Distributional sentiment modeling and anomaly detection for consumer complaint assessment
Authors: Peiheng Gao, Chen Yang, Shimin Zhang
Organizations: School of Mathematical and Statistical Sciences, Western University, London, ON N6A 3K7, Canada · Department of Population Health Science and Policy, Icahn School of Medicine at Mount Sinai, New York, New York 10029, USA · Institute for Health Care Delivery Science, Icahn School of Medicine at Mount Sinai, New York, New York 10029, USA · Asian Institute of Digital Finance, National University of Singapore, Singapore, 119077
Sentiment analysis is a common tool for converting unstructured text into quantitative signals in finance and risk management. Yet most applications reduce the output to a discrete polarity label or a single predictive feature, overlooking the distributional structure of sentiment intensity in consumer complaint narratives. In this paper we treat negative sentiment in consumer complaints as a bounded continuous variable and study its full distribution rather than a single label. We score each narrative with a transformer classifier, model the scores with Beta distributions, and compare the fitted distributions of meritorious and non-meritorious complaints through the Kullback Leibler divergence and the squared Hellinger distance. The fitted distributions are then linked with dollar amounts and company response outcomes to construct anomaly diagnostics that flag complaints whose textual severity is inconsistent with the recorded relief. We find that the two groups have strongly overlapping distributions, so negative sentiment intensity is not a sharp classifier of outcomes on its own; combined with monetary and categorical attributes, it isolates unusually severe complaints for operational risk monitoring. Treating sentiment analysis as continuous distributional measurement, this study links sentiment extraction, bounded response modeling, and anomaly detection in a unified framework for consumer complaint assessment.
Figures & tables
Step
Records
After date restriction
2,280,111
Credit reporting product category
1,662,544
At least one detected dollar amount
222,261
Average dollar amount in 1≤Ai<10,000
181,316
Meritorious
85,501
Non-meritorious
95,815
Table 2.1 : Data cleaning steps and record counts.
Figure 2.1 : Distribution of average dollar amounts by complaint outcome.
Require
1. Cleaned complaint narrative corpus Cclean .
2. Complaint outcome labels Yi∈{0,1} , where Yi=1 denotes meritorious.
3. Extracted average dollar amounts Ai satisfying 1≤Ai<10,000 .
Compute distributional sentiment and anomaly diagnostics
1. Apply a transformer based sentiment classifier to each narrative ci .
2. Extract the negative sentiment probability si=pi,neg .
Algorithm 3.1 : Algorithmic summary of the distributional sentiment modeling.
Figure 4.1 : Negative sentiment score distributions and fitted Beta distributions by complaint outcome.
Sample
N
α^
β^
Fitted mean
Fitted var.
Sample mean
Sample var.
Full sample
181,316
1.473
2.296
0.391
0.050
0.382
0.052
Meritorious
85,501
1.593
2.648
0.376
0.045
0.367
0.046
Non-meritorious
95,815
1.394
2.058
0.404
0.054
0.395
0.057
Table 4.1 : Beta fits for negative sentiment scores in the cleaned sample and by outcome group.
Figure 4.2 : QQ diagnostics for the fitted Beta models of negative sentiment scores. Each panel plots empirical against fitted Beta quantiles for the full sample and the two outcome groups; the red line is the 45∘ reference.
Metric
Value
DKL(F1∥F0)
0.0168
DKL(F0∥F1)
0.0202
Symmetric KL average
0.0185
Squared Hellinger distance ( H2 )
0.0046
Table 4.2 : Distributional separation between the fitted Beta sentiment distributions. F1 and F0 denote the meritorious and non-meritorious fits.
Figure 4.3 : Overlap between the fitted Beta densities for meritorious and non-meritorious complaints.
Observed outcome
Sentiment region
Diagnostic interpretation
Meritorious
si∗<0.0666 or si∗>0.5392
More consistent with the non-meritorious density
Non-meritorious
0.0666<si∗<0.5392
More consistent with the meritorious density
Table 4.3 : Anomaly regions implied by the fitted Beta distributions
Diagnostic
Threshold
Meritorious
Non-meritorious
Total
Total rate
Outcome inconsistency
η=0
20,572
66,754
87,326
48.16%
Outcome inconsistency
η=0.01
19,546
65,422
84,968
46.86%
Outcome inconsistency
η=0.05
15,518
58,179
73,697
40.65%
Outcome inconsistency
η=0.10
12,081
39,802
51,883
28.61%
Tail anomaly
τ=0.01
1,257
795
2,052
1.13%
Tail anomaly
τ=0.05
4,412
4,561
8,973
4.95%
Table 4.4 : Anomaly diagnostics on the cleaned sample: baseline and threshold sensitivity.