XGBoost is known for its powerful performance in machine learning tasks, and the model training is (mostly) deterministic.

Deterministic model training means that the same model is reproduced given the same model parameters (hyperparameters) and training data. Generally, this is called “reproducibility”.

When using a fixed random seed, XGBoost will mostly produce identical models that generate the same predictions, even across multiple training runs.

This example showcases this deterministic nature by training both simple and complex XGBoost models twice with the same random seed and comparing their predictions.

## Deterministic Simple Model

Let’s start by generating a synthetic dataset for binary classification and defining a simple XGBoost model with a fixed random seed:

```
import numpy as np
from sklearn.datasets import make_classification
import xgboost as xgb
# Generate a synthetic dataset
X, y = make_classification(n_samples=1000, n_features=10, n_informative=5, n_redundant=2, random_state=42)
# Define a simple XGBoost model with a fixed random seed
simple_params = {
'objective': 'binary:logistic',
'max_depth': 3,
'learning_rate': 0.1,
'n_estimators': 50,
'random_state': 42
}
# Train the simple model twice
simple_model_1 = xgb.XGBClassifier(**simple_params)
simple_model_1.fit(X, y)
simple_model_2 = xgb.XGBClassifier(**simple_params)
simple_model_2.fit(X, y)
# Compare predictions from the two simple models
simple_preds_1 = simple_model_1.predict(X)
simple_preds_2 = simple_model_2.predict(X)
print(f"Simple model predictions are equal: {np.array_equal(simple_preds_1, simple_preds_2)}")
```

After training the simple model twice, we generate predictions using both models and compare them using `np.array_equal()`

. As expected, the predictions are identical, confirming the deterministic nature of XGBoost training.

## Deterministic Complex Model

Now, let’s define a more complex XGBoost model with different sampling techniques but still using the same fixed random seed:

```
import numpy as np
from sklearn.datasets import make_classification
import xgboost as xgb
# Generate a synthetic dataset
X, y = make_classification(n_samples=1000, n_features=10, n_informative=5, n_redundant=2, random_state=42)
# Define a complex XGBoost model with different sampling techniques
complex_params = {
'objective': 'binary:logistic',
'max_depth': 5,
'learning_rate': 0.05,
'n_estimators': 100,
'subsample': 0.8,
'colsample_bytree': 0.8,
'random_state': 42
}
# Train the complex model twice
complex_model_1 = xgb.XGBClassifier(**complex_params)
complex_model_1.fit(X, y)
complex_model_2 = xgb.XGBClassifier(**complex_params)
complex_model_2.fit(X, y)
# Compare predictions from the two complex models
complex_preds_1 = complex_model_1.predict(X)
complex_preds_2 = complex_model_2.predict(X)
print(f"Complex model predictions are equal: {np.array_equal(complex_preds_1, complex_preds_2)}")
```

Despite the increased complexity and the use of different sampling techniques, the predictions from the complex models are still identical when using the same fixed random seed.

This deterministic behavior of XGBoost is highly valuable in many scenarios, such as reproducing results, comparing model performance, and ensuring consistency in production environments. By setting a fixed random seed, you can confidently train XGBoost models knowing that they will generate consistent predictions across multiple runs.

## Model Equality

Determining whether two models are “equal” can be challenging.

In the above cases we have used the predictions made by the model to check if two models are identical.

This is one approach, that has limitations.

Some additional approaches for comparing XGBoost models include:

- Model Evaluation Metrics
- Feature Importances
- Tree Structures
- Model Parameters
- SHAP Values
- Serialization and File Comparison

## Limits to Reproducibility

Fixing the random number seed is a common practice to ensure reproducibility when training XGBoost models.

However, there are several scenarios where fixing the seed alone might not be sufficient to ensure that training the model is entirely deterministic and results in identical models.

Here are some cases:

### 1. **Non-deterministic Operations**

Certain operations, particularly those that leverage hardware accelerations like GPUs, may have non-deterministic behaviors due to asynchronous execution and precision differences. For example, some matrix multiplications or reductions may produce slightly different results on different runs even with the same seed.

### 2. **Multithreading and Parallelism**

When training involves multithreading or parallel processing, the order of execution might vary between runs, leading to different results. This can happen in libraries like OpenMP or when using multi-core CPUs/GPUs. Ensuring deterministic behavior in such cases often requires setting specific environment variables or flags that control thread behavior.

### 3. **Different Hardware or Software Environments**

Training the same model on different hardware (e.g., different types of GPUs or CPUs) or under different software environments (e.g., different versions of libraries, drivers, or compilers) can lead to variations in the model due to differences in numerical precision, rounding errors, and implementation details.

### 4. **External Data Sources**

If the training process involves fetching data from external sources (e.g., databases, APIs) that might change or have some level of non-determinism in response time or content, the model may differ between runs.

### 5. **Data Augmentation**

In scenarios where data augmentation is applied during training, even with the same random seed, the order in which data augmentations are applied can be non-deterministic if parallel processing is involved.

### 6. **Libraries and Frameworks Updates**

Updates or changes in the machine learning libraries and frameworks (e.g., XGBoost, TensorFlow, PyTorch) might introduce changes in the underlying algorithms or default parameters, leading to different models even with the same code and random seed.

### 7. **Floating-point Arithmetic**

Floating-point arithmetic can introduce non-determinism, especially when reductions (like summations) are involved. The order of operations in floating-point arithmetic can affect the result due to rounding errors.

### 8. **File System and I/O Operations**

Variations in file system behavior, such as reading order of files or slight differences in file handling across different file systems, can introduce non-determinism. This is particularly relevant when training involves loading large datasets from disk.

### 9. **Stochastic Elements in Algorithms**

Some algorithms might have inherent stochastic elements that are not fully controlled by the random seed. For example, certain optimization techniques or decision rules in the algorithm might introduce variability.

### 10. **Distributed Training**

In distributed training scenarios, where multiple machines are involved in the training process, network latency, communication delays, and synchronization issues can lead to non-deterministic training outcomes.

Ensuring complete determinism often requires addressing these factors by configuring the environment, controlling the execution order, and sometimes accepting that minor differences might still occur due to the inherent nature of some computations.