Introduction to Pilz¶
What is Pilz?¶
Pilz (German for "mushroom" / "fungus") is a machine learning library for classification tasks. The name reflects its nature: like mushrooms are neither plants nor animals, Pilz is neither a traditional decision tree nor a neural network - it's something in between that captures the best of both worlds.
flowchart TB
subgraph Nature
P[Plants] --> M[Mushrooms/Fungi]
A[Animals] --> M
end
subgraph ML
NN[Neural Networks] --> Pilz[Pilz]
DT[Decision Trees] --> Pilz
end
style M fill:#ccffcc
style Pilz fill:#e0f0ff```
Unlike traditional ML tools that create "black box" models, Pilz generates **readable SQL rules** that you can directly deploy to your database.
The core innovation of Pilz is its ability to handle **feature correlations naturally** through multi-dimensional cuts.
## The Core Idea: Multi-Dimensional Feature Cuts
### The Problem with Traditional Approaches
Traditional machine learning approaches have limitations:
```mermaid
flowchart TD
subgraph "Traditional Tree"
A[Data] --> B{Split on X?}
B -->|Yes| C[X is high]
B -->|No| D{X is low}
D --> E{Y split?}
end```
mermaid
flowchart TD
subgraph "Traditional Tree"
A[Data] --> B{Split on X?}
B -->|Yes| C[X is high]
B -->|No| D{X is low}
D --> E{Y split?}
end
A -->|"Problem"| P[Correlation: X + Y togetherpredict better than alone]
style P fill:#ffcccc```
### Pilz's Solution: Cut in Multiple Dimensions
Pilz can cut on **feature combinations** directly:
```mermaid
flowchart TD
subgraph "Pilz Multi-Dimensional Cut"
A[Data] --> B{Split on X AND Ycombination?}
B -->|"X=low, Y=low"| C[Group 1]
B -->|"X=low, Y=high"| D[Group 2]
B -->|"X=high, Y=low"| E[Group 3]
B -->|"X=high, Y=high"| F[Group 4]
end
style B fill:#ccffcc```
This naturally captures corre
```mermaid
flowchart TD
subgraph "Pilz Multi-Dimensional Cut"
A[Data] --> B{Split on X AND Ycombination?}
B -->|"X=low, Y=low"| C[Group 1]
B -->|"X=low, Y=high"| D[Group 2]
B -->|"X=high, Y=low"| E[Group 3]
B -->|"X=high, Y=high"| F[Group 4]
end
style B fill:#ccffcc```
: A, BBin 1: CBin 2: D, E]
end
subgraph Numerical_Features
N1[Values: 1, 2, ..., 100] --> N2[Equal-size bins]
N2 --> N3[Bin 0: 1-50Bin 1: 51-100]
end```
- **Categorical**: Groups similar categories together until `n_cat` bins reached
- **Numerical**: Creates quantile bins (with `n_cat=2`, uses the median)
### Step 2: Build Correlation Tables
For `n_dims=2`, Pilz builds
```mermaid
flowchart TB
subgraph Categorical_Features
C1[Categories: A, B, C, D, E] --> C2[Group until n_cat]
C2 --> C3[Bin 0: A, BBin 1: CBin 2: D, E]
end
subgraph Numerical_Features
N1[Values: 1, 2, ..., 100] --> N2[Equal-size bins]
N2 --> N3[Bin 0: 1-50Bin 1: 51-100]
end```
T4["X=1, Y=1: target=80, non-target=20"]
end```
### Step 3: Find Best Split
Pilz evaluates which combinations best distinguish target from non-target:
```mermaid
flowchart TB
subgraph "Score Each Combination"
S1["Target Rate = target / (target + non-target)"]
end
S1 --> C[Compare all combinations]
C -->|"Best discrimination"| B[Best split found]
C -->|"Unclear"| N[Go to neutral]```
- **
```mermaid
flowchart LR
subgraph "Feature X: [0,1]"
end
subgraph "Feature Y: [0,1]"
end
subgraph "Correlation Table"
T1["X=0, Y=0: target=15, non-target=85"]
T2["X=0, Y=1: target=45, non-target=55"]
T3["X=1, Y=0: target=60, non-target=40"]
T4["X=1, Y=1: target=80, non-target=20"]
end```
tyle B fill:#e0f0ff
style D fill:#ccffcc```
### Step 5: Downsampling
To handle everything appropriately, Pilz always uses a **downsampled subset** of the original data:
```mermaid
flowchart LR
A[Start] --> B[Process]
B --> C[End]
style A fill:#e0f0ff
style C fill:#ccffcc```
mermaid
flowchart TB
subgraph "Score Each Combination"
S1["Target Rate = target / (target + non-target)"]
end
S1 --> C[Compare all combinations]
C -->|"Best discrimination"| B[Best split found]
C -->|"Unclear"| N[Go to neutral]```
fast.
## Why This Matters
### Natural Correlation Handling
```mermaid
flowchart LR
subgraph "Example: Churn"
C1["Contract=MonthlyTechSupport=No"]
C2["Both togetherchurn=85%"]
C1 --> C2
end
C1 -->|"Traditional treeneeds 2 splits"| T[Split 1 + Split 2]
style C2 fill:#ccffcc```
When features correlate, Pil
```mermaid
flowchart TB
A[Split 1] --> B{Minimum eventsreached?}
B -->|No| C[Split again]
B -->|Yes| D[Create leaf]
C --> E[Refine Neutral]
E --> A
style B fill:#e0f0ff
style D fill:#ccffcc```
ontract = 'Two year' THEN 0.12
ELSE 0.35
END
Comparison with Other Approaches¶
| Aspect | Neural Networks | Traditional Trees | Pilz |
|--------|----------------|-------------------|----------|
| Feature correlations | Learned implicitly | Multiple splits | Single cut |
| Interpretability | Low | Medium
```mermaid flowchart LR subgraph Original_Data O1[100,000 rows] end
subgraph Downsampled
D1[Target: 5,000]
D2[Non-target: 5,000]
end
O1 -->|"Sample target"| D1
O1 -->|"Sample non-target"| D2
style D1 fill:#ffff99
style D2 fill:#ffff99```
n in database
- Tabular data - Customer data, transactions
✗ Not Ideal For¶
-
Image/audio/video - Use neural networks
-
Very large datasets - May need tuning
-
No correlations - Simpler models may suffice
Core Parameters¶
| Parameter | What it controls |
|-----------|-----------------|
| n_dims | D
```mermaid flowchart LR subgraph "Example: Churn" C1["Contract=MonthlyTechSupport=No"] C2["Both togetherchurn=85%"]
C1 --> C2
end
C1 -->|"Traditional treeneeds 2 splits"| T[Split 1 + Split 2]
style C2 fill:#ccffcc```
g 2. First Project - Try the Iris example 3. Feature Categorization - Deep dive into binning 4. Multi-Dimensional Splits - Deep dive into n_dims
Pilz: Capturing feature correlations naturally through multi-dimensional cuts.