sampling. In experiments on eight challenging real-world domains, we ﬁnd that the methods based on sampling and learning work best: one such method (AC2 -F) is faster and usually more accurate than loopy belief propagation, mean ﬁeld, and Gibbs sampling; another (AC2 -G) has a running time similar to Gibbs sampling but is consistently more accurate than all baselines. 1

4 0.99742496 187 nips-2010-Occlusion Detection and Motion Estimation with Convex Optimization

Author: Alper Ayvaci, Michalis Raptis, Stefano Soatto

Abstract: We tackle the problem of simultaneously detecting occlusions and estimating optical ﬂow. We show that, under standard assumptions of Lambertian reﬂection and static illumination, the task can be posed as a convex minimization problem. Therefore, the solution, computed using efﬁcient algorithms, is guaranteed to be globally optimal, for any number of independently moving objects, and any number of occlusion layers. We test the proposed algorithm on benchmark datasets, expanded to enable evaluation of occlusion detection performance. 1

5 0.99729621 100 nips-2010-Gaussian Process Preference Elicitation

Author: Shengbo Guo, Scott Sanner, Edwin V. Bonilla

Abstract: Bayesian approaches to preference elicitation (PE) are particularly attractive due to their ability to explicitly model uncertainty in users’ latent utility functions. However, previous approaches to Bayesian PE have ignored the important problem of generalizing from previous users to an unseen user in order to reduce the elicitation burden on new users. In this paper, we address this deﬁciency by introducing a Gaussian Process (GP) prior over users’ latent utility functions on the joint space of user and item features. We learn the hyper-parameters of this GP on a set of preferences of previous users and use it to aid in the elicitation process for a new user. This approach provides a ﬂexible model of a multi-user utility function, facilitates an efﬁcient value of information (VOI) heuristic query selection strategy, and provides a principled way to incorporate the elicitations of multiple users back into the model. We show the effectiveness of our method in comparison to previous work on a real dataset of user preferences over sushi types. 1

6 0.99704158 255 nips-2010-Static Analysis of Binary Executables Using Structural SVMs

7 0.99638987 11 nips-2010-A POMDP Extension with Belief-dependent Rewards

8 0.99582207 133 nips-2010-Kernel Descriptors for Visual Recognition

9 0.99165571 108 nips-2010-Graph-Valued Regression

10 0.97612053 240 nips-2010-Simultaneous Object Detection and Ranking with Weak Supervision

11 0.97357023 83 nips-2010-Evidence-Specific Structures for Rich Tractable CRFs

12 0.96944571 141 nips-2010-Layered image motion with explicit occlusions, temporal consistency, and depth ordering

13 0.96752471 169 nips-2010-More data means less inference: A pseudo-max approach to structured learning

14 0.96715176 144 nips-2010-Learning Efficient Markov Networks

15 0.96634853 197 nips-2010-Optimal Bayesian Recommendation Sets and Myopically Optimal Choice Query Sets

16 0.96530867 212 nips-2010-Predictive State Temporal Difference Learning

17 0.9630698 118 nips-2010-Implicit Differentiation by Perturbation

18 0.96209639 94 nips-2010-Feature Set Embedding for Incomplete Data

19 0.95969319 86 nips-2010-Exploiting weakly-labeled Web images to improve object classification: a domain adaptation approach

20 0.95963967 93 nips-2010-Feature Construction for Inverse Reinforcement Learning