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analysis:cosmo2014:module4 [2014/08/16 16:05] mvdm [Building the two-step decoder] |
analysis:cosmo2014:module4 [2018/07/07 10:19] (current) |
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In the previous module, we applied the decoder to each time bin independently, using a flat spatial prior. In effect, this assumes that the place representation can move around arbitrarily from one time step to the next. Clearly, however, a rat cannot move around arbitrarily but instead moves subject to smoothness and continuity constraints! We can use this domain knowledge to improve the performance of our decoder. | In the previous module, we applied the decoder to each time bin independently, using a flat spatial prior. In effect, this assumes that the place representation can move around arbitrarily from one time step to the next. Clearly, however, a rat cannot move around arbitrarily but instead moves subject to smoothness and continuity constraints! We can use this domain knowledge to improve the performance of our decoder. | ||
- | Our approach will be similar to Kalman filtering, in that we can construct a model of the rat's movement. We can then use this model to generate a prediction of the rat's position ($P(\hat{\mathbf{x}}_t)|P(\hat{\mathbf{x}}_{t-1}))$) which can function as a prior in out Bayesian decoder. The hat is meant to indicate that these are all estimates, since the decoder does not have access to the rat's true position $x$. | + | Our approach will be similar to Kalman filtering, in that we can construct a model of the rat's movement. We can then use this model to generate a prediction of the rat's position ($P(\hat{\mathbf{x}}_t)|P(\hat{\mathbf{x}}_{t-1}))$) which can function as a prior in our Bayesian decoder. The hat is meant to indicate that these are all estimates, since the decoder does not have access to the rat's true position $x$. |
- | Do do this, first we need to estimate $P(\hat{\mathbf{x}}_t)|P(\hat{\mathbf{x}}_{t-1}))$ from the data. | + | To do this, first we need to estimate $P(\hat{\mathbf{x}}_t)|P(\hat{\mathbf{x}}_{t-1}))$ from the data. |
==== Estimating movement kernels ==== | ==== Estimating movement kernels ==== |