On the Geometry of Message Passing Algorithms for Gaussian Reciprocal Processes

Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This opens the way to the application of efficient inference algorithms in the machine learning literature to solve the smoothing problem for reciprocal processes. Such algorithms are known to converge if the underlying graph is a tree. This is not the case for a reciprocal process, whose associated graphical model is a single loop network. The contribution of this paper is twofold. First, we introduce belief propagation for Gaussian reciprocal processes. Second, we establish a link between convergence analysis of belief propagation for Gaussian reciprocal processes and stability theory for differentially positive systems.Comment: 15 pages; Typos corrected; This paper introduces belief propagation for Gaussian reciprocal processes and extends the convergence analysis in arXiv:1603.04419 to the Gaussian cas

Unscented Kalman Filter for Brain-Machine Interfaces

Brain machine interfaces (BMIs) are devices that convert neural signals into commands to directly control artificial actuators, such as limb prostheses. Previous real-time methods applied to decoding behavioral commands from the activity of populations of neurons have generally relied upon linear models of neural tuning and were limited in the way they used the abundant statistical information contained in the movement profiles of motor tasks. Here, we propose an n-th order unscented Kalman filter which implements two key features: (1) use of a non-linear (quadratic) model of neural tuning which describes neural activity significantly better than commonly-used linear tuning models, and (2) augmentation of the movement state variables with a history of n-1 recent states, which improves prediction of the desired command even before incorporating neural activity information and allows the tuning model to capture relationships between neural activity and movement at multiple time offsets simultaneously. This new filter was tested in BMI experiments in which rhesus monkeys used their cortical activity, recorded through chronically implanted multielectrode arrays, to directly control computer cursors. The 10th order unscented Kalman filter outperformed the standard Kalman filter and the Wiener filter in both off-line reconstruction of movement trajectories and real-time, closed-loop BMI operation

From thought to action

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references.Systems engineering is rapidly assuming a prominent role in neuroscience that could unify scientific theories, experimental evidence, and medical development. In this three-part work, I study the neural representation of targets before reaching movements and the generation of prosthetic control signals through stochastic modeling and estimation. In the first part, I show that temporal and history dependence contributes to the representation of targets in the ensemble spiking activity of neurons in primate dorsal premotor cortex (PMd). Point process modeling of target representation suggests that local and possibly also distant neural interactions influence the spiking patterns observed in PMd. In the second part, I draw on results from surveillance theory to reconstruct reaching movements from neural activity related to the desired target and the path to that target. This approach combines movement planning and execution to surpass estimation with either target or path related neural activity alone. In the third part, I describe the principled design of brain-driven neural prosthetic devices as a filtering problem on interacting discrete and continuous random processes. This framework subsumes four canonical Bayesian approaches and supports emerging applications to neural prosthetic devices.(cont.) Results of a simulated reaching task predict that the method outperforms previous approaches in the control of arm position and velocity based on trajectory and endpoint mean squared error. These results form the starting point for a systems engineering approach to the design and interpretation of neuroscience experiments that can guide the development of technology for human-computer interaction and medical treatment.by Lakshminarayan Srinivasan.Ph.D

Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.DFG, 103586207, GRK 1589: Verarbeitung sensorischer Informationen in neuronalen Systeme

Dynamic Analysis of Naive Adaptive Brain-Machine Interfaces

The closed-loop operation of brain-machine interfaces (BMI) provides a context to discover foundational principles behind human-computer interaction, with emerging clinical applications to stroke, neuromuscular diseases, and trauma. In the canonical BMI, a user controls a prosthetic limb through neural signals that are recorded by electrodes and processed by a decoder into limb movements. In laboratory demonstrations with able-bodied test subjects, parameters of the decoder are commonly tuned using training data that include neural signals and corresponding overt arm movements. In the application of BMI to paralysis or amputation, arm movements are not feasible, and imagined movements create weaker, partially unrelated patterns of neural activity. BMI training must begin naive, without access to these prototypical methods for parameter initialization used in most laboratory BMI demonstrations. Naive adaptive BMI refer to a class of methods recently introduced to address this problem. We first identify the basic elements of existing approaches based on adaptive filtering and define a decoder, ReFIT-PPF to represent these existing approaches. We then present Joint RSE, a novel approach that logically extends prior approaches. Using recently developed human- and synthetic-subjects closed-loop BMI simulation platforms, we show that Joint RSE significantly outperforms ReFIT-PPF and nonadaptive (static) decoders. Control experiments demonstrate the critical role of jointly estimating neural parameters and user intent. In addition, we show that nonzero sensorimotor delay in the user significantly degrades ReFIT-PPF but not Joint RSE, owing to differences in the prior on intended velocity. Paradoxically, substantial differences in the nature of sensory feedback between these methods do not contribute to differences in performance between Joint RSE and ReFIT-PPF. Instead, BMI performance improvement is driven by machine learning, which outpaces rates of human learning in the human-subjects simulation platform. In this regime, nuances of error-related feedback to the human user are less relevant to rapid BMI mastery

Contributions to statistical analysis methods for neural spiking activity

With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity. This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models. In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model. In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior. Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application

Advances in point process modeling: feature selection, goodness-of-fit and novel applications

The research contained in this thesis extends multivariate marked point process modeling methods for neuroscience, generalizes goodness-of-fit techniques for the class of marked point processes, and introduces the use of a general history-dependent point process model to the domain of sleep apnea. Our first project involves further development of a modeling tool for spiking data from neural populations using the theory of marked point processes. This marked point process model uses features of spike waveforms as marks in order to estimate a state variable of interest. We examine the informational content of geometric features as well as principal components of the waveforms at hippocampal place cell activity by comparing decoding accuracies of a rat's position along a track. We determined that there was additional information available beyond that contained in traditional geometric features used for decoding in practice. The expanded use of this marked point process model in neuroscience necessitates corresponding goodness-of-fit protocols for the marked case. In our second project, we develop a generalized time-rescaling method for marked point processes that produces uniformly distributed spikes under a proper model. Once rescaled, the ground process then behaves as a Poisson process and can be analyzed using traditional point process goodness-of-fit methods. We demonstrate the method's ability to detect quality and manner of fit through both simulation and real neural data analysis. In the final project, we introduce history-dependent point process modeling as a superior method for characterizing severe sleep apnea over the current clinical standard known as the apnea-hypopnea index (AHI). We analyze model fits using combinations of both clinical covariates and event observations themselves through functions of history. Ultimately, apnea onset times were consistently estimated with significantly higher accuracy when history was incorporated alongside sleep stage. We present this method to the clinical audience as a means to gain detailed information on patterns of apnea and to provide more customized diagnoses and treatment prescriptions. These separate yet complementary projects extend existing point process modeling methods and further demonstrate their value in the neurosciences, sleep sciences, and beyond

Methods toward improved lower extremity rehabilitation

Thesis (Ph. D. in Electrical and Medical Engineering)--Harvard-MIT Program in Health Sciences and Technology, 2012.Cataloged from PDF version of thesis.Includes bibliographical references.Ambulation is a very important part of everyday life and its absence has a detrimental effect on an individual's quality of life. While much is understood about the neurobiological systems involved in locomotion through detailed anatomical connectivity and lesion studies, it is not well understood how neurons across different regions of the nervous system share information and coordinate their firing activity to achieve ambulation. Moreover, while it is clear that understanding the processes involved in healthy ambulation are essential to understanding how diseases affect an individual's ability to walk, diseases such as stroke tend to "take out" large portions of the underlying system. Until technologies are developed to allow restoration of damaged neural tissue back to its original state, physical therapy (which aims to restore function by establishing new motor-cortical connections among the remaining neurons) remains the most viable option for patients. The aim of this thesis is to elucidate some of the underlying neurobiological mechanisms of walking and to develop tools for rehabilitation robotics that allow finer quantification of patient improvement. To elucidate the neural mechanisms of locomotion, we studied how task relevant information (e.g. positions, velocities, and forces) modulate single unit neural activity from hindlimb/trunk region of the rat motor cortex during adaptations to robot-applied elastic loads and closed-loop brain-machine-interface (BMI) control during treadmill locomotion. Using the Point Process-Generalized Linear Model (PP-GLM) statistical framework we systematically tested parametric and non-parametric point process models of increased complexity for 573 individual neurons recorded over multiple days in six animals. The developed statistical model captures within gait-cycle modulation, load-specific modulation, and intrinsic neural dynamics. Our proposed model accurately describes the firing statistics of 98.5% (563/573) of all the recorded units and allows characterization of the neural receptive fields associated with gait phase and loading force. Understanding how these receptive fields change during training and with experience will be central to developing rehabilitation strategies that optimize motor adaptations and motor learning. The methods utilized for this analysis were developed into an open source neural Spike Train Analysis Toolbox (nSTAT) for Matlab (Mathworks, Natick MA). Systematic analyses have demonstrated the effectiveness of physical therapy, but have been unable to determine which approaches tend to be most effective in restoring function. This is likely due to the multitude of approaches, diseases, and assessment scales used. To address this issue, we develop an extension of the Force Field Adaptation Paradigm, originally developed to quantitatively assess upper extremity motor adaptation, to the lower extremity. The algorithm is implemented on the Lokomat (Hocoma HG) lower extremity gait orthosis and is currently being utilized to assess short-term motor adaptation in 40 healthy adult subjects (ClinicalTrials.gov NCT01361867). Establishing an understanding of how healthy adults' motor systems adapt to external perturbations will be important to understanding how the adaptive mechanisms involved in gait integrate information and how this process is altered by disease.by Iahn Cajigas González.Ph.D.in Electrical and Medical Engineerin