"""Uses ridge regression to find a linear transformation of [stim] that approximates

[resp]. The regularization parameter is [alpha].

Parameters

----------

stim : array_like, shape (T, N)

Stimuli with T time points and N features.

resp : array_like, shape (T, M)

Responses with T time points and M separate responses.

alpha : float or array_like, shape (M,)

Regularization parameter. Can be given as a single value (which is applied to

all M responses) or separate values for each response.

normalpha : boolean

Whether ridge parameters should be normalized by the largest singular value of stim. Good for

comparing models with different numbers of parameters.

Returns

-------

wt : array_like, shape (N, M)

Linear regression weights.

"""

try:

# TODO determine if this should be a GPU op

# stim is TRxN (~1000x200 or 5000x15000)

# stim_gpu = gpuarray.to_gpu(stim)

# U_gpu, S_gpu, Vh_gpu = linalg.svd(stim, jobvt="O", jobu="O")

# U = U_gpu.get()

# S = S_gpu.get()

# del S_gpu

# del U_gpu

U,S,Vh = np.linalg.svd(stim, full_matrices=False)

except np.linalg.LinAlgError, e:

logger.info("NORMAL SVD FAILED, trying more robust dgesvd..")

from svd_dgesvd import svd_dgesvd

U,S,Vh = svd_dgesvd(stim, full_matrices=False)

#origsize = S.shape[0]

#ngoodS = np.sum(S>singcutoff)

#nbad = origsize-ngoodS

#U = U[:,:ngoodS]

#S = S[:ngoodS]

#Vh = Vh[:ngoodS]

# EXAMPLE FOR RUNNING GPU LINALG OPERATIONS

# Export data to GPU

# U_gpu = gpuarray.to_gpu(U)

# Do a transpose op on GPU

# UT_gpu = linalg.transpose(U_gpu)

# Export more data to GPU

# resp_gpu = gpuarray.to_gpu(np.nan_to_num(resp))

# Run a dot product

# UR_gpu = linalg.dot(UT_gpu, resp_gpu)

# Fetch data from the GPU

# UR = UR_gpu.get()

# The above GPU code can replace the following line:

UR = np.dot(U.T, np.nan_to_num(resp))

# TODO determine if this should be a GPU op

# U is output from SVD, I think TRxTR (~1000x1000 or 5000x5000)

# resp is TRxM (~1000x3000 or 5000x30000)

# Expand alpha to a collection if it's just a single value

if isinstance(alpha, float):

alpha = np.ones(resp.shape[1]) * alpha

# Normalize alpha by the LSV norm

norm = S[0]

if normalpha:

nalphas = alpha * norm

else:

nalphas = alpha

# Compute weights for each alpha

ualphas = np.unique(nalphas)

wt = np.zeros((stim.shape[1], resp.shape[1]), order='F') # Make wt column major

Vh_gpu = gpuarray.to_gpu(np.copy(Vh, order='F'))

for ua in ualphas:

selvox = np.nonzero(nalphas==ua)[0] # list of indices equal to ua

# TODO determine if this should be a GPU op

# Vh is output from SVD, i think NxN (~200x200 or 15000x15000)

# TODO determine how reduce works

Sd = S/(S**2+ua**2)

Sd_gpu = gpuarray.to_gpu(Sd)

UR_gpu = gpuarray.to_gpu(np.copy(UR[:,selvox], order='F'))

linalg.dot_diag(Sd_gpu, UR_gpu, overwrite=True)

del Sd_gpu

if selvox.shape[0] > 5000:

N=selvox.shape[0]/4

inter_gpu = linalg.dot(Vh_gpu, UR_gpu[:,0:N], transa='T')

wt[:,selvox[0:N]] = inter_gpu.get()

del inter_gpu

inter_gpu = linalg.dot(Vh_gpu, UR_gpu[:,N:2*N], transa='T')

wt[:,selvox[N:2*N]] = inter_gpu.get()

del inter_gpu

inter_gpu = linalg.dot(Vh_gpu, UR_gpu[:,2*N:3*N], transa='T')

wt[:,selvox[2*N:3*N]] = inter_gpu.get()

del inter_gpu

inter_gpu = linalg.dot(Vh_gpu, UR_gpu[:,3*N:], transa='T')

wt[:,selvox[3*N:]] = inter_gpu.get()

del inter_gpu

else:

awt_gpu = linalg.dot(Vh_gpu, UR_gpu, transa='T')

wt[:,selvox] = awt_gpu.get()

del UR_gpu

del Vh_gpu

singcutoff=1e-10, use_corr=True, logger=ridge_logger):

"""Uses ridge regression to find a linear transformation of [Rstim] that approximates [Rresp],

then tests by comparing the transformation of [Pstim] to [Presp]. This procedure is repeated

for each regularization parameter alpha in [alphas]. The correlation between each prediction and

each response for each alpha is returned. The regression weights are NOT returned, because

computing the correlations without computing regression weights is much, MUCH faster.

Parameters

----------

Rstim : array_like, shape (TR, N)

Training stimuli with TR time points and N features. Each feature should be Z-scored across time.

Pstim : array_like, shape (TP, N)

Test stimuli with TP time points and N features. Each feature should be Z-scored across time.

Rresp : array_like, shape (TR, M)

Training responses with TR time points and M responses (voxels, neurons, what-have-you).

Each response should be Z-scored across time.

Presp : array_like, shape (TP, M)

Test responses with TP time points and M responses.

alphas : list or array_like, shape (A,)

Ridge parameters to be tested. Should probably be log-spaced. np.logspace(0, 3, 20) works well.

normalpha : boolean

Whether ridge parameters should be normalized by the largest singular value (LSV) norm of

Rstim. Good for comparing models with different numbers of parameters.

corrmin : float in [0..1]

Purely for display purposes. After each alpha is tested, the number of responses with correlation

greater than corrmin minus the number of responses with correlation less than negative corrmin

will be printed. For long-running regressions this vague metric of non-centered skewness can

give you a rough sense of how well the model is working before it's done.

singcutoff : float

The first step in ridge regression is computing the singular value decomposition (SVD) of the

stimulus Rstim. If Rstim is not full rank, some singular values will be approximately equal

to zero and the corresponding singular vectors will be noise. These singular values/vectors

should be removed both for speed (the fewer multiplications the better!) and accuracy. Any

singular values less than singcutoff will be removed.

use_corr : boolean

If True, this function will use correlation as its metric of model fit. If False, this function

will instead use variance explained (R-squared) as its metric of model fit. For ridge regression

this can make a big difference -- highly regularized solutions will have very small norms and

will thus explain very little variance while still leading to high correlations, as correlation

is scale-free while R**2 is not.

Returns

-------

Rcorrs : array_like, shape (A, M)

The correlation between each predicted response and each column of Presp for each alpha.

"""

## Calculate SVD of stimulus matrix

logger.info("Doing SVD...")

try:

U,S,Vh = np.linalg.svd(Rstim, full_matrices=False)

except np.linalg.LinAlgError, e:

logger.info("NORMAL SVD FAILED, trying more robust dgesvd..")

from svd_dgesvd import svd_dgesvd

U,S,Vh = svd_dgesvd(Rstim, full_matrices=False)

## Truncate tiny singular values for speed

origsize = S.shape[0]

ngoodS = np.sum(S>singcutoff)

nbad = origsize-ngoodS

U = U[:,:ngoodS]

S = S[:ngoodS]

Vh = Vh[:ngoodS]

logger.info("Dropped %d tiny singular values.. (U is now %s)"%(nbad, str(U.shape)))

## Normalize alpha by the LSV norm

norm = S[0]

logger.info("Training stimulus has LSV norm: %0.03f"%norm)

if normalpha:

nalphas = alphas * norm

else:

nalphas = alphas

## Precompute some products for speed

# TODO determine if this should be a GPU

# U is svd output. I think TRxTR (~1000x1000 or 5000x5000)

# Rresp is TRxM (~1000x3000 or 5000x30000)

UR = np.dot(U.T, Rresp) ## Precompute this matrix product for speed

# TODO determine if this should be a GPU op

# Pstim is TPxN (~200x200 or 1000x15000)

# Vh is output from SVD, I think NxN (~200x200 or 15000x15000)

PVh = np.dot(Pstim, Vh.T) ## Precompute this matrix product for speed

#Prespnorms = np.apply_along_axis(np.linalg.norm, 0, Presp) ## Precompute test response norms

zPresp = zs(Presp)

Prespvar = Presp.var(0)

Rcorrs = [] ## Holds training correlations for each alpha

for na, a in zip(nalphas, alphas):

#D = np.diag(S/(S**2+a**2)) ## Reweight singular vectors by the ridge parameter

D = S/(S**2+na**2) ## Reweight singular vectors by the (normalized?) ridge parameter

# TODO determine if this should be a GPU op

# mult_diag is diagonal matrix.

# UR is TRxM (~1000x3000 or 5000x30000)

pred = np.dot(mult_diag(D, PVh, left=False), UR) ## Best (1.75 seconds to prediction in test)

# pred = np.dot(mult_diag(D, np.dot(Pstim, Vh.T), left=False), UR) ## Better (2.0 seconds to prediction in test)

# pvhd = reduce(np.dot, [Pstim, Vh.T, D]) ## Pretty good (2.4 seconds to prediction in test)

# pred = np.dot(pvhd, UR)

# wt = reduce(np.dot, [Vh.T, D, UR]).astype(dtype) ## Bad (14.2 seconds to prediction in test)

# wt = reduce(np.dot, [Vh.T, D, U.T, Rresp]).astype(dtype) ## Worst

# pred = np.dot(Pstim, wt) ## Predict test responses

if use_corr:

#prednorms = np.apply_along_axis(np.linalg.norm, 0, pred) ## Compute predicted test response norms

#Rcorr = np.array([np.corrcoef(Presp[:,ii], pred[:,ii].ravel())[0,1] for ii in range(Presp.shape[1])]) ## Slowly compute correlations

#Rcorr = np.array(np.sum(np.multiply(Presp, pred), 0)).squeeze()/(prednorms*Prespnorms) ## Efficiently compute correlations

Rcorr = (zPresp*zs(pred)).mean(0)

else:

## Compute variance explained

resvar = (Presp-pred).var(0)

Rcorr = np.clip(1-(resvar/Prespvar), 0, 1)

Rcorr[np.isnan(Rcorr)] = 0

Rcorrs.append(Rcorr)

#log_template = "Training: alpha=%0.3f, mean corr=%0.5f, max corr=%0.5f, over-under(%0.2f)=%d"

#log_msg = log_template % (a,

# np.mean(Rcorr),

# np.max(Rcorr),

# corrmin,

# (Rcorr>corrmin).sum()-(-Rcorr>corrmin).sum())

#logger.info(log_msg)

corrmin=0.2, joined=None, singcutoff=1e-10, normalpha=False, single_alpha=False,

use_corr=True, logger=ridge_logger, test_bootstrap=False):

"""Uses ridge regression with a bootstrapped held-out set to get optimal alpha values for each response.

[nchunks] random chunks of length [chunklen] will be taken from [Rstim] and [Rresp] for each regression

run. [nboots] total regression runs will be performed. The best alpha value for each response will be

averaged across the bootstraps to estimate the best alpha for that response.

If [joined] is given, it should be a list of lists where the STRFs for all the voxels in each sublist

will be given the same regularization parameter (the one that is the best on average).

Parameters

----------

Rstim : array_like, shape (TR, N)

Training stimuli with TR time points and N features. Each feature should be Z-scored across time.

Rresp : array_like, shape (TR, M)

Training responses with TR time points and M different responses (voxels, neurons, what-have-you).

Each response should be Z-scored across time.

Pstim : array_like, shape (TP, N)

Test stimuli with TP time points and N features. Each feature should be Z-scored across time.

Presp : array_like, shape (TP, M)

Test responses with TP time points and M different responses. Each response should be Z-scored across

time.

alphas : list or array_like, shape (A,)

Ridge parameters that will be tested. Should probably be log-spaced. np.logspace(0, 3, 20) works well.

nboots : int

The number of bootstrap samples to run. 15 to 30 works well.

chunklen : int

On each sample, the training data is broken into chunks of this length. This should be a few times

longer than your delay/STRF. e.g. for a STRF with 3 delays, I use chunks of length 10.

nchunks : int

The number of training chunks held out to test ridge parameters for each bootstrap sample. The product

of nchunks and chunklen is the total number of training samples held out for each sample, and this

product should be about 20 percent of the total length of the training data.

corrmin : float in [0..1]

Purely for display purposes. After each alpha is tested for each bootstrap sample, the number of

responses with correlation greater than this value will be printed. For long-running regressions this

can give a rough sense of how well the model works before it's done.

joined : None or list of array_like indices

If you want the STRFs for two (or more) responses to be directly comparable, you need to ensure that

the regularization parameter that they use is the same. To do that, supply a list of the response sets

that should use the same ridge parameter here. For example, if you have four responses, joined could

be [np.array([0,1]), np.array([2,3])], in which case responses 0 and 1 will use the same ridge parameter

(which will be parameter that is best on average for those two), and likewise for responses 2 and 3.

singcutoff : float

The first step in ridge regression is computing the singular value decomposition (SVD) of the

stimulus Rstim. If Rstim is not full rank, some singular values will be approximately equal

to zero and the corresponding singular vectors will be noise. These singular values/vectors

should be removed both for speed (the fewer multiplications the better!) and accuracy. Any

singular values less than singcutoff will be removed.

normalpha : boolean

Whether ridge parameters (alphas) should be normalized by the largest singular value (LSV)

norm of Rstim. Good for rigorously comparing models with different numbers of parameters.

single_alpha : boolean

Whether to use a single alpha for all responses. Good for identification/decoding.

use_corr : boolean

If True, this function will use correlation as its metric of model fit. If False, this function

will instead use variance explained (R-squared) as its metric of model fit. For ridge regression

this can make a big difference -- highly regularized solutions will have very small norms and

will thus explain very little variance while still leading to high correlations, as correlation

is scale-free while R**2 is not.

Returns

-------

wt : array_like, shape (N, M)

Regression weights for N features and M responses.

corrs : array_like, shape (M,)

Validation set correlations. Predicted responses for the validation set are obtained using the regression

weights: pred = np.dot(Pstim, wt), and then the correlation between each predicted response and each

column in Presp is found.

alphas : array_like, shape (M,)

The regularization coefficient (alpha) selected for each voxel using bootstrap cross-validation.

bootstrap_corrs : array_like, shape (A, M, B)

Correlation between predicted and actual responses on randomly held out portions of the training set,

for each of A alphas, M voxels, and B bootstrap samples.

valinds : array_like, shape (TH, B)

The indices of the training data that were used as "validation" for each bootstrap sample.

"""

nresp, nvox = Rresp.shape

bestalphas = np.zeros((nboots, nvox)) # Will hold the best alphas for each voxel

comm = MPI.COMM_WORLD

rank = comm.Get_rank()

size = comm.Get_size()

# Keep it super simple by enforcing that the num of

# bootstraps be divisible by the number of workers;

# else, the number of bootstraps will be truncated

local_boots = nboots / size

if (nboots/size)*size != nboots:

logger.info("Number of workers do not cleanly divide requested bootstrap count. Doing %d bootstraps total instead" % (local_boots*size,))

if test_bootstrap:

k = rank

else:

k = None

Rcmats = []

valinds = [] # Will hold the indices into the validation data for each bootstrap

for i in range(local_boots):

if k < nboots:

logger.info("Rank " + str(rank) + " running bootstrap " + str(i+1) +

"/"+ str(local_boots) + " with seed " + str(k))

if test_bootstrap:

random.seed(k)

logger.info("Selecting held-out test set..")

allinds = range(nresp)

indchunks = zip(*[iter(allinds)]*chunklen)

random.shuffle(indchunks)

logger.info(str(indchunks[0:3]))

heldinds = list(itools.chain(*indchunks[:nchunks]))

notheldinds = list(set(allinds)-set(heldinds))

RRstim = Rstim[notheldinds,:]

PRstim = Rstim[heldinds,:]

RRresp = Rresp[notheldinds,:]

PRresp = Rresp[heldinds,:]

# Run ridge regression using this test set

Rcmat = ridge_corr(RRstim, PRstim, RRresp, PRresp, alphas,

corrmin=corrmin, singcutoff=singcutoff,

normalpha=normalpha, use_corr=use_corr,

logger=logger)

else:

Rcmat = None

heldinds = None

Rcmat = np.array(Rcmat)

# Allocate an empty numpy array to hold MPI collected data

recv_Rcmats = np.empty((size*len(alphas), nvox), dtype=np.float64)

comm.barrier()

comm.Allgather(Rcmat, recv_Rcmats)

# Split recv'd data into 'size' separate arrays (from each worker)

Rcmats += np.split(recv_Rcmats, size)

comm.barrier()

valinds += comm.allgather(heldinds)

comm.barrier()

if test_bootstrap:

k += size

# for local_bootstrap_result in global_Rcmats:

# Rcmats += local_bootstrap_result

# for local_valinds_result in global_valinds:

# valinds += local_valinds_result

valinds = [ x for x in valinds if x != None ]

valinds = np.array(valinds)

# Find best alphas

if nboots>0:

Rcmats = [ x for x in Rcmats if x != None ]

allRcorrs = np.dstack(Rcmats)

else:

allRcorrs = None

if not single_alpha:

if nboots==0:

raise ValueError("You must run at least one cross-validation step to assign "

"different alphas to each response.")

logger.info("Finding best alpha for each voxel..")

if joined is None:

# Find best alpha for each voxel

meanbootcorrs = allRcorrs.mean(2)

bestalphainds = np.argmax(meanbootcorrs, 0)

valphas = alphas[bestalphainds]

else:

# Find best alpha for each group of voxels

valphas = np.zeros((nvox,))

for jl in joined:

# Mean across voxels in the set, then mean across bootstraps

jcorrs = allRcorrs[:,jl,:].mean(1).mean(1)

bestalpha = np.argmax(jcorrs)

valphas[jl] = alphas[bestalpha]

else:

logger.info("Finding single best alpha..")

if nboots==0:

if len(alphas)==1:

bestalphaind = 0

bestalpha = alphas[0]

else:

raise ValueError("You must run at least one cross-validation step "

"to choose best overall alpha, or only supply one"

"possible alpha value.")

else:

meanbootcorr = allRcorrs.mean(2).mean(1)

bestalphaind = np.argmax(meanbootcorr)

bestalpha = alphas[bestalphaind]

valphas = np.array([bestalpha]*nvox)

logger.info("Best alpha = %0.3f"%bestalpha)

# Find weights

logger.info("Computing weights for each response using entire training set..")

wt = ridge(Rstim, Rresp, valphas, singcutoff=singcutoff, normalpha=normalpha)

# Predict responses on prediction set

logger.info("Predicting responses for predictions set..")

#pred = np.dot(Pstim, wt)

pred = splitdot.left_dot_col_major_gpu(Pstim, wt)

# Find prediction correlations

nnpred = np.nan_to_num(pred)

corrs = np.nan_to_num(np.array([np.corrcoef(Presp[:,ii], nnpred[:,ii].ravel())[0,1]

for ii in range(Presp.shape[1])]))