def make_term_frequency_adjustments(self, df_e: DataFrame):
"""Take the outputs of 'get_scored_comparisons' and make term frequency adjustments on designated columns in the settings dictionary
Args:
df_e (DataFrame): A dataframe produced by the get_scored_comparisons method
Returns:
DataFrame: A spark dataframe including a column with term frequency adjusted match probabilities
"""
return make_adjustment_for_term_frequencies(
df_e,
self.model,
retain_adjustment_columns=True,
spark=self.spark,
)
def test_term_frequency_adjustments(spark):
settings = {
"link_type":
"dedupe_only",
"proportion_of_matches":
0.1,
"comparison_columns": [
{
"col_name":
"name",
"term_frequency_adjustments":
True,
"m_probabilities": [
0.1, # Amonst matches, 10% are have typose
0.9 # The reamining 90% have a match
],
"u_probabilities": [
4 /
5, # Among non matches, 80% of the time there's no match
1 /
5 # But 20% of the time names 'collide' WE WANT THESE U PROBABILITIES TO BE DEPENDENT ON NAME.
],
},
{
"col_name": "cat_12",
"m_probabilities": [0.05, 0.95],
"u_probabilities": [11 / 12, 1 / 12],
},
{
"col_name": "cat_20",
"m_probabilities": [0.2, 0.8],
"u_probabilities": [19 / 20, 1 / 20],
}
],
"em_convergence":
0.001
}
from string import ascii_letters
import statistics
import random
from splink.settings import complete_settings_dict
settings = complete_settings_dict(settings, spark="supress_warnings")
def is_match(settings):
p = settings["proportion_of_matches"]
return random.choices([0, 1], [1 - p, p])[0]
def get_row_portion(match, comparison_col, skew="auto"):
# Problem is that at the moment we're guaranteeing that a match on john is just as likely to be a match as a match on james
# What we want is to generate more 'collisions' for john than robin i.e. if it's a non match, we want more gamma = 1 on name for john
if match:
gamma_pdist = comparison_col["m_probabilities"]
else:
gamma_pdist = comparison_col["u_probabilities"]
# To decide whether gamma = 0 or 1 in the case of skew, we first need to decide on what value the left hand value column will take (well, what probability it has of selection)
# How many distinct values should be choose?
num_values = int(round(1 / comparison_col["u_probabilities"][1]))
if skew == "auto":
skew = comparison_col["term_frequency_adjustments"]
if skew:
prob_dist = range(
1, num_values +
1)[::-1] # a most freqent, last value least frequent
# Normalise
prob_dist = [p / sum(prob_dist) for p in prob_dist]
index_of_value = random.choices(range(num_values), prob_dist)[0]
if not match: # If it's a u probability
this_prob = prob_dist[index_of_value]
gamma_pdist = [1 - this_prob, this_prob]
else:
prob_dist = [1 / num_values] * num_values
index_of_value = random.choices(range(num_values), prob_dist)[0]
levels = comparison_col["num_levels"]
gamma = random.choices(range(levels), gamma_pdist)[0]
values = ascii_letters[:26]
if num_values > 26:
values = [
a + b for a in ascii_letters[:26] for b in ascii_letters[:26]
] #aa, ab etc
values = values[:num_values]
if gamma == 1:
value_1 = values[index_of_value]
value_2 = value_1
if gamma == 0:
value_1 = values[index_of_value]
same_value = True
while same_value:
value_2 = random.choices(values, prob_dist)[0]
if value_1 != value_2:
same_value = False
cname = comparison_col["col_name"]
return {
f"{cname}_l": value_1,
f"{cname}_r": value_2,
f"gamma_{cname}": gamma
}
import uuid
rows = []
for uid in range(100000):
m = is_match(settings)
row = {
"unique_id_l": str(uuid.uuid4()),
"unique_id_r": str(uuid.uuid4()),
"match": m
}
for cc in settings["comparison_columns"]:
row_portion = get_row_portion(m, cc)
row = {**row, **row_portion}
rows.append(row)
all_rows = pd.DataFrame(rows)
df_gammas = spark.createDataFrame(all_rows)
settings["comparison_columns"][1]["term_frequency_adjustments"] = True
from splink import Splink
from splink.params import Params
from splink.iterate import iterate
from splink.term_frequencies import make_adjustment_for_term_frequencies
# We have table of gammas - need to work from there within splink
params = Params(settings, spark)
df_e = iterate(df_gammas, params, settings, spark, compute_ll=False)
df_e_adj = make_adjustment_for_term_frequencies(
df_e, params, settings, retain_adjustment_columns=True, spark=spark)
df_e_adj.createOrReplaceTempView("df_e_adj")
sql = """
select name_l, name_tf_adj, count(*)
from df_e_adj
where name_l = name_r
group by name_l, name_tf_adj
order by name_l
"""
df = spark.sql(sql).toPandas()
df = df.set_index("name_l")
df_dict = df.to_dict(orient='index')
assert df_dict['a']["name_tf_adj"] < 0.5
assert df_dict['e']["name_tf_adj"] > 0.5
assert df_dict['e'][
"name_tf_adj"] > 0.6 #Arbitrary numbers, but we do expect a big uplift here
assert df_dict['e'][
"name_tf_adj"] < 0.95 #Arbitrary numbers, but we do expect a big uplift here
df_e_adj.createOrReplaceTempView("df_e_adj")
sql = """
select cat_12_l, cat_12_tf_adj, count(*) as count
from df_e_adj
where cat_12_l = cat_12_r
group by cat_12_l, cat_12_tf_adj
order by cat_12_l
"""
spark.sql(sql).toPandas()
df = spark.sql(sql).toPandas()
assert df["cat_12_tf_adj"].max(
) < 0.55 # Keep these loose because when generating random data anything can happen!
assert df["cat_12_tf_adj"].min() > 0.45
# Test adjustments applied coorrectly when there is one
df_e_adj.createOrReplaceTempView("df_e_adj")
sql = """
select *
from df_e_adj
where name_l = name_r and cat_12_l != cat_12_r
limit 1
"""
df = spark.sql(sql).toPandas()
df_dict = df.loc[0, :].to_dict()
def bayes(p1, p2):
return p1 * p2 / (p1 * p2 + (1 - p1) * (1 - p2))
assert df_dict["tf_adjusted_match_prob"] == pytest.approx(
bayes(df_dict["match_probability"], df_dict["name_tf_adj"]))
# Test adjustments applied coorrectly when there are multiple
df_e_adj.createOrReplaceTempView("df_e_adj")
sql = """
select *
from df_e_adj
where name_l = name_r and cat_12_l = cat_12_r
limit 1
"""
df = spark.sql(sql).toPandas()
df_dict = df.loc[0, :].to_dict()
double_b = bayes(
bayes(df_dict["match_probability"], df_dict["name_tf_adj"]),
df_dict["cat_12_tf_adj"])
assert df_dict["tf_adjusted_match_prob"] == pytest.approx(double_b)
def test_term_frequency_adjustments(spark):
# The strategy is going to be to create a fake dataframe
# where we have different levels to model frequency imbalance
# gamma=3 is where name matches and name is robin (unusual name)
# gamma=2 is where name matches and name is matt (normal name)
# gamma=1 is where name matches and name is john (v common name)
# We simulate the term frequency imbalance
# by pooling this together, setting all gamma >0
# to equal 1
# We then expect that
# term frequency adjustments should adjust up the
# robins but adjust down the johns
# We also expect that the tf adjusted match probability should be more accurate
forename_probs = _probabilities_from_freqs([3, 2, 1])
surname_probs = _probabilities_from_freqs([10, 5, 1])
settings_true = {
"link_type":
"dedupe_only",
"proportion_of_matches":
0.5,
"comparison_columns": [
{
"col_name": "forename",
"term_frequency_adjustments": True,
"m_probabilities": forename_probs["m_probabilities"],
"u_probabilities": forename_probs["u_probabilities"],
"num_levels": 4,
},
{
"col_name": "surname",
"term_frequency_adjustments": True,
"m_probabilities": surname_probs["m_probabilities"],
"u_probabilities": surname_probs["u_probabilities"],
"num_levels": 4,
},
{
"col_name": "cat_20",
"m_probabilities": [0.2, 0.8],
"u_probabilities": [19 / 20, 1 / 20],
},
],
}
settings_true = complete_settings_dict(settings_true, spark)
df = generate_df_gammas_random(10000, settings_true)
# Create new binary columns that binarise the more granular gammas to 0 and 1
df["gamma_forename_binary"] = df["gamma_forename"].where(
df["gamma_forename"] == 0, 1)
df["gamma_surname_binary"] = df["gamma_surname"].where(
df["gamma_surname"] == 0, 1)
# Populate non matches with random value
# Then assign left and right values ased on the gamma values
df["forename_binary_l"] = df["unique_id_l"]
df["forename_binary_r"] = df["unique_id_r"]
f1 = df["gamma_forename"] == 3
df.loc[f1, "forename_binary_l"] = "Robin"
df.loc[f1, "forename_binary_r"] = "Robin"
f1 = df["gamma_forename"] == 2
df.loc[f1, "forename_binary_l"] = "Matt"
df.loc[f1, "forename_binary_r"] = "Matt"
f1 = df["gamma_forename"] == 1
df.loc[f1, "forename_binary_l"] = "John"
df.loc[f1, "forename_binary_r"] = "John"
# Populate non matches with random value
df["surname_binary_l"] = df["unique_id_l"]
df["surname_binary_r"] = df["unique_id_r"]
f1 = df["gamma_surname"] == 3
df.loc[f1, "surname_binary_l"] = "Linacre"
df.loc[f1, "surname_binary_r"] = "Linacre"
f1 = df["gamma_surname"] == 2
df.loc[f1, "surname_binary_l"] = "Hughes"
df.loc[f1, "surname_binary_r"] = "Hughes"
f1 = df["gamma_surname"] == 1
df.loc[f1, "surname_binary_l"] = "Smith"
df.loc[f1, "surname_binary_r"] = "Smith"
# cat20
df["cat_20_l"] = df["unique_id_l"]
df["cat_20_r"] = df["unique_id_r"]
f1 = df["gamma_cat_20"] == 1
df.loc[f1, "cat_20_l"] = "a"
df.loc[f1, "cat_20_r"] = "a"
df = add_match_prob(df, settings_true)
df["match_probability"] = df["true_match_probability_l"]
df_e = spark.createDataFrame(df)
def four_to_two(probs):
return [probs[0], sum(probs[1:])]
settings_binary = {
"link_type":
"dedupe_only",
"proportion_of_matches":
0.5,
"comparison_columns": [
{
"col_name": "forename_binary",
"term_frequency_adjustments": True,
"num_levels": 2,
"m_probabilities":
four_to_two(forename_probs["m_probabilities"]),
"u_probabilities":
four_to_two(forename_probs["u_probabilities"]),
},
{
"col_name": "surname_binary",
"term_frequency_adjustments": True,
"num_levels": 2,
"m_probabilities":
four_to_two(surname_probs["m_probabilities"]),
"u_probabilities":
four_to_two(surname_probs["u_probabilities"]),
},
{
"col_name": "cat_20",
"m_probabilities": [0.2, 0.8],
"u_probabilities": [19 / 20, 1 / 20],
},
],
"retain_intermediate_calculation_columns":
True,
"max_iterations":
0,
"additional_columns_to_retain": ["true_match_probability"],
}
# Can't use linker = Splink() because we have df_gammas, not df
settings_binary = complete_settings_dict(settings_binary, spark)
model = Model(settings_binary, spark)
df_e = iterate(df_e, model, spark)
df_e = make_adjustment_for_term_frequencies(df_e,
model,
spark,
retain_adjustment_columns=True)
df = df_e.toPandas()
#########
# Tests start here
#########
# Test that overall square error is better for tf adjusted match prob
df["e1"] = (df["match_probability"] - df["true_match_probability_l"])**2
df["e2"] = (df["tf_adjusted_match_prob"] -
df["true_match_probability_l"])**2
assert df["e1"].sum() > df["e2"].sum()
# We expect Johns to be adjusted down...
f1 = df["forename_binary_l"] == "John"
df_filtered = df[f1]
adj = df_filtered["forename_binary_tf_adj"].mean()
assert adj < 0.5
# And Robins to be adjusted up
f1 = df["forename_binary_l"] == "Robin"
df_filtered = df[f1]
adj = df_filtered["forename_binary_tf_adj"].mean()
assert adj > 0.5
# We expect Smiths to be adjusted down...
f1 = df["surname_binary_l"] == "Smith"
df_filtered = df[f1]
adj = df_filtered["surname_binary_tf_adj"].mean()
assert adj < 0.5
# And Linacres to be adjusted up
f1 = df["surname_binary_l"] == "Linacre"
df_filtered = df[f1]
adj = df_filtered["surname_binary_tf_adj"].mean()
assert adj > 0.5
# Check adjustments are applied correctly
f1 = df["forename_binary_l"] == "Robin"
f2 = df["surname_binary_l"] == "Linacre"
df_filtered = df[f1 & f2]
row = df_filtered.head(1).to_dict(orient="records")[0]
prior = row["match_probability"]
posterior = row["tf_adjusted_match_prob"]
b1 = row["forename_binary_tf_adj"]
b2 = row["surname_binary_tf_adj"]
expected_post = (prior * b1 * b2 / (prior * b1 * b2 + (1 - prior) *
(1 - b1) * (1 - b2)))
assert posterior == pytest.approx(expected_post)
# We expect match probability to be equal to tf_adjusted match probability in cases where surname and forename don't match
f1 = df["surname_binary_l"] != df["surname_binary_r"]
f2 = df["forename_binary_l"] != df["forename_binary_r"]
df_filtered = df[f1 & f2]
sum_difference = (df_filtered["tf_adjusted_match_prob"] -
df_filtered["match_probability"]).sum()
assert 0 == pytest.approx(sum_difference)