From Silence to Truth: Auditing the Knowledge Graph via Logistic Regression

By Doc. John Bob

In our previous discussion, we addressed the necessity of silence—the application of Laplace noise to protect the sanctity of the individual record. We explored how we might cloak the specific so that the general utility remains.

But now, we must traverse the bridge from protection to interrogation. It is not enough to simply secure our data; we must ensure that the structures we build upon it are just.

This brings us to the Platform-Agnostic Knowledge Graph. Imagine, if you will, a vast, interconnected map that sits above your specific tools—above your Python scripts, your R environments, your AWS or Azure containers. This graph defines the ontology of your enterprise: it links "Customer" to "Loan Application" to "Algorithm ID." It is the single source of structural truth.

Within this graph, Logistic Regression ceases to be a mere classifier. It becomes a Lens of Audit. It is the mathematical probe we insert into the graph to ask the most uncomfortable

question of all: Is this system fair?

Here lies the heart of the matter: How has this classical statistical tool historically served to confirm bias and converge our understanding of identity?

The Historical Instrument: Confirming Bias

Why, in an age of Deep Learning, do we return to Logistic Regression? Because it possesses a virtue that black-box models lack: Transparency.

Logistic regression models the probability of a binary outcome (Hired/Not Hired, Stopped/Not Stopped) while allowing us to control for confounding variables. It produces odds ratios—metrics that are not only mathematically rigorous but legally admissible.

1. The Audit of Civil Systems (Hiring, Lending, and Policing)

Since the 1970s, this tool has been the bedrock of systemic accountability.

In Employment:

Courts and regulators utilise logistic regression to determine if a protected characteristic (Race, Gender) predicts an outcome after we have controlled for legitimate qualifications.

We are looking at evidence of gender-based bias. The Knowledge Graph allows us to map the equation across every hiring model in a global organisation, regardless of the software used to deploy it.

In Financial Stewardship:

Regulators (such as the CFPB or FCA) employ this to detect "Redlining" and discriminatory interest rates. We ask: does the postcode predict the loan rejection, even when the income is identical?

In Policing and Justice:

Perhaps the most sombre application is in the analysis of custodial sentencing and "stop and search" practices. We test whether race predicts the likelihood of being searched, even when controlling for the severity of the suspected offence or prior record. Here, mathematics serves the cause of civil liberty.

2. The Fairness Audit in Machine Learning

Before we had modern fairness metrics, logistic regression was our primary sentinel.

The methodology is stark and effective:

1. Take the output of a complex, opaque Machine Learning model (e.g., "Approved").

2. Fit a logistic regression to predict that output using only demographic variables.

3. If the demographics predict the decision, the model is biased.

   
   

The Knowledge Graph enables us to automate this. We can trigger these audits continuously, ensuring that our complex models do not drift into prejudice.

The Convergence of Identity Models

The phrase "Converging Identity Models" is nuanced. In our context, it refers to the crystallisation of group dynamics within the data.

1. Inferring Latent Identity

Social scientists have long used logistic regression to infer probabilistic group membership—be it political, ethnic, or ideological.

We say these models "converge" because, as data accumulates, the coefficients stabilise. The boundaries between groups become statistically separable. When mapped onto a Knowledge Graph, these probabilities allow us to understand the composition of our user base, even when explicit labels are missing.

2. Bias-Corrected Calibration

In fairness research, we often encounter missing data (e.g., a credit dataset lacking "race" labels). We use logistic regression to estimate the probability of a user belonging to a protected group.

We then use these probabilities to:

• Adjust downstream models to remove disparate impact.

• Perform Counterfactual Fairness Tests: ("What would the decision have been if this user's gender were different?")

  
  

3. The Baseline of Convergence

Because logistic regression relies on convex optimisation, it is guaranteed to find the global minimum of the loss function. It does not get "stuck" in local optima like a neural network might. Therefore, it serves as the Baseline of Truth.

If a complex neural network cannot outperform a simple logistic regression on a task involving human behaviour, we must ask: Is the complexity adding signal, or is it merely obscuring bias?

Why This Tool Endures

In the architecture of a Platform-Agnostic Knowledge Graph, we value tools that are robust and universal. Logistic regression remains the tool of choice for specific reasons:

• Transparency

• Admissibility

• Stability

• Categorical Fit

  
  

Final Reflection

We build Knowledge Graphs to connect data, but we must use tools like Logistic Regression to understand the nature of those connections.

A graph without audit is merely a map of our own negligence. By applying these statistical rigors, we ensure that as we build the future of intelligence, we do not inadvertently reconstruct the prejudices of the past. We verify. We converge. We steward.