A Neuron as a Signal Processing Device

A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing device that represents the incoming streaming data matrix as a sparse vector of synaptic weights scaled by an outgoing sparse activity vector. Formally, a neuron minimizes a cost function comprising a cumulative squared representation error and regularization terms. We derive an online algorithm that minimizes such cost function by alternating between the minimization with respect to activity and with respect to synaptic weights. The steps of this algorithm reproduce well-known physiological properties of a neuron, such as weighted summation and leaky integration of synaptic inputs, as well as an Oja-like, but parameter-free, synaptic learning rule. Our theoretical framework makes several predictions, some of which can be verified by the existing data, others require further experiments. Such framework should allow modeling the function of neuronal circuits without necessarily measuring all the microscopic biophysical parameters, as well as facilitate the design of neuromorphic electronics.Comment: 2013 Asilomar Conference on Signals, Systems and Computers, see http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=681029

Stochastic models of evidence accumulation in changing environments

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information gained over an average environmental epoch. A plausible neural implementation of an optimal observer in a changing environment shows that, in contrast to previous models, neural populations representing alternate choices are coupled through excitation. Our work builds a bridge between statistical decision making in volatile environments and stochastic nonlinear dynamics.Comment: 26 pages, 7 figure

A Novel Framework of Online, Task-Independent Cognitive State Transition Detection and Its Applications

Complex reach, grasp, and object manipulation tasks require sequential, temporal coordination of a movement plan by neurons in the brain. Detecting cognitive state transitions associated with motor tasks from sequential neural data is pivotal in rehabilitation engineering. The cognitive state detectors proposed thus far rely on task-dependent (TD) models, i.e., the detection strategy exploits a priori knowledge of the movement goals to determine the actual states, regardless of whether these cognitive states actually depend on the movement tasks or not. This approach, however, is not viable when the tasks are not known a priori (e.g., the subject performs many different tasks) or when there is a paucity of neural data for each task. Moreover, some cognitive states (e.g., holding) are invariant to the tasks performs. I first develop an offline, task-dependent cognitive state transition detector and a kinematics decoder to show the feasibility of distinguishing between cognitive states based on their inherent features extracted via a hidden Markov model (HMM) based detection framework. The proposed framework is designed to decode both cognitive states and kinematics from ensemble neural activity. The proposed decoding framework is able to a) automatically differentiate between baseline, plan, and movement, and b) determine novel holding epochs of neural activity and also estimate the epoch-dependent kinematics. Specifically, the framework is mainly composed of a hidden Markov model (HMM) state decoder and a switching linear system (S-LDS) kinematics decoder. I take a supervised approach and use a generative framework of neural activity and kinematics. I demonstrate the decoding framework using neural recordings from ventral premotor (PMv) and dorsal premotor (PMd) neurons of a non-human primate executing four complex reach-to-grasp tasks along with the corresponding kinematics recording. Using the HMM state decoder, I demonstrate that the transitions between neighboring epochs of neural activity, regardless of the existence of any external kinematics changes, can be detected with high accuracy (>85%) and short latencies (<150 ms). I further show that the joint angle kinematics can be estimated reliably with high accuracy (mean = 88%) using a S-LDS kinematics decoder. In addition, I demonstrate that the use of multiple latent state variables to model the within-epoch neural activity variability can improve the decoder performance. This unified decoding framework combining a HMM state decoder and a S-LDS may be useful in neural decoding of cognitive states and complex movements of prosthetic limbs in practical brain-computer interface implementations. I then develop a real-time (online) task-independent (TI) framework to detect cognitive state transitions from spike trains and kinematic measurements. I applied this framework to 226 single-unit recordings collected via multi-electrode arrays in the premotor dorsal and ventral (PMd and PMv) regions of the cortex of two non-human primates performing 3D multi-object reach-to-grasp tasks, and I used the detection latency and accuracy of state transitions to measure the performance. I found that, in both online and offline detection modes, (i) TI models have significantly better performance than TD models when using neuronal data alone, however (ii) during movements, the addition of the kinematics history to the TI models further improves detection performance. These findings suggest that TI models may be able to more accurately detect cognitive state transitions than TD under certain circumstances. The proposed framework could pave the way for a TI control of prosthesis from cortical neurons, a beneficial outcome when the choice of tasks is vast, but despite that the basic movement cognitive states need to be decoded. Based on the online cognitive state transition detector, I further construct an online task-independent kinematics decoder. I constructed our framework using single-unit recordings from 452 neurons and synchronized kinematics recordings from two non-human primates performing 3D multi-object reach-to-grasp tasks. I find that (i) the proposed TI framework performs significantly better than current frameworks that rely on TD models (p = 0.03); and (ii) modeling cognitive state information further improves decoding performance. These findings suggest that TI models with cognitive-state-dependent parameters may more accurately decode kinematics and could pave the way for more clinically viable neural prosthetics

Data-Driven Quickest Change Detection

The quickest change detection (QCD) problem is to detect abrupt changes in a sensing environment as quickly as possible in real time while limiting the risk of false alarm. Statistical inference about the monitored stochastic process is performed through observations acquired sequentially over time. After each observation, QCD algorithm either stops and declares a change or continues to have a further observation in the next time interval. There is an inherent tradeoff between speed and accuracy in the decision making process. The design goal is to optimally balance the average detection delay and the false alarm rate to have a timely and accurate response to abrupt changes. The objective of this thesis is to investigate effective and scalable QCD approaches for real-world data streams. The classical QCD framework is model-based, that is, statistical data model is assumed to be known for both the pre- and post-change cases. However, real-world data often exhibit significant challenges for data modeling such as high dimensionality, complex multivariate nature, lack of parametric models, unknown post-change (e.g., attack or anomaly) patterns, and complex temporal correlation. Further, in some cases, data is privacy-sensitive and distributed over a system, and it is not fully available to QCD algorithm. This thesis addresses these challenges and proposes novel data-driven QCD approaches that are robust to data model mismatch and hence widely applicable to a variety of practical settings. In Chapter 2, online cyber-attack detection in the smart power grid is formulated as a partially observable Markov decision process (POMDP) problem based on the QCD framework. A universal robust online cyber-attack detection algorithm is proposed using the model-free reinforcement learning (RL) for POMDPs. In Chapter 3, online anomaly detection for big data streams is studied where the nominal (i.e., pre-change) and anomalous (i.e., post-change) high-dimensional statistical data models are unknown. A data-driven solution approach is proposed, where firstly a set of useful univariate summary statistics is computed from a nominal dataset in an offline phase and next, online summary statistics are evaluated for a persistent deviation from the nominal statistics. In Chapter 4, a generic data-driven QCD procedure is proposed, called DeepQCD, that learns the change detection rule directly from the observed raw data via deep recurrent neural networks. With sufficient amount of training data including both pre- and post-change samples, DeepQCD can effectively learn the change detection rule for all complex, high-dimensional, and temporally correlated data streams. Finally, in Chapter 5, online privacy-preserving anomaly detection is studied in a setting where the data is distributed over a network and locally sensitive to each node, and its statistical model is unknown. A data-driven differentially private distributed detection scheme is proposed, which infers network-wide anomalies based on the perturbed and encrypted statistics received from nodes. Furthermore, analytical privacy-security tradeoff in the network-wide anomaly detection problem is investigated

Optimal change-detection and spiking neurons

Survival in a non-stationary, potentially adversarial environment requires animals to detect sensory changes rapidly yet accurately, two oft competing desiderata. Neurons subserving such detections are faced with the corresponding challenge to discern “real ” changes in inputs as quickly as possible, while ignoring noisy fluctuations. Mathematically, this is an example of a change-detection problem that is actively researched in the controlled stochastic processes community. In this paper, we utilize sophisticated tools developed in that community to formalize an instantiation of the problem faced by the nervous system, and characterize the Bayes-optimal decision policy under certain assumptions. We will derive from this optimal strategy an information accumulation and decision process that remarkably resembles the dynamics of a leaky integrate-and-fire neuron. This correspondence suggests that neurons are optimized for tracking input changes, and sheds new light on the computational import of intracellular properties such as resting membrane potential, voltage-dependent conductance, and post-spike reset voltage. We also explore the influence that factors such as timing, uncertainty, neuromodulation, and reward should and do have on neuronal dynamics and sensitivity, as the optimal decision strategy depends critically on these factors.