Doya, et al.; Bayesian Brain | |||||

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Doya, et al.; Bayesian Brain | 0 | The Bayesian approach is a mathematically rigorous computational mechanism for combining prior knowledge with incoming evidence. | |||

Doya, et al.; Bayesian Brain | 0 | A classical example of Bayesian inference is the Kalman filter, which has been extensively used in engineering, communication, and control over the past few decades. | 0 | ||

Doya, et al.; Bayesian Brain | 0 | The Kalman filter utilizes knowledge about the noise in sensory observations and the dynamics of the observed system to keep track of the best estimate of the system's current state and its variance. | 0 | ||

Doya, et al.; Bayesian Brain | 0 | Although Kalman filters assume linear dynamics and Gaussian noise, recent Bayesian filters such as particle filters have extended the basic idea to nonlinear, non-Gaussian systems. | 0 | ||

Doya, et al.; Bayesian Brain | 0 | A Bayesian approach can contribute to an understanding of the brain at multiple levels. | 0 | ||

Doya, et al.; Bayesian Brain | 17 | Spike trains are the primary means of communication in the nervous system. | 17 | ||

Doya, et al.; Bayesian Brain | 53 | Neurons exhibit stochastic variability. Even for repeated presentations of a fixed stimulus, a neuron's spike response cannot be predicted with certainty. | 36 | ||

Doya, et al.; Bayesian Brain | 115 | Many variables in the brain are encoded with population codes. | 62 | ||

Doya, et al.; Bayesian Brain | 115 | A major focus of theoretical neuroscience has been understanding how populations of neurons encode information about single variables and how this information can be decoded from the population activity. | 0 | ||

Doya, et al.; Bayesian Brain | 131 | One of the few things in systems neuroscience we are fairly certain about is that information is encoded in population activity. | 16 | ||

Doya, et al.; Bayesian Brain | 131 | The brain receives information about the outside world; that information is represented in population activity at the sensory level; and to perform an action, such as reaching for an object, population codes in motor cortex must be generated to drive the appropriate joint movements. | 0 | ||

Doya, et al.; Bayesian Brain | 132 | Networks of neurons implement input-output functions: they take as input population activity from one set of neurons and produce as output population activity on another. | 1 | ||

Doya, et al.; Bayesian Brain | 132 | We will assume that the activity of each neuron is described by one number, its firing rate. | 0 | ||

Doya, et al.; Bayesian Brain | 132 | Noise is partially inherited from the input and is partially generated from internal noise in the network. | 0 | ||

Doya, et al.; Bayesian Brain | 139 | The noise has zero mean and covariance matrix R. | 7 | ||

Doya, et al.; Bayesian Brain | 139 | We will assume that the noise is small, linearize the equations of motion around an equilibrium on the attractor, and solve explicitly for the variance. | 0 | ||

Doya, et al.; Bayesian Brain | 142 | Networks compute with population codes by taking as input one set of noisy population codes and producing as output another set. | 3 | ||

Doya, et al.; Bayesian Brain | 145 | Areas V1 and V2, in addition to encoding fine details of images in terms of filter responses, compute a segmentation of images which allows a more compact and parsimonious encoding of images in terms of the properties of regions and surfaces in the visual scene. | 3 | ||

Doya, et al.; Bayesian Brain | 145 | Neurons and their retinotopic arrangement in visual areas can represent information precisely, thus furnishing an appropriate computational and representational infrastructure for the task. | 0 | ||

Doya, et al.; Bayesian Brain | 145 | Segmentation detects and extracts coherent regions in an image and then encodes the image in terms of probabilistic models of surfaces and regions in it. | 0 | ||

Doya, et al.; Bayesian Brain | 189 | Bayesian probability theory provides a framework for modeling how an observer should combine information from multiple cues and from prior knowledge about objects in the world to make perceptual inferences. | 44 | ||

Doya, et al.; Bayesian Brain | 204 | Experiments that have quantitatively tested the prediction of Bayesian models of cue integration have largely supported the hypothesis that human observers are "Bayes optimal" in their interpretation of image data. | 15 | ||

Doya, et al.; Bayesian Brain | 209 | A decision is a commitment to a proposition among multiple options. | 5 | ||

Doya, et al.; Bayesian Brain | 209 | Sequential sampling has been used to explain a variety of reaction-time decision tasks. This framework has a rich history in statistical decision theory and mathematical psychology. | 0 | ||

Doya, et al.; Bayesian Brain | 209 | We include recent data that suggests a possible neural implementation of the computational principles of reaction time decision tasks in the parietal cortex. | 0 | ||

Doya, et al.; Bayesian Brain | 269 | Optimal control theory is a mature mathematical discipline with numerous applications in both science and engineering. It is emerging as a computational framework of choice for studying the neural control of movement, in much the same way that probabilistic inference is emerging as the computational framework of choice for studying sensory information processing. | 60 | ||

Doya, et al.; Bayesian Brain | 269 | Duality of optimal control and probabilistic inference. | 0 | ||

Doya, et al.; Bayesian Brain | 269 | Neural information processing in sensory and motor areas. | 0 | ||

Doya, et al.; Bayesian Brain | 269 | Recursive estimation, Kalman filter. | 0 | ||

Doya, et al.; Bayesian Brain | 269 | Duality of optimal control and optimal estimation. | 0 | ||

Doya, et al.; Bayesian Brain | 270 | Markoff property of stochastic processes -- a process is Markoff if its future is conditionally independent of the past, given the present state. | 1 | ||

Doya, et al.; Bayesian Brain | 277 | Optimal control theory is based on two fundamental ideas -- One is dynamic programming and the associated optimality principle introduced by Bellman in the United States. The other is the maximum principle, introduced by Pontryagin in the Soviet Union. | 7 | ||

Doya, et al.; Bayesian Brain | 287 | Kalman filter | 10 | ||

Doya, et al.; Bayesian Brain | 289 | When the estimation problem involves nonlinear dynamics or non-Gaussian noise the solution must rely on numerical approximations, the most widely used being the extended Kalman filter (EKF). | 2 | ||

Doya, et al.; Bayesian Brain | 290 | Optimal control and optimal estimation are closely related mathematical problems, the best-known example being the linear quadratic regulator and the Kalman filter. | 1 | ||

Doya, et al.; Bayesian Brain | 294 | The brain generates the best behavior it can, subject to the constraints imposed by the body and environment. This makes optimal control theory an appealing computational framework for studying the neural control of movement. | 4 | ||

Doya, et al.; Bayesian Brain | 299 | Decision Theory -- the decision theory framework combines a probabilistic Bayesian model of the world with desires or goals of an agent that are formalized by a utility function. | 5 | ||

Doya, et al.; Bayesian Brain | 302 | Uncertainty that stems from noise of the lack of complete knowledge places estimation of attributes of the world and control of our actuators firmly within a statistical framework. The knowledge about movement outcomes must be described by a probability distribution. | 3 | ||

Doya, et al.; Bayesian Brain | 305 | Bayesian statistics is such a powerful and versatile concept that we should expect the neural networks to use it in a large range of circumstances. | 3 | ||

Doya, et al.; Bayesian Brain | 305 | Perception does not supply us with perfect knowledge about events, making it necessary to estimate the characteristics of events. | 0 | ||

Doya, et al.; Bayesian Brain | 305 | Research studies have shown that people's behavior is well predicted by the assumption that they use optimal Bayesian statistics as a strategy. | 0 | ||

Doya, et al.; Bayesian Brain | 305 | Bayesian statistics not only specifies how to combine new information, likelihood, and prior knowledge, but just as well specifies how two sources of information should be combined into a joint estimate. | 0 | ||

Doya, et al.; Bayesian Brain | 305 | Bayesian statistics is a general framework that states how people's neural networks could optimally combine different sources of information into a joint estimate. Human performance indicates that in many cases they operate very close to the theoretical optimum. | 0 | ||

Doya, et al.; Bayesian Brain | |||||

Doya, et al.; Bayesian Brain | |||||