GaussianProcessRegressor ValueError: array is too big; `arr.size * arr.dtype.itemsize` is larger than the maximum possible size

I am running the following code:

from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel
print(X.shape)
print(X.values[:,list_of_relevant_features].dtype)
print(y.values.dtype)
kernel = DotProduct() + WhiteKernel()
model_gp = GaussianProcessRegressor(kernel=kernel, random_state=42)
model_gp.fit(X.values[:,list_of_relevant_features], y.values)
print("GP: R2 score: ", model_gp.score(X.values[:,list_of_relevant_features], y.values))

The shape of my input is: (19142, 21) dtypes are each: float64

Added in Edit: X and y are Pandas Dataframes. After .values they’re each numpy arrays

And I get the Error:

ValueError: array is too big; `arr.size * arr.dtype.itemsize` is larger than the maximum possible size.

I cant image a dataset of 20000 * 20 to be actually too big for gaussian processes, am I wrong?

The entire error message:

ValueError                                Traceback (most recent call last)
filepath in 
      482 kernel = DotProduct() + WhiteKernel()
      483 model_gp = GaussianProcessRegressor(kernel=kernel, random_state=42)
----> 484 model_gp.fit(X.values[:,list_of_relevant_features], y.values)
      485 print("GP: R2 score: ", model_gp.score(X.values[:,list_of_relevant_features], y.values))
      486 

d:Toms_venvvenvlibsite-packagessklearngaussian_process_gpr.py in fit(self, X, y)
    238             optima = [(self._constrained_optimization(obj_func,
    239                                                       self.kernel_.theta,
--> 240                                                       self.kernel_.bounds))]
    241 
    242             # Additional runs are performed from log-uniform chosen initial

d:Toms_venvvenvlibsite-packagessklearngaussian_process_gpr.py in _constrained_optimization(self, obj_func, initial_theta, bounds)
    503             opt_res = scipy.optimize.minimize(
    504                 obj_func, initial_theta, method="L-BFGS-B", jac=True,
--> 505                 bounds=bounds)
    506             _check_optimize_result("lbfgs", opt_res)
    507             theta_opt, func_min = opt_res.x, opt_res.fun

d:Toms_venvvenvlibsite-packagesscipyoptimize_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
    616     elif meth == 'l-bfgs-b':
    617         return _minimize_lbfgsb(fun, x0, args, jac, bounds,
--> 618                                 callback=callback, **options)
    619     elif meth == 'tnc':
    620         return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,

d:Toms_venvvenvlibsite-packagesscipyoptimizelbfgsb.py in _minimize_lbfgsb(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, maxls, finite_diff_rel_step, **unknown_options)
    306     sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, epsilon=eps,
    307                                   bounds=new_bounds,
--> 308                                   finite_diff_rel_step=finite_diff_rel_step)
    309 
    310     func_and_grad = sf.fun_and_grad

d:Toms_venvvenvlibsite-packagesscipyoptimizeoptimize.py in _prepare_scalar_function(fun, x0, jac, args, bounds, epsilon, finite_diff_rel_step, hess)
    260     # calculation reduces overall function evaluations.
    261     sf = ScalarFunction(fun, x0, args, grad, hess,
--> 262                         finite_diff_rel_step, bounds, epsilon=epsilon)
    263 
    264     return sf

d:Toms_venvvenvlibsite-packagesscipyoptimize_differentiable_functions.py in __init__(self, fun, x0, args, grad, hess, finite_diff_rel_step, finite_diff_bounds, epsilon)
     74 
     75         self._update_fun_impl = update_fun
---> 76         self._update_fun()
     77 
     78         # Gradient evaluation

d:Toms_venvvenvlibsite-packagesscipyoptimize_differentiable_functions.py in _update_fun(self)
    164     def _update_fun(self):
    165         if not self.f_updated:
--> 166             self._update_fun_impl()
    167             self.f_updated = True
    168 

d:Toms_venvvenvlibsite-packagesscipyoptimize_differentiable_functions.py in update_fun()
     71 
     72         def update_fun():
---> 73             self.f = fun_wrapped(self.x)
     74 
     75         self._update_fun_impl = update_fun

d:Toms_venvvenvlibsite-packagesscipyoptimize_differentiable_functions.py in fun_wrapped(x)
     68         def fun_wrapped(x):
     69             self.nfev += 1
---> 70             return fun(x, *args)
     71 
     72         def update_fun():

d:Toms_venvvenvlibsite-packagesscipyoptimizeoptimize.py in __call__(self, x, *args)
     72     def __call__(self, x, *args):
     73         """ returns the the function value """
---> 74         self._compute_if_needed(x, *args)
     75         return self._value
     76 

d:Toms_venvvenvlibsite-packagesscipyoptimizeoptimize.py in _compute_if_needed(self, x, *args)
     66         if not np.all(x == self.x) or self._value is None or self.jac is None:
     67             self.x = np.asarray(x).copy()
---> 68             fg = self.fun(x, *args)
     69             self.jac = fg[1]
     70             self._value = fg[0]

d:Toms_venvvenvlibsite-packagessklearngaussian_process_gpr.py in obj_func(theta, eval_gradient)
    229                 if eval_gradient:
    230                     lml, grad = self.log_marginal_likelihood(
--> 231                         theta, eval_gradient=True, clone_kernel=False)
    232                     return -lml, -grad
    233                 else:

d:Toms_venvvenvlibsite-packagessklearngaussian_process_gpr.py in log_marginal_likelihood(self, theta, eval_gradient, clone_kernel)
    460 
    461         if eval_gradient:
--> 462             K, K_gradient = kernel(self.X_train_, eval_gradient=True)
    463         else:
    464             K = kernel(self.X_train_)

d:Toms_venvvenvlibsite-packagessklearngaussian_processkernels.py in __call__(self, X, Y, eval_gradient)
    813         if eval_gradient:
--> 814             K1, K1_gradient = self.k1(X, Y, eval_gradient=True)
    815             K2, K2_gradient = self.k2(X, Y, eval_gradient=True)
    816             return K1 + K2, np.dstack((K1_gradient, K2_gradient))

d:Toms_venvvenvlibsite-packagessklearngaussian_processkernels.py in __call__(self, X, Y, eval_gradient)
   2110         X = np.atleast_2d(X)
   2111         if Y is None:
-> 2112             K = np.inner(X, X) + self.sigma_0 ** 2
   2113         else:
   2114             if eval_gradient:

<__array_function__ internals> in inner(*args, **kwargs)

ValueError: array is too big; `arr.size * arr.dtype.itemsize` is larger than the maximum possible size.

Answer

I believe this happened because of the dot product kernel: The traceback in line 2112 leads to the numpy inner product. So, the memory error you get actually arises in numpy and not in Scikit-learn. See also this SO question and this answer where it suggests that error is raised when numpy is calculating the expected array size of the result of the inner prosuct which could lead to an integer overflow in 32-bit Python. My python setup is 64-bit so I can’t do a consistent test but the following snippet runs without error:

import numpy as np
import pandas as pd
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel
from sklearn.datasets import load_boston

b = load_boston()

X = [pd.DataFrame(b['data'])]
y = b['target']
for i in range(50):
    X.append(pd.DataFrame(b['data']))
    y = np.append(y,b['target'])
    
X = pd.concat(X)
X = pd.concat([X,X[X.columns[0:8]]],axis=1)
print(X.values.shape,y.shape)

kernel = DotProduct() + WhiteKernel()
model_gp = GaussianProcessRegressor(kernel=kernel, random_state=42)
model_gp.fit(X.values, y)

I would suggest running your model with less features in order to see at which array shape the memory error is raised. Alternatively you may try different kernels that don’t require the inner product of X.

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Answer