| Identifying high-dimensional subspaces | The nonlinearity f is parametrized using basis functions {(p,(-)}, i = 1, . |
| Identifying high-dimensional subspaces | If we fix 9 and the basis functions {(p,} in advance, fitting the nonlinearity simply involves estimating the parameters a,- from the projected stimuli and associated spike counts. |
| Identifying high-dimensional subspaces | Standard MID can be seen as a special case of this general framework: it sets gto the identity function and the basis functions (p,- to histogram-bin indicator functions (denoted lBi(-) in Equation 7). |
| Introduction | For MDPs, the development of approximation techniques using basis functions has opened up the solution of a much larger class of problems than was tractable previously [26]. |
| Markov decision processes | In all cases we used fixed basis functions so we could calculate the basis coefficients, ai using least squares techniques. |
| Markov decision processes | We assembled a matrix (bl-J- : (bl(sj), Which contains the values of the basis functions for specific states, sj. |
| Markov decision processes | We then plug the approximation into the right hand side of equation 3, new values 13 For basis functions we used piecewise polynomials and/or b-splines [44]. |
| Overview | The test statistic for F24 is the projection of the data onto the 24 h Fourier basis function , and the null distribution is obtained by recom-puting the test statistic over repeated random permutations of the data. |
| Overview | The phase is determined by projecting the data onto the cosine part of the Fourier basis function and finding the optimal phase for the projection. |
| Overview | Testing periods other than 24 h is accomplished simply by changing the period of the Fourier basis function used to compute the test statistic. |