SklearnSVM - ArpackNoConvergence

[fishgoesbloop]

Information

• Qiskit Aqua version: {'qiskit-terra': '0.16.0', 'qiskit-aer': '0.7.0', 'qiskit-ignis': '0.5.0', 'qiskit-ibmq-provider': '0.11.0', 'qiskit-aqua': '0.8.0', 'qiskit': '0.23.0'}
• Python version:3.8.5
• Operating system:Windows

What is the current behavior?

---

ArpackNoConvergence                       Traceback (most recent call last)
~\Anaconda3\envs\qc\lib\site-packages\cvxpy\expressions\constants\constant.py in extremal_eig_near_ref(A, ref, low)
    242         sigma = -ref if low else ref
--> 243         ev = SA_eigsh(sigma)
    244     except ArpackError:

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\expressions\constants\constant.py in SA_eigsh(sigma)
    237     def SA_eigsh(sigma):
--> 238         return eigsh(A, k=1, sigma=sigma, return_eigenvectors=False)
    239     # Run eigsh in shift-invert mode, since we're particularly interested in finding

~\Anaconda3\envs\qc\lib\site-packages\scipy\sparse\linalg\eigen\arpack\arpack.py in eigsh(A, k, M, sigma, which, v0, ncv, maxiter, tol, return_eigenvectors, Minv, OPinv, mode)
   1686         while not params.converged:
-> 1687             params.iterate()
   1688 

~\Anaconda3\envs\qc\lib\site-packages\scipy\sparse\linalg\eigen\arpack\arpack.py in iterate(self)
    570             elif self.info == 1:
--> 571                 self._raise_no_convergence()
    572             else:

~\Anaconda3\envs\qc\lib\site-packages\scipy\sparse\linalg\eigen\arpack\arpack.py in _raise_no_convergence(self)
    376             k_ok = 0
--> 377         raise ArpackNoConvergence(msg % (num_iter, k_ok, self.k), ev, vec)
    378 

ArpackNoConvergence: ARPACK error -1: No convergence (501 iterations, 0/1 eigenvectors converged)

During handling of the above exception, another exception occurred:

ArpackNoConvergence                       Traceback (most recent call last)
<ipython-input-30-95ef4f118c4c> in <module>
     10 )
     11 
---> 12 csvm = SklearnSVM(training_input,test_input).run()
     13 print("testing success ratio: ", csvm['testing_accuracy'])

~\Anaconda3\envs\qc\lib\site-packages\qiskit\aqua\algorithms\classical_algorithm.py in run(self)
     41         """
     42 
---> 43         return self._run()
     44 
     45     @abstractmethod

~\Anaconda3\envs\qc\lib\site-packages\qiskit\aqua\algorithms\classifiers\sklearn_svm\sklearn_svm.py in _run(self)
    129 
    130     def _run(self):
--> 131         return self.instance.run()
    132 
    133     @property

~\Anaconda3\envs\qc\lib\site-packages\qiskit\aqua\algorithms\classifiers\sklearn_svm\_sklearn_svm_binary.py in run(self)
    141         """
    142 
--> 143         self.train(self.training_dataset[0], self.training_dataset[1])
    144         if self.test_dataset is not None:
    145             self.test(self.test_dataset[0], self.test_dataset[1])

~\Anaconda3\envs\qc\lib\site-packages\qiskit\aqua\algorithms\classifiers\sklearn_svm\_sklearn_svm_binary.py in train(self, data, labels)
     48         kernel_matrix = self.construct_kernel_matrix(data, data, self.gamma)
     49         self._ret['kernel_matrix_training'] = kernel_matrix
---> 50         [alpha, b, support] = optimize_svm(kernel_matrix, labels)
     51         alphas = np.array([])
     52         svms = np.array([])

~\Anaconda3\envs\qc\lib\site-packages\qiskit\aqua\utils\qp_solver.py in optimize_svm(kernel_matrix, y, scaling, maxiter, show_progress, max_iters)
     90         [G@x <= h,
     91          A@x == b])
---> 92     prob.solve(verbose=show_progress, qcp=True)
     93     result = np.asarray(x.value).reshape((n, 1))
     94     alpha = result * scaling

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\problems\problem.py in solve(self, *args, **kwargs)
    394         else:
    395             solve_func = Problem._solve
--> 396         return solve_func(self, *args, **kwargs)
    397 
    398     @classmethod

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\problems\problem.py in _solve(self, solver, warm_start, verbose, gp, qcp, requires_grad, enforce_dpp, **kwargs)
    730             if gp and qcp:
    731                 raise ValueError("At most one of `gp` and `qcp` can be True.")
--> 732             if qcp and not self.is_dcp():
    733                 if not self.is_dqcp():
    734                     raise error.DQCPError("The problem is not DQCP.")

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\utilities\performance_utils.py in _compute_once(self, *args, **kwargs)
     68             return cache[key]
     69         else:
---> 70             result = func(self, *args, **kwargs)
     71             cache[key] = result
     72             return result

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\problems\problem.py in is_dcp(self, dpp)
    163             True if the Expression is DCP, False otherwise.
    164         """
--> 165         return all(
    166           expr.is_dcp(dpp) for expr in self.constraints + [self.objective])
    167 

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\problems\problem.py in <genexpr>(.0)
    164         """
    165         return all(
--> 166           expr.is_dcp(dpp) for expr in self.constraints + [self.objective])
    167 
    168     @perf.compute_once

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\problems\objective.py in is_dcp(self, dpp)
    149             with scopes.dpp_scope():
    150                 return self.args[0].is_convex()
--> 151         return self.args[0].is_convex()
    152 
    153     def is_dgp(self, dpp=False):

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\utilities\performance_utils.py in _compute_once(self, *args, **kwargs)
     68             return cache[key]
     69         else:
---> 70             result = func(self, *args, **kwargs)
     71             cache[key] = result
     72             return result

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\atoms\atom.py in is_convex(self)
    171         elif self.is_atom_convex():
    172             for idx, arg in enumerate(self.args):
--> 173                 if not (arg.is_affine() or
    174                         (arg.is_convex() and self.is_incr(idx)) or
    175                         (arg.is_concave() and self.is_decr(idx))):

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\utilities\performance_utils.py in _compute_once(self, *args, **kwargs)
     68             return cache[key]
     69         else:
---> 70             result = func(self, *args, **kwargs)
     71             cache[key] = result
     72             return result

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\expressions\expression.py in is_affine(self)
    175         """Is the expression affine?
    176         """
--> 177         return self.is_constant() or (self.is_convex() and self.is_concave())
    178 
    179     @abc.abstractmethod

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\utilities\performance_utils.py in _compute_once(self, *args, **kwargs)
     68             return cache[key]
     69         else:
---> 70             result = func(self, *args, **kwargs)
     71             cache[key] = result
     72             return result

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\atoms\atom.py in is_convex(self)
    171         elif self.is_atom_convex():
    172             for idx, arg in enumerate(self.args):
--> 173                 if not (arg.is_affine() or
    174                         (arg.is_convex() and self.is_incr(idx)) or
    175                         (arg.is_concave() and self.is_decr(idx))):

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\utilities\performance_utils.py in _compute_once(self, *args, **kwargs)
     68             return cache[key]
     69         else:
---> 70             result = func(self, *args, **kwargs)
     71             cache[key] = result
     72             return result

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\expressions\expression.py in is_affine(self)
    175         """Is the expression affine?
    176         """
--> 177         return self.is_constant() or (self.is_convex() and self.is_concave())
    178 
    179     @abc.abstractmethod

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\utilities\performance_utils.py in _compute_once(self, *args, **kwargs)
     68             return cache[key]
     69         else:
---> 70             result = func(self, *args, **kwargs)
     71             cache[key] = result
     72             return result

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\atoms\atom.py in is_convex(self)
    169         if self.is_constant():
    170             return True
--> 171         elif self.is_atom_convex():
    172             for idx, arg in enumerate(self.args):
    173                 if not (arg.is_affine() or

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\atoms\quad_form.py in is_atom_convex(self)
     62         """
     63         P = self.args[1]
---> 64         return P.is_constant() and P.is_psd()
     65 
     66     def is_atom_concave(self):

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\utilities\performance_utils.py in _compute_once(self, *args, **kwargs)
     68             return cache[key]
     69         else:
---> 70             result = func(self, *args, **kwargs)
     71             cache[key] = result
     72             return result

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\expressions\constants\constant.py in is_psd(self)
    204         # Compute bottom eigenvalue if absent.
    205         if self._bottom_eig is None:
--> 206             ev = extremal_eig_near_ref(self.value, EIGVAL_TOL, low=True)
    207             self._bottom_eig = ev
    208 

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\expressions\constants\constant.py in extremal_eig_near_ref(A, ref, low)
    245         temp = ref - np.finfo(A.dtype).eps
    246         sigma = -temp if low else temp
--> 247         ev = SA_eigsh(sigma)
    248     else:
    249         if np.isnan(ev):

~\Anaconda3\envs\qc\lib\site-packages\cvxpy\expressions\constants\constant.py in SA_eigsh(sigma)
    236 
    237     def SA_eigsh(sigma):
--> 238         return eigsh(A, k=1, sigma=sigma, return_eigenvectors=False)
    239     # Run eigsh in shift-invert mode, since we're particularly interested in finding
    240     # eigenvalues in a certain region.

~\Anaconda3\envs\qc\lib\site-packages\scipy\sparse\linalg\eigen\arpack\arpack.py in eigsh(A, k, M, sigma, which, v0, ncv, maxiter, tol, return_eigenvectors, Minv, OPinv, mode)
   1685     with _ARPACK_LOCK:
   1686         while not params.converged:
-> 1687             params.iterate()
   1688 
   1689         return params.extract(return_eigenvectors)

~\Anaconda3\envs\qc\lib\site-packages\scipy\sparse\linalg\eigen\arpack\arpack.py in iterate(self)
    569                 pass
    570             elif self.info == 1:
--> 571                 self._raise_no_convergence()
    572             else:
    573                 raise ArpackError(self.info, infodict=self.iterate_infodict)

~\Anaconda3\envs\qc\lib\site-packages\scipy\sparse\linalg\eigen\arpack\arpack.py in _raise_no_convergence(self)
    375             vec = np.zeros((self.n, 0))
    376             k_ok = 0
--> 377         raise ArpackNoConvergence(msg % (num_iter, k_ok, self.k), ev, vec)
    378 
    379 

ArpackNoConvergence: ARPACK error -1: No convergence (501 iterations, 0/1 eigenvectors converged)

Steps to reproduce the problem

from qiskit.ml.datasets import *
from qiskit.aqua.algorithms import SklearnSVM
feature_dim=2

sample_Total, training_input, test_input, class_labels = breast_cancer(
    training_size=25,
    test_size=10,
    n=feature_dim,
    plot_data=True
)

csvm = SklearnSVM(training_input,test_input).run()
print("testing success ratio: ", csvm['testing_accuracy'])

What is the expected behavior?

No error

Suggested solutions

It seems like increasing the 'training_size' to above 20 will create this error.

[EliasCombarro]

To me, this seems related to similar issues me and other users (see, for instance https://github.com/Qiskit/qiskit-aqua/issues/1402) are having with QSVM. To me, it seems to be related to non-separability in the data. In this case, with the SklearnSVM, some warnings start appearing when the training size is set to 16, which is exactly the moment in which a point is added that makes the data not linearly-separable (it is apparent by inspection from the data plot).

Maybe the solver used to obtain the SVM model is somehow expecting the data to be separable? Is there a flag to activate a "soft margin" mode or something?

[fishgoesbloop]

I ran the same training samples on the sklearn version of svm and managed to successfully train and test the model though.

Hmm, I had thought qiskit's SklearnSVM was based on it. Maybe there are slight differences?

[vbelis]

Try using the latest version of the qp_solver.py, from qiskit aqua master branch and see if it converges. As stated in #1378, a L2 regularization term was added to the SVM optimizer. Maybe the sklearn svm is soft margin by default (i.e. has L2 regularization) and the qiskit SklearnSVM until the aforementioned recent change was not. Let us know if this change fixes your issue. It fixed mine #1402