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Pyspark udf doesn't work while Python function works

I have a Python function:

def get_log_probability(string, transition_log_probabilities):
    string = ngrams(string, 2)
    terms = [transition_log_probabilities[bigram]
                       for bigram in string]
    log_probability = sum(terms)/len(terms) if len(terms) > 0 else sum(terms)
    return log_probability

I want to use this function for Pyspark DataFrame column with transition_log_probabilities as a constant as follows:

transition_log_probabilities = {('a', 'a'): -3.688879454113936,
('a', 'b'): -3.688879454113936,
('a', 'c'): -3.688879454113936,
('b', 'a'): -3.688879454113936,
('b', 'b'): -3.688879454113936,
('b', 'c'): -3.688879454113936,
('c', 'a'): -3.688879454113936,
('c', 'b'): -3.688879454113936,
('c', 'c'): -3.688879454113936}

So I change it to Pyspark UDF:

def get_log_prob_udf(dictionary):
    return udf(lambda string: get_log_probability(string, dictionary), FloatType())

Even though get_log_probability("abc", transition_log_probabilities) works and gives a result of -3.688879454113936 , when I apply its UDF into Pyspark as follows:

df = df \
.withColumn("string_log_probability", get_log_prob_udf(transition_log_probabilities)(col('string')))

It doesn't work and throws out the error of

An error occurred while calling o3463.showString.
: org.apache.spark.SparkException: Job aborted due to stage failure: Task 0 in stage 
182.0 failed 1 times, most recent failure: Lost task 0.0 in stage 182.0 (TID 774) 
(kubernetes.docker.internal executor driver): net.razorvine.pickle.PickleException: 
expected zero arguments for construction of ClassDict (for numpy.dtype)

Does anyone know how to solve it? Thank you very much.

Hope that's the outcome you are looking for.

df = spark.createDataFrame( [ (1, "bc"), (2, "aa"), (3, "ca") ], ["id", "string"] )
                           
from pyspark.sql import functions as F, types as T
from nltk import ngrams
                           
transition_log_probabilities = {('a', 'a'): -3.688879454113936,
        ('a', 'b'): -3.688879454113936,
        ('a', 'c'): -3.688879454113936,
        ('b', 'a'): -3.688879454113936,
        ('b', 'b'): -3.688879454113936,
        ('b', 'c'): -3.688879454113936,
        ('c', 'a'): -3.688879454113936,
        ('c', 'b'): -3.688879454113936,
        ('c', 'c'): -3.688879454113936}
    
def get_log_probability(string):
    
    string = ngrams(string, 2)
    terms = [transition_log_probabilities[bigram]
                       for bigram in string]
    log_probability = sum(terms)/len(terms) if len(terms) > 0 else sum(terms)
    return log_probability


get_log_prob_udf = udf(get_log_probability, T.FloatType())

df.withColumn('string_log_probability', get_log_prob_udf(F.col('string'))).show()
+---+------+----------------------+
| id|string|string_log_probability|
+---+------+----------------------+
|  1|    bc|            -3.6888795|
|  2|    aa|            -3.6888795|
|  3|    ca|            -3.6888795|
+---+------+----------------------+

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