Drift Detection in categorical variables of high cardinality (10000+) - machine-learning

Question

I am trying to solve a drift detection problem where I have to find out the drift in high cardinality (10000+) categorical variables such as ip_address, zipcode, cities. I have data points in the order of millions. I have tried the following methods -
chi square test from evidently python package https://github.com/evidentlyai/evidently/blob/main/src/evidently/analyzers/stattests/chisquare_stattest.py
maximum mean discrepancy test with GaussianRBF Kernel from alibi-detecthttps://github.com/SeldonIO/alibi-detect/blob/master/alibi_detect/cd/mmd.py
I have faced the below problems while applying these methods on my data
In chi square test, there is a constraint that we should have same set of categories in both training and inference datasets. This is highly unlikely for the features like ip address and zipcode. There are some data points which are available in training data but not in inference data. For such data points, I don't get observed frequency. I can assume their frequency as 0 as a work around.
But there are data points which have been newly introduced in the inference dataset and don't have their presence in the training dataset. So I would not be able to find out their expected frequency from training dataset. For such data points, I would have 0 in the denominator of the chi square formula and test statistic will be NaN. As a workaround, I can assume their minimum expected frequency equal to 1. But I wonder whether this is the correct way to approach the drift detection.
Moreover, the larger problem is the following -
The nature of these categorical feature variables is such that they can take any possible value from a very very large set of values. I don't have any control over these features taking a value. The users of the system can login from any IP address and from any zipcode. This becomes very difficult to find out the real drift in the data. Methods like chi square test can always give the significant result for such features. Is their any method which can handle such features for drift detection which takes into consideration the high cardinality and the aforementioned nature of the data.
In MMD test with GaussianRBF kernel, we use to calculate pairwise distance between two vectors. X is my training dataset which is having 15 millions records and 10 features. and Y is my inference dataset which is having 10 millions records and 10 features. Now when I perform MMD test on these datasets. I get the following -
a) K_XX = within similarity of X
b) K_YY = within similarity of Y
c) K_XY = cross similarity between X and Y
K_XX will try to generate a matrix (15 million X 15 million). This gives me "ResourceExhaustedError".
ResourceExhaustedError Traceback (most recent call last)
<command-574623167633967> in <module>
1 from alibi_detect.cd import MMDDrift
---> 2 detector = MMDDrift(x_ref=X, backend='tensorflow')
3 res = detector.predict(x=Y)
/databricks/python/lib/python3.8/site-packages/alibi_detect/utils/warnings.py in wrapper(*args, **kwargs)
15 def wrapper(*args, **kwargs):
16 _rename_kwargs(f.__name__, kwargs, aliases)
---> 17 return f(*args, **kwargs)
18 return wrapper
19 return deco
/databricks/python/lib/python3.8/site-packages/alibi_detect/cd/mmd.py in __init__(self, x_ref, backend, p_val, x_ref_preprocessed, preprocess_at_init, update_x_ref, preprocess_fn, kernel, sigma, configure_kernel_from_x_ref, n_permutations, device, input_shape, data_type)
101 if backend == 'tensorflow' and has_tensorflow:
102 kwargs.pop('device', None)
--> 103 self._detector = MMDDriftTF(*args, **kwargs) # type: ignore
104 else:
105 self._detector = MMDDriftTorch(*args, **kwargs) # type: ignore
/databricks/python/lib/python3.8/site-packages/alibi_detect/utils/warnings.py in wrapper(*args, **kwargs)
15 def wrapper(*args, **kwargs):
16 _rename_kwargs(f.__name__, kwargs, aliases)
---> 17 return f(*args, **kwargs)
18 return wrapper
19 return deco
/databricks/python/lib/python3.8/site-packages/alibi_detect/cd/tensorflow/mmd.py in __init__(self, x_ref, p_val, x_ref_preprocessed, preprocess_at_init, update_x_ref, preprocess_fn, kernel, sigma, configure_kernel_from_x_ref, n_permutations, input_shape, data_type)
86 # compute kernel matrix for the reference data
87 if self.infer_sigma or isinstance(sigma, tf.Tensor):
---> 88 self.k_xx = self.kernel(self.x_ref, self.x_ref, infer_sigma=self.infer_sigma)
89 self.infer_sigma = False
90 else:
/databricks/python/lib/python3.8/site-packages/keras/utils/traceback_utils.py in error_handler(*args, **kwargs)
65 except Exception as e: # pylint: disable=broad-except
66 filtered_tb = _process_traceback_frames(e.__traceback__)
---> 67 raise e.with_traceback(filtered_tb) from None
68 finally:
69 del filtered_tb
/databricks/python/lib/python3.8/site-packages/alibi_detect/utils/tensorflow/kernels.py in call(self, x, y, infer_sigma)
75 y = tf.cast(y, x.dtype)
76 x, y = tf.reshape(x, (x.shape[0], -1)), tf.reshape(y, (y.shape[0], -1)) # flatten
---> 77 dist = distance.squared_pairwise_distance(x, y) # [Nx, Ny]
78
79 if infer_sigma or self.init_required:
/databricks/python/lib/python3.8/site-packages/alibi_detect/utils/tensorflow/distance.py in squared_pairwise_distance(x, y, a_min, a_max)
28 x2 = tf.reduce_sum(x ** 2, axis=-1, keepdims=True)
29 y2 = tf.reduce_sum(y ** 2, axis=-1, keepdims=True)
---> 30 dist = x2 + tf.transpose(y2, (1, 0)) - 2. * x # tf.transpose(y, (1, 0))
31 return tf.clip_by_value(dist, a_min, a_max)
32
ResourceExhaustedError: Exception encountered when calling layer "gaussian_rbf_20" (type GaussianRBF).
OOM when allocating tensor with shape[14335347,14335347] and type float on /job:localhost/replica:0/task:0/device:CPU:0 by allocator cpu [Op:AddV2]
The error seems pretty obvious given the quadratic complexity of MMD. Is their any way to mitigate this issue given the constraints that number of records in millions and high cardinality of categorical features.