

nnregCI(funfits)                             R Documentation

_F_i_n_d_s _a _c_o_n_f_i_d_e_n_c_e _s_e_t _o_f _p_a_r_a_m_e_t_e_r_s _f_o_r _a _n_e_u_r_a_l _n_e_t _f_i_t_.

_D_e_s_c_r_i_p_t_i_o_n_:

     The joint parameter confidence set for a neural net fit
     is all the neural net parameter sets (theta) such that
     S(theta) <= S(theta^hat)*[1+(p/n-p)*F(p,n-p,alpha)],
     where S(theta) is the residual sum of squares,
     theta^hat is the least- squares estimate of theta, p is
     the number of parameters of the model and n is the num-
     ber of data points. For the F distribution, alpha is
     the probability level.

     The program finds parameter sets which satisfy the
     above inequality.  The value of cut1 is
     RMSE(theta^hat)*sqrt([1+(p/n-p)*F(p,n-p,alpha)]).  The
     value of cut2 is .8*cut1. Approximately 20% of the fits
     will have a RMSE of cut1 and the remaining 80% will be
     uniform between RMSE(theta^hat) and cut1. This distri-
     bution of parameter sets is to make sure that the
     parameter sets cover the confidence region. The actual
     value of cut2 is used only as a check for the covering
     of the confidence region. The returned component sum-
     mary has a count of the fits between cut1 and cut2 and
     also below cut2.

     Parameters of the model are estimated by nonlinear
     least squares. The parameter space has a large number
     of local minimum so the strategy is to generate "many"
     parameter sets at random and iterate these starts with
     a minimization algorithm. The two function parameters
     ntries and ngrid are used in generating the many start-
     ing parameter sets for nonlinear least squares. Ngrind
     is the number of cubes growing geometrically over a
     range of magnitude of parameters. Ntries is the number
     of parameter sets generated at random by a uniform dis-
     tribution in each cube. The best parameter set ( out
     the Ntries ) in each cube is used as the start of a
     coarse optimization.  Npol of these coarse fits are
     selected for further refinement by a minimization with
     smaller tolerance.

     The target RMS for a fit is generated as described
     above. The parameter sets for the confidence sets are
     generated in the polishing stage and in groups of the
     optional argument npol. The file nnregCI.cut contains
     information about the polished fits. The 7th column is
     target RMSE value the 8th column is the difference
     between target RMSE and the root finder's RMSE. The 9th
     column is the value of cut1 and the 10th column is the
     value of cut2.

_U_s_a_g_e_:

     nnregCI(fit, model=fit$best.model, ngrind=250, ntries=100, npol=20,
     clevel=0.95, cut1=NA, cut2=NA, nfits=500, tol1=1e-06, tol2=1e-09,
     itmax1=250, itmax2=10000, fdata, fout="nnci.out", seed)

_A_r_g_u_m_e_n_t_s_:

     fit: A nnreg object.

   model: Model number used in finding joint parameter con-
          fidence set. Default is the best model based on
          GCV(2).

  ngrind: Number of coarse optimizations.

  ntries: Number of random starting values for each coarse
          optimization.

    npol: Number of coarse fits improved, i.e polish, using
          smaller minimization tolerance.

  clevel: Confidence level used in finding joint parameter
          confidence set. Default is the 0.95 level.

    cut1: RMSE value corresponding to the clevel confidence
          level.

    cut2: RMSE value corresponding to 80% of the RMSE value
          corresponding to the clevel confidence level.

   nfits: Number of fits (parameter sets) found in the con-
          fidence set. Maximum is 500.

    tol1: Minimization tolerance for coarse optimizations.

    tol2: Minimization tolerance for polish optimizations.

  itmax1: Maximum number of iterations performed in the min-
          imization routine for coarse optimizations.

  itmax2: Maximum number of iterations performed in the min-
          imization routine for polish optimizations.

   fdata: Temporary UNIX file name for the data.

    fout: Temporary UNIX file name for the output.

    seed: Seed used in generating the random parameter
          starts.

_V_a_l_u_e_:

     Object of class nnreg. The component model is a list of
     the parameters for each fitted model. Each component
     model is of class netfit.

   model: Component model of class netfit. Includes a list
          of the dimension of the x matrix, the number of
          hidden units used in the model, the mean of each
          column of the x matrix, the mean of the y values,
          the standard deviation of each column of the x
          matrix, the standard deviation of the y values,
          the number of parameters in the model and the
          parameters of model.

 summary: Partial Fortan program output. Summary of the
          nnreg fit. Includes a summary of the specified
          number of fitted values.

    call: Call to the function.

       x: Matrix of independent variables.

       y: Vector of dependent variables.

       n: Number of observations or length of y.

   nfits: Number of fits (parameter sets) found in the con-
          fidence set.

    seed: Seed used in generating the random parameter
          starts.

_S_i_d_e _E_f_f_e_c_t_s_:

     This function does the bulk of the computation using a
     stand-alone FORTRAN program running in the UNIX shell.
     This operation is transparent to the user. For large
     problems the input files can be setup using this func-
     tion and the fitting program can be run separately in
     the background.

_R_e_f_e_r_e_n_c_e_s_:

     B.A. Bailey, S. Ellner, D.W. Nychka. 1996. Chaos with
     Confidence: Asymptotics and Applications of Local Lya-
     punov Exponents. Proceedings on Nonlinear Dynamics and
     Time Series, Building a Bridge Between the Natural and
     Statistical Sciences. Fields Institute Communications.

     S. Ellner, D.W. Nychka, and A.R. Gallant. 1992. LENNS,
     a program to estimate the dominant Lyapunov exponent of
     noisy nonlinear systems from time series data. Insti-
     tute of Statistics Mimeo Series #2235, Statistics
     Department, North Carolina State University, Raleigh,
     NC 27695-8203.

     D.W. Nychka, S. Ellner, D. McCaffrey, and A.R. Gallant.
     1992. Finding Chaos in Noisy Systems. J. R. Statist.
     Soc. B 54:399-426.

_S_e_e _A_l_s_o_:

     predict.nnreg, predict.netfit, plot.nnreg, sum-
     mary.nnreg, print.nnreg

_E_x_a_m_p_l_e_s_:

     nnreg(ozone$x,ozone$y,1,2) -> fit # fitting a surface to ozone
     # measurements, from 1 to 2 hidden units

     nnregCI(fit) -> fit.ci # finds 500 fits in the .95 confidence set based
     # on the best model from the above fit

