🔭 Explore Predictions

Focus question: How does my model’s behavior change across different input conditions?

1 Global Prediction Summaries

Global Predictions by Inputs

(Predictive space by input variables)

Predictive space by input variables

What it is: A grid of partial dependence plots that marginalize over other inputs to show the model’s average predicted output: 1D PDPs per input (diagonal) and 2D PDPs for input pairs (lower triangle).

How to use it:

• Diagonal (1D PDP):
• • **Continuous** inputs → line for mean PDP with a shaded ±1σ band hidden in this mean-only matrix (your 1D function draws the band; in mean mode it reflects local variation across the marginalization set).
• • **Categorical/Chemical/Discrete/Temporal** inputs → bar chart with error bars; bar height is the mean PDP at each level.
• Lower triangle (2D PDP):
• • **Continuous–Continuous** → contour/heatmap (Viridis) of mean predictions; ridges/peaks indicate favorable regions; a colorbar encodes the output level.
• • **Categorical–Categorical** → heatmap over level combinations; bright cells mark promising pairs.
• • **Mixed (Categorical×Continuous)** → heatmap with categories on one axis and the continuous grid on the other; compare rows/columns to spot category-dependent trends.
• Overlays (when provided): white circles = training data density; red stars = recommended experiments.
• Use consistent color scale across cells (global zmin/zmax) to make intensities comparable.

Why it matters:

• Reveals **global response structure**—monotonic trends, thresholds, plateaus, and interactions—to guide constraints and target regions before BO.
• Highlights **robust operating windows** (broad high plateaus) versus sharp spikes that may be fragile.
• Supports **feature prioritization**: steep gradients or strong contrasts indicate influential inputs.

Limitations:

• **Marginalization bias**: PDPs assume independence while averaging; with correlated inputs, surfaces can be misleading.
• **Extrapolation**: grid edges may extend beyond data support—interpret faint/empty regions cautiously.
• **Resolution & smoothing**: coarse grids can alias features; too-smooth contours can hide narrow optima.
• **Category imbalance** can skew bar/heatmap expectations; check sample counts per level.

(a) output_1

(b) output_2

Figure 1: Partial dependence matrix summarizing the model’s mean prediction as inputs vary, with 1D PDPs on the diagonal and 2D PDPs in the lower triangle. Handles mixed variable types: continuous (lines/contours), categorical/chemical/discrete/temporal (bars/heatmaps). Overlays may include training points and recommended experiments.

Global Uncertainty by Inputs

(Uncertain regions by input variables)

Uncertain regions by input variables

What it is: A PDP matrix computed on **uncertainty** instead of the mean: diagonal 1D PDPs plot uncertainty vs. each input; lower-triangle 2D PDPs plot uncertainty over input pairs using heatmaps/contours (continuous–continuous), categorical heatmaps (categorical–categorical), and mixed heatmaps (categorical×continuous).

How to use it:

• Diagonal (1D):
• • **Continuous** → line for uncertainty magnitude (e.g., posterior std); look for peaks/shoulders indicating inputs where the model is least confident.
• • **Categorical/Chemical/Discrete/Temporal** → bars with error bars (if provided) showing uncertainty per level.
• Lower triangle (2D):
• • **Continuous–Continuous** → contour/heatmap where brighter/higher values indicate **greater uncertainty**; target these for exploration.
• • **Categorical–Categorical** → heatmap across level pairs to spot poorly known combinations.
• • **Mixed** → heatmap with categories vs. continuous grid to see category-specific uncertainty bands.
• Overlays: training points (white) reveal where data already exist; red stars show recommendations—ideally balancing **high mean** (from the mean PDP matrix) and **high uncertainty** here.
• Keep a **global uncertainty scale** across cells (zmin/zmax from global ranges) to compare magnitude between plots.

Why it matters:

• Directly supports **exploration** in BO by exposing **information-rich** regions (high uncertainty) that would most reduce posterior variance.
• Prevents premature **over-exploitation**, especially when mean PDPs suggest attractive but poorly known areas.
• Helps design **balanced batches**: mix high-mean and high-uncertainty selections across inputs.

Limitations:

• **Uncertainty definition** matters: use **predictive** uncertainty (epistemic + aleatoric) if your reports/intervals are predictive; epistemic-only maps can bias selection.
• Same **correlation/marginalization** caveats as mean PDPs; uncertainty can be inflated in low-support regions.
• Small datasets yield **noisy** uncertainty surfaces; consider smoothing or showing confidence bands around uncertainty estimates.
• For temporal/discrete axes, stepwise patterns are expected and do not imply abrupt physics.

(a) output_1

(b) output_2

Figure 2: Partial dependence matrix of model predictive uncertainty (e.g., posterior standard deviation or interval width). 1D PDPs show uncertainty vs. each input; 2D PDPs show uncertainty surfaces for input pairs. Overlays (training data, recommended points) help identify informative regions for exploration.

Compare Multiple Variables

(Visualizing Input-Output Predictive Relationships)

Visualizing Input-Output Predictive Relationships

(a) output_1

(b) output_2

Figure 3: Parallel coordinates plot showing relationships between input variables and outputs. It helps identify patterns and trade-offs across multiple variables, aiding in decision-making for optimization.