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The Discriminative Kalman Filter for Bayesian Filtering with Nonlinear and Nongaussian Observation Models
Neural Computation (2020) 32 (5): 969–1017.
Published: 01 May 2020
AbstractView article PDF
The Kalman filter provides a simple and efficient algorithm to compute the posterior distribution for state-space models where both the latent state and measurement models are linear and gaussian. Extensions to the Kalman filter, including the extended and unscented Kalman filters, incorporate linearizations for models where the observation model p ( observation | state ) is nonlinear. We argue that in many cases, a model for p ( state | observation ) proves both easier to learn and more accurate for latent state estimation. Approximating p ( state | observation ) as gaussian leads to a new filtering algorithm, the discriminative Kalman filter (DKF), which can perform well even when p ( observation | state ) is highly nonlinear and/or nongaussian. The approximation, motivated by the Bernstein–von Mises theorem, improves as the dimensionality of the observations increases. The DKF has computational complexity similar to the Kalman filter, allowing it in some cases to perform much faster than particle filters with similar precision, while better accounting for nonlinear and nongaussian observation models than Kalman-based extensions. When the observation model must be learned from training data prior to filtering, off-the-shelf nonlinear and nonparametric regression techniques can provide a gaussian model for p ( observation | state ) that cleanly integrates with the DKF. As part of the BrainGate2 clinical trial, we successfully implemented gaussian process regression with the DKF framework in a brain-computer interface to provide real-time, closed-loop cursor control to a person with a complete spinal cord injury. In this letter, we explore the theory underlying the DKF, exhibit some illustrative examples, and outline potential extensions.
Includes: Supplementary data
Robust Closed-Loop Control of a Cursor in a Person with Tetraplegia using Gaussian Process Regression
Neural Computation (2018) 30 (11): 2986–3008.
Published: 01 November 2018
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AbstractView article PDF
Intracortical brain computer interfaces can enable individuals with paralysis to control external devices through voluntarily modulated brain activity. Decoding quality has been previously shown to degrade with signal nonstationarities—specifically, the changes in the statistics of the data between training and testing data sets. This includes changes to the neural tuning profiles and baseline shifts in firing rates of recorded neurons, as well as nonphysiological noise. While progress has been made toward providing long-term user control via decoder recalibration, relatively little work has been dedicated to making the decoding algorithm more resilient to signal nonstationarities. Here, we describe how principled kernel selection with gaussian process regression can be used within a Bayesian filtering framework to mitigate the effects of commonly encountered nonstationarities. Given a supervised training set of (neural features, intention to move in a direction)-pairs, we use gaussian process regression to predict the intention given the neural data. We apply kernel embedding for each neural feature with the standard radial basis function. The multiple kernels are then summed together across each neural dimension, which allows the kernel to effectively ignore large differences that occur only in a single feature. The summed kernel is used for real-time predictions of the posterior mean and variance under a gaussian process framework. The predictions are then filtered using the discriminative Kalman filter to produce an estimate of the neural intention given the history of neural data. We refer to the multiple kernel approach combined with the discriminative Kalman filter as the MK-DKF. We found that the MK-DKF decoder was more resilient to nonstationarities frequently encountered in-real world settings yet provided similar performance to the currently used Kalman decoder. These results demonstrate a method by which neural decoding can be made more resistant to nonstationarities.
Neural Computation (2015) 27 (1): 1–31.
Published: 01 January 2015
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Increased emphasis on circuit level activity in the brain makes it necessary to have methods to visualize and evaluate large-scale ensemble activity beyond that revealed by raster-histograms or pairwise correlations. We present a method to evaluate the relative similarity of neural spiking patterns by combining spike train distance metrics with dimensionality reduction. Spike train distance metrics provide an estimate of similarity between activity patterns at multiple temporal resolutions. Vectors of pair-wise distances are used to represent the intrinsic relationships between multiple activity patterns at the level of single units or neuronal ensembles. Dimensionality reduction is then used to project the data into concise representations suitable for clustering analysis as well as exploratory visualization. Algorithm performance and robustness are evaluated using multielectrode ensemble activity data recorded in behaving primates. We demonstrate how spike train SIMilarity space (SSIMS) analysis captures the relationship between goal directions for an eight-directional reaching task and successfully segregates grasp types in a 3D grasping task in the absence of kinematic information. The algorithm enables exploration of virtually any type of neural spiking (time series) data, providing similarity-based clustering of neural activity states with minimal assumptions about potential information encoding models.