Glossary

Individual Conditional Expectation (ICE) Plots

A visualization method that plots the relationship between a feature and the model's prediction for each individual instance, disaggregating the average effect shown in a Partial Dependence Plot to reveal heterogeneous relationships.

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MODEL INTERPRETABILITY

What is Individual Conditional Expectation (ICE) Plots?

ICE plots disaggregate the average effect shown in a Partial Dependence Plot to reveal heterogeneous relationships between a feature and the model's prediction for each individual instance.

An Individual Conditional Expectation (ICE) plot is a visualization method that plots the relationship between a selected feature and a model's prediction for every single instance in a dataset, generating one line per observation. Unlike a Partial Dependence Plot (PDP), which averages these lines into a single global effect, ICE plots expose heterogeneous relationships and interaction effects that the averaging process would otherwise obscure, making them essential for auditing black-box models where a uniform trend cannot be assumed.

In financial fraud detection, ICE plots are critical for identifying subpopulations where a feature's effect reverses direction—for example, a transaction amount increase might lower risk for one customer segment while elevating it for another. Analysts use centered ICE plots, where all curves are anchored to zero at a specific feature value, to visually isolate the differential effect of a feature change across instances, directly supporting the generation of precise adverse action reason codes required by model governance frameworks.

Disaggregating Model Behavior

Key Characteristics of ICE Plots

Individual Conditional Expectation (ICE) plots reveal heterogeneous relationships between a feature and the model's prediction for each instance, exposing interactions that Partial Dependence Plots (PDPs) average away.

Instance-Level Disaggregation

Unlike a PDP which shows a single average marginal effect, an ICE plot draws one line per instance. This visual disaggregation reveals whether all instances respond similarly to a feature change or if distinct subgroups exhibit divergent behaviors, a critical capability for identifying heterogeneous treatment effects in fraud scoring models.

Interaction Detection

ICE plots are a primary visual diagnostic for feature interactions. When the curves for different instances have varying slopes or directions, it signals that the effect of the plotted feature depends on the values of other features. For example, an ICE plot might reveal that increasing transaction amount raises fraud probability for new accounts but lowers it for established, high-net-worth clients.

Centered ICE (c-ICE)

A common variant that anchors all curves to zero at a chosen point, removing level differences to focus purely on marginal effects. By subtracting each instance's prediction at the anchor point, c-ICE makes it easier to compare the shape and slope of the response function across a heterogeneous population, highlighting divergent risk trajectories.

Derivative ICE (d-ICE)

An extension that plots the partial derivative of the prediction function with respect to the feature of interest for each instance. d-ICE directly visualizes where and for whom a feature is most influential, revealing threshold effects and non-linearities in the model's decision boundary that are critical for auditing fraud detection logic.

Computational Mechanism

To generate an ICE plot for a feature X_s:

Hold all other features constant for a specific instance
Iteratively replace the value of X_s with a sequence of grid values
Record the model's prediction at each grid point
Repeat for every instance in the dataset This brute-force approach reveals the conditional prediction surface for each individual.

Limitations in Practice

ICE plots suffer from visual clutter with large datasets, requiring downsampling or clustering of curves. More critically, they extrapolate into regions of the feature space with no empirical support, generating unrealistic synthetic instances when correlated features are held fixed. Accumulated Local Effects (ALE) plots address this correlation bias.

VISUALIZATION COMPARISON

ICE Plots vs. Partial Dependence Plots (PDP)

A technical comparison of Individual Conditional Expectation plots and Partial Dependence Plots for interpreting machine learning model behavior.

Feature	ICE Plots	Partial Dependence Plots (PDP)
Visualization Granularity	Instance-level: One line per observation	Global average: One line per feature
Heterogeneous Effects Detection
Reveals Interaction Effects
Computational Cost	Higher: N lines for N instances	Lower: Single aggregated curve
Susceptible to Correlated Feature Bias
Interpretability for Non-Technical Audiences	Lower: Visual clutter with many instances	Higher: Clean, single trend line
Centered Variant Available	c-ICE centers all lines at origin
Primary Use Case	Discovering subpopulations and interactions	Summarizing average marginal effect

UNDERSTANDING ICE PLOTS

Frequently Asked Questions

Clear answers to common questions about Individual Conditional Expectation plots and their role in explaining machine learning model predictions.

An Individual Conditional Expectation (ICE) plot is a visualization method that displays the functional relationship between a selected input feature and the model's predicted outcome for each individual instance in a dataset. Unlike a Partial Dependence Plot (PDP), which shows a single average effect, an ICE plot draws one line per instance, revealing heterogeneous relationships and interactions that the average may obscure. Each line represents how the prediction for one specific data point changes as the feature of interest is varied while holding all other features constant at their observed values. This disaggregation makes ICE plots essential for detecting when a model's behavior differs across subgroups, such as when a transaction amount feature affects fraud probability differently for new versus established accounts.

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Related Terms

ICE plots are a foundational disaggregation technique. Master these complementary methods to build a complete model explanation toolkit for high-stakes fraud auditing.

Partial Dependence Plots (PDP)

The global, averaged counterpart to ICE plots. While ICE shows one line per instance, a PDP displays the average marginal effect of a feature on the predicted outcome. In fraud detection, a PDP might show that increasing transaction amount generally increases risk, but it masks heterogeneity—a critical flaw when some accounts have inverted relationships. ICE plots reveal this by un-averaging the PDP.

EXPLORE

Centered ICE Plots (c-ICE)

A refinement of standard ICE plots that anchors all curves at a common origin, typically the feature's minimum value. This removes level effects and focuses purely on the differential prediction change for each instance. For fraud analysts, c-ICE makes it easier to spot instances where a feature's marginal effect diverges from the cohort—crucial for identifying accounts with anomalous risk sensitivity.

Derivative ICE Plots (d-ICE)

Plots the instantaneous rate of change of the prediction with respect to the feature for each instance. This reveals where and how quickly a feature's influence changes. In fraud models, d-ICE can pinpoint transaction amount thresholds where risk scores suddenly spike for specific account segments, uncovering non-linear decision boundaries that PDPs completely smooth over.

Accumulated Local Effects (ALE)

An unbiased alternative to PDP that correctly handles correlated features—a pervasive problem in financial data where income and transaction amount are linked. ALE calculates local differences in predictions over conditional distributions rather than marginal ones. When features are correlated, ICE plots inherit PDP's extrapolation bias; ALE provides the statistically valid complement for robust regulatory reporting.

SHAP Dependence Plots

Combines SHAP values with feature visualization to show how a feature's attribution changes with its value, with automatic coloring by an interacting feature. Unlike ICE plots, which show prediction changes, SHAP dependence plots show additive feature contributions grounded in game theory. For fraud model auditing, this provides the mathematically rigorous attribution that ICE's visual disaggregation lacks.

Feature Interaction (H-Statistic)

Quantifies the degree of interaction between features using the Friedman's H-statistic, measuring how much of a model's prediction variance comes from joint feature effects. If ICE curves for different instances cross or diverge significantly, it signals strong interactions. Computing the H-statistic alongside ICE plots provides a numerical validation of the visual heterogeneity observed, strengthening audit documentation.

About the author

Prasad Kumkar

CEO & MD, Inference Systems

Prasad Kumkar is the CEO & MD of Inference Systems and writes about AI systems architecture, LLM infrastructure, model serving, evaluation, and production deployment. Over 5+ years, he has worked across computer vision models, L5 autonomous vehicle systems, and LLM research, with a focus on taking complex AI ideas into real-world engineering systems.

His work and writing cover AI systems, large language models, AI agents, multimodal systems, autonomous systems, inference optimization, RAG, evaluation, and production AI engineering.

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