METAINFERENCE
 This is part of the isdb module

Calculates the Metainference energy for a set of experimental data.

Metainference [18] is a Bayesian framework to model heterogeneous systems by integrating prior information with noisy, ensemble-averaged data. Metainference models a system and quantifies the level of noise in the data by considering a set of replicas of the system.

Calculated experimental data are given in input as ARG while reference experimental values can be given either from fixed components of other actions using PARARG or as numbers using PARAMETERS. The default behavior is that of averaging the data over the available replicas, if this is not wanted the keyword NOENSEMBLE prevent this averaging.

Metadynamics Metainference [19] or more in general biased Metainference requires the knowledge of biasing potential in order to calculate the weighted average. In this case the value of the bias can be provided as the last argument in ARG and adding the keyword REWEIGHT. To avoid the noise resulting from the instantaneous value of the bias the weight of each replica can be averaged over a give time using the keyword AVERAGING.

The data can be averaged by using multiple replicas and weighted for a bias if present. The functional form of Metainference can be chosen among four variants selected with NOISE=GAUSS,MGAUSS,OUTLIERS,MOUTLIERS,GENERIC which correspond to modelling the noise for the arguments as a single gaussian common to all the data points, a gaussian per data point, a single long-tailed gaussian common to all the data points, a log-tailed gaussian per data point or using two distinct noises as for the most general formulation of Metainference. In this latter case the noise of the replica-averaging is gaussian (one per data point) and the noise for the comparison with the experimental data can chosen using the keyword LIKELIHOOD between gaussian or log-normal (one per data point), furthermore the evolution of the estimated average over an infinite number of replicas is driven by DFTILDE.

As for Metainference theory there are two sigma values: SIGMA_MEAN represent the error of calculating an average quantity using a finite set of replica and should be set as small as possible following the guidelines for replica-averaged simulations in the framework of the Maximum Entropy Principle. Alternatively, this can be obtained automatically using the internal sigma mean optimization as introduced in [69] (OPTSIGMAMEAN=SEM), in this second case sigma_mean is estimated from the maximum standard error of the mean either over the simulation or over a defined time using the keyword AVERAGING. SIGMA_BIAS is an uncertainty parameter, sampled by a MC algorithm in the bounded interval defined by SIGMA_MIN and SIGMA_MAX. The initial value is set at SIGMA0. The MC move is a random displacement of maximum value equal to DSIGMA. If the number of data point is too large and the acceptance rate drops it is possible to make the MC move over mutually exclusive, random subset of size MC_CHUNKSIZE and run more than one move setting MC_STEPS in such a way that MC_CHUNKSIZE*MC_STEPS will cover all the data points.

Calculated and experimental data can be compared modulo a scaling factor and/or an offset using SCALEDATA and/or ADDOFFSET, the sampling is obtained by a MC algorithm either using a flat or a gaussian prior setting it with SCALE_PRIOR or OFFSET_PRIOR.

Description of components

By default this Action calculates the following quantities. These quantities can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.

 Quantity Description bias the instantaneous value of the bias potential sigma uncertainty parameter sigmaMean uncertainty in the mean estimate acceptSigma MC acceptance for sigma values

In addition the following quantities can be calculated by employing the keywords listed below

 Quantity Keyword Description acceptScale SCALEDATA MC acceptance for scale value acceptFT GENERIC MC acceptance for general metainference f tilde value weight REWEIGHT weights of the weighted average biasDer REWEIGHT derivatives with respect to the bias scale SCALEDATA scale parameter offset ADDOFFSET offset parameter ftilde GENERIC ensemble average estimator
Compulsory keywords
 NOISETYPE ( default=MGAUSS ) functional form of the noise (GAUSS,MGAUSS,OUTLIERS,MOUTLIERS,GENERIC) LIKELIHOOD ( default=GAUSS ) the likelihood for the GENERIC metainference model, GAUSS or LOGN DFTILDE ( default=0.1 ) fraction of sigma_mean used to evolve ftilde SCALE0 ( default=1.0 ) initial value of the scaling factor SCALE_PRIOR ( default=FLAT ) either FLAT or GAUSSIAN OFFSET0 ( default=0.0 ) initial value of the offset OFFSET_PRIOR ( default=FLAT ) either FLAT or GAUSSIAN SIGMA0 ( default=1.0 ) initial value of the uncertainty parameter SIGMA_MIN ( default=0.0 ) minimum value of the uncertainty parameter SIGMA_MAX ( default=10. ) maximum value of the uncertainty parameter OPTSIGMAMEAN ( default=NONE ) Set to NONE/SEM to manually set sigma mean, or to estimate it on the fly WRITE_STRIDE ( default=10000 ) write the status to a file every N steps, this can be used for restart/continuation
Options
 NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically NOENSEMBLE ( default=off ) don't perform any replica-averaging REWEIGHT ( default=off ) simple REWEIGHT using the latest ARG as energy SCALEDATA ( default=off ) Set to TRUE if you want to sample a scaling factor common to all values and replicas ADDOFFSET ( default=off ) Set to TRUE if you want to sample an offset common to all values and replicas ARG the input for this action is the scalar output from one or more other actions. The particular scalars that you will use are referenced using the label of the action. If the label appears on its own then it is assumed that the Action calculates a single scalar value. The value of this scalar is thus used as the input to this new action. If * or *.* appears the scalars calculated by all the proceeding actions in the input file are taken. Some actions have multi-component outputs and each component of the output has a specific label. For example a DISTANCE action labelled dist may have three components x, y and z. To take just the x component you should use dist.x, if you wish to take all three components then use dist.*.More information on the referencing of Actions can be found in the section of the manual on the PLUMED Getting Started. Scalar values can also be referenced using POSIX regular expressions as detailed in the section on Regular Expressions. To use this feature you you must compile PLUMED with the appropriate flag. You can use multiple instances of this keyword i.e. ARG1, ARG2, ARG3... PARARG reference values for the experimental data, these can be provided as arguments without derivatives PARAMETERS reference values for the experimental data AVERAGING Stride for calculation of averaged weights and sigma_mean SCALE_MIN minimum value of the scaling factor SCALE_MAX maximum value of the scaling factor DSCALE maximum MC move of the scaling factor OFFSET_MIN minimum value of the offset OFFSET_MAX maximum value of the offset DOFFSET maximum MC move of the offset REGRES_ZERO stride for regression with zero offset DSIGMA maximum MC move of the uncertainty parameter SIGMA_MEAN0 starting value for the uncertainty in the mean estimate TEMP the system temperature - this is only needed if code doesn't pass the temperature to plumed MC_STEPS number of MC steps MC_CHUNKSIZE MC chunksize STATUS_FILE write a file with all the data useful for restart/continuation of Metainference SELECTOR name of selector NSELECT range of values for selector [0, N-1] RESTART allows per-action setting of restart (YES/NO/AUTO)
Examples

In the following example we calculate a set of RDC, take the replica-average of them and comparing them with a set of experimental values. RDCs are compared with the experimental data but for a multiplication factor SCALE that is also sampled by MC on-the-fly

RDC ...
LABEL=rdc
SCALE=0.0001
GYROM=-72.5388
ATOMS1=22,23
ATOMS2=25,27
ATOMS3=29,31
ATOMS4=33,34
... RDC

METAINFERENCE ...
ARG=rdc.*
NOISETYPE=MGAUSS
PARAMETERS=1.9190,2.9190,3.9190,4.9190
SCALEDATA SCALE0=1 SCALE_MIN=0.1 SCALE_MAX=3 DSCALE=0.01
SIGMA0=0.01 SIGMA_MIN=0.00001 SIGMA_MAX=3 DSIGMA=0.01
SIGMA_MEAN0=0.001
LABEL=spe
... METAINFERENCE

PRINT ARG=spe.bias FILE=BIAS STRIDE=1


in the following example instead of using one uncertainty parameter per data point we use a single uncertainty value in a long-tailed gaussian to take into account for outliers, furthermore the data are weighted for the bias applied to other variables of the system.

RDC ...
LABEL=rdc
SCALE=0.0001
GYROM=-72.5388
ATOMS1=22,23
ATOMS2=25,27
ATOMS3=29,31
ATOMS4=33,34
... RDC

cv1: TORSION ATOMS=1,2,3,4
cv2: TORSION ATOMS=2,3,4,5
mm: METAD ARG=cv1,cv2 HEIGHT=0.5 SIGMA=0.3,0.3 PACE=200 BIASFACTOR=8 WALKERS_MPI

METAINFERENCE ...
ARG=rdc.*,mm.bias
REWEIGHT
NOISETYPE=OUTLIERS
PARAMETERS=1.9190,2.9190,3.9190,4.9190
SCALEDATA SCALE0=1 SCALE_MIN=0.1 SCALE_MAX=3 DSCALE=0.01
SIGMA0=0.01 SIGMA_MIN=0.00001 SIGMA_MAX=3 DSIGMA=0.01
SIGMA_MEAN=0.001
LABEL=spe
... METAINFERENCE