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PyTorch MLflow tutorial

This tutorial covers the full lifecycle of experimentation, training, tuning, registration, evaluation, and deployment for a deep learning modeling project. It shows you how to use MLflow to keep track of every aspect of the model development and deployment processes.

In this step-by-step tutorial, you'll discover how to:

  • Generate and visualize data: Create synthetic data to simulate real-world scenarios, and visualize feature relationships.
  • Design and train neural networks: Build a PyTorch neural network for regression and train it with proper optimization techniques.
  • Track with MLflow: Log important metrics, parameters, artifacts, and models using MLflow, including visualizations.
  • Tune hyperparameters: Use Optuna for hyperparameter optimization with PyTorch models.
  • Register models: Register your model with Unity Catalog, preparing it for review and future deployment.
  • Deploy models: Load your registered model, make predictions, and perform error analysis, both locally and in a distributed setting.
(Optional) Install the latest version of MLflow
%pip install -Uqqq mlflow pytorch-lightning optuna skorch uv optuna-integration[pytorch_lightning]
%restart_python
3
from typing import Tuple, Optional, Dict, List, Any

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score


import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import DataLoader, TensorDataset

import pytorch_lightning as pl
from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint

import mlflow
from mlflow.models import infer_signature
from mlflow.tracking import MlflowClient
from mlflow.entities import Metric, Param  

import optuna
from optuna.integration import PyTorchLightningPruningCallback

import time

0. Configure the Model Registry with Unity Catalog

One of the key advantages of using MLflow on Databricks is the seamless integration with Unity Catalog. This integration simplifies model management and governance, ensuring that every model you develop is tracked, versioned, and secure. For more information about Unity Catalog, see (AWS | Azure | GCP).

Set the registry URI

The following cell configures MLflow to use Unity Catalog for model registration.

mlflow.set_registry_uri("databricks-uc")

1. Create a synthetic regression dataset

The next cell defines the create_regression_data function. This function generates synthetic data for regression. The resulting dataset includes linear and non-linear relationships between the features and the target, noise, and features with varying importance. These features are designed to mimic real-world data scenarios.

def create_regression_data(
    n_samples: int, 
    n_features: int,
    seed: int = 1994,
    noise_level: float = 0.3,
    nonlinear: bool = True
) -> Tuple[pd.DataFrame, pd.Series]:
    """Generates synthetic regression data with interesting correlations for MLflow and PyTorch demonstrations.

    This function creates a DataFrame of continuous features and computes a target variable with nonlinear
    relationships and interactions between features. The data is designed to be complex enough to demonstrate
    the capabilities of deep learning, but not so complex that a reasonable model can't be learned.

    Args:
        n_samples (int): Number of samples (rows) to generate.
        n_features (int): Number of feature columns.
        seed (int, optional): Random seed for reproducibility. Defaults to 1994.
        noise_level (float, optional): Level of Gaussian noise to add to the target. Defaults to 0.3.
        nonlinear (bool, optional): Whether to add nonlinear feature transformations. Defaults to True.

    Returns:
        Tuple[pd.DataFrame, pd.Series]:
            - pd.DataFrame: DataFrame containing the synthetic features.
            - pd.Series: Series containing the target labels.

    Example:
        >>> df, target = create_regression_data(n_samples=1000, n_features=10)
    """
    rng = np.random.RandomState(seed)
    
    # Generate random continuous features
    X = rng.uniform(-5, 5, size=(n_samples, n_features))
    
    # Create feature DataFrame with meaningful names
    columns = [f"feature_{i}" for i in range(n_features)]
    df = pd.DataFrame(X, columns=columns)
    
    # Generate base target variable with linear relationship to a subset of features
    # Use only the first n_features//2 features to create some irrelevant features
    weights = rng.uniform(-2, 2, size=n_features//2)
    target = np.dot(X[:, :n_features//2], weights)
    
    # Add some nonlinear transformations if requested
    if nonlinear:
        # Add square term for first feature
        target += 0.5 * X[:, 0]**2
        
        # Add interaction between the second and third features
        if n_features >= 3:
            target += 1.5 * X[:, 1] * X[:, 2]
        
        # Add sine transformation of fourth feature
        if n_features >= 4:
            target += 2 * np.sin(X[:, 3])
        
        # Add exponential of fifth feature, scaled down
        if n_features >= 5:
            target += 0.1 * np.exp(X[:, 4] / 2)
            
        # Add threshold effect for sixth feature
        if n_features >= 6:
            target += 3 * (X[:, 5] > 1.5).astype(float)
    
    # Add Gaussian noise
    noise = rng.normal(0, noise_level * target.std(), size=n_samples)
    target += noise
    
    # Add a few more interesting features to the DataFrame
    
    # Add a correlated feature (but not used in target calculation)
    if n_features >= 7:
        df['feature_correlated'] = df['feature_0'] * 0.8 + rng.normal(0, 0.2, size=n_samples)
    
    # Add a cyclical feature
    df['feature_cyclical'] = np.sin(np.linspace(0, 4*np.pi, n_samples))
    
    # Add a feature with outliers
    df['feature_with_outliers'] = rng.normal(0, 1, size=n_samples)
    # Add outliers to ~1% of samples
    outlier_idx = rng.choice(n_samples, size=n_samples//100, replace=False)
    df.loc[outlier_idx, 'feature_with_outliers'] = rng.uniform(10, 15, size=len(outlier_idx))
    
    return df, pd.Series(target, name='target')

2. Exploratory data analysis (EDA) visualizations

Visualizations help you understand the data. The code in the following cell creates 6 functions, each of which generates a different plot to help you visually inspect your dataset.

You can use MLflow to log visualizations as artifacts, making your experimentation fully reproducible.

def plot_feature_distributions(X: pd.DataFrame, y: pd.Series, n_cols: int = 3) -> plt.Figure:
    """
    Creates a grid of histograms for each feature in the dataset.

    Args:
        X (pd.DataFrame): DataFrame containing features.
        y (pd.Series): Series containing the target variable.
        n_cols (int): Number of columns in the grid layout.

    Returns:
        plt.Figure: The matplotlib Figure object containing the distribution plots.
    """
    features = X.columns
    n_features = len(features)
    n_rows = (n_features + n_cols - 1) // n_cols
    
    fig, axes = plt.subplots(n_rows, n_cols, figsize=(15, 4 * n_rows))
    axes = axes.flatten() if n_rows * n_cols > 1 else [axes]
    
    for i, feature in enumerate(features):
        if i < len(axes):
            ax = axes[i]
            sns.histplot(X[feature], ax=ax, kde=True, color='skyblue')
            ax.set_title(f'Distribution of {feature}')
    
    # Hide any unused subplots
    for i in range(n_features, len(axes)):
        axes[i].set_visible(False)
    
    plt.tight_layout()
    fig.suptitle('Feature Distributions', y=1.02, fontsize=16)
    plt.close(fig)
    return fig

def plot_correlation_heatmap(X: pd.DataFrame, y: pd.Series) -> plt.Figure:
    """
    Creates a correlation heatmap of all features and the target variable.

    Args:
        X (pd.DataFrame): DataFrame containing features.
        y (pd.Series): Series containing the target variable.

    Returns:
        plt.Figure: The matplotlib Figure object containing the heatmap.
    """
    # Combine features and target into one DataFrame
    data = X.copy()
    data['target'] = y
    
    # Calculate correlation matrix
    corr_matrix = data.corr()
    
    # Set up the figure
    fig, ax = plt.subplots(figsize=(12, 10))
    
    # Draw the heatmap with a color bar
    cmap = sns.diverging_palette(220, 10, as_cmap=True)
    sns.heatmap(corr_matrix, annot=True, fmt='.2f', cmap=cmap,
                center=0, square=True, linewidths=0.5, ax=ax)
    
    ax.set_title('Feature Correlation Heatmap', fontsize=16)
    plt.close(fig)
    return fig

def plot_feature_target_relationships(X: pd.DataFrame, y: pd.Series, n_cols: int = 3) -> plt.Figure:
    """
    Creates a grid of scatter plots showing the relationship between each feature and the target.

    Args:
        X (pd.DataFrame): DataFrame containing features.
        y (pd.Series): Series containing the target variable.
        n_cols (int): Number of columns in the grid layout.

    Returns:
        plt.Figure: The matplotlib Figure object containing the relationship plots.
    """
    features = X.columns
    n_features = len(features)
    n_rows = (n_features + n_cols - 1) // n_cols
    
    fig, axes = plt.subplots(n_rows, n_cols, figsize=(15, 4 * n_rows))
    axes = axes.flatten() if n_rows * n_cols > 1 else [axes]
    
    for i, feature in enumerate(features):
        if i < len(axes):
            ax = axes[i]
            # Scatter plot with regression line
            sns.regplot(x=X[feature], y=y, ax=ax, 
                       scatter_kws={'alpha': 0.5, 'color': 'blue'}, 
                       line_kws={'color': 'red'})
            ax.set_title(f'{feature} vs Target')
    
    for i in range(n_features, len(axes)):
        axes[i].set_visible(False)
    
    plt.tight_layout()
    fig.suptitle('Feature vs Target Relationships', y=1.02, fontsize=16)
    plt.close(fig)
    return fig

def plot_pairwise_relationships(X: pd.DataFrame, y: pd.Series, features: list[str]) -> plt.Figure:
    """
    Creates a pairplot showing relationships between selected features and the target.

    Args:
        X (pd.DataFrame): DataFrame containing features.
        y (pd.Series): Series containing the target variable.
        features (List[str]): List of feature names to include in the plot.

    Returns:
        plt.Figure: The matplotlib Figure object containing the pairplot.
    """
    # Ensure features exist in the DataFrame
    valid_features = [f for f in features if f in X.columns]
    
    if not valid_features:
        fig, ax = plt.subplots()
        ax.text(0.5, 0.5, "No valid features provided", ha='center', va='center')
        return fig
    
    # Combine selected features and target
    data = X[valid_features].copy()
    data['target'] = y
    
    # Create pairplot
    pairgrid = sns.pairplot(data, diag_kind="kde", 
                          plot_kws={"alpha": 0.6, "s": 50},
                          corner=True)
    
    pairgrid.fig.suptitle("Pairwise Feature Relationships", y=1.02, fontsize=16)
    plt.close(pairgrid.fig)
    return pairgrid.fig

def plot_outliers(X: pd.DataFrame, n_cols: int = 3) -> plt.Figure:
    """
    Creates a grid of box plots to detect outliers in each feature.

    Args:
        X (pd.DataFrame): DataFrame containing features.
        n_cols (int): Number of columns in the grid layout.

    Returns:
        plt.Figure: The matplotlib Figure object containing the outlier plots.
    """
    features = X.columns
    n_features = len(features)
    n_rows = (n_features + n_cols - 1) // n_cols
    
    fig, axes = plt.subplots(n_rows, n_cols, figsize=(15, 4 * n_rows))
    axes = axes.flatten() if n_rows * n_cols > 1 else [axes]
    
    for i, feature in enumerate(features):
        if i < len(axes):
            ax = axes[i]
            # Box plot to detect outliers
            sns.boxplot(x=X[feature], ax=ax, color='skyblue')
            ax.set_title(f'Outlier Detection for {feature}')
            ax.set_xlabel(feature)
    
    # Hide any unused subplots
    for i in range(n_features, len(axes)):
        axes[i].set_visible(False)
    
    plt.tight_layout()
    fig.suptitle('Outlier Detection for Features', y=1.02, fontsize=16)
    plt.close(fig)
    return fig

def plot_residuals(y_true: pd.Series, y_pred: np.ndarray) -> plt.Figure:
    """
    Creates a residual plot to analyze model prediction errors.
    
    Args:
        y_true (pd.Series): True target values.
        y_pred (np.ndarray): Predicted target values.
        
    Returns:
        plt.Figure: The matplotlib Figure object containing the residual plot.
    """
    residuals = y_true - y_pred
    
    fig, ax = plt.subplots(figsize=(10, 6))
    
    # Scatter plot of predicted values vs residuals
    ax.scatter(y_pred, residuals, alpha=0.5)
    ax.axhline(y=0, color='r', linestyle='-')
    
    ax.set_xlabel('Predicted Values')
    ax.set_ylabel('Residuals')
    ax.set_title('Residual Plot')
    
    plt.tight_layout()
    plt.close(fig)
    return fig

3. Design a PyTorch neural network for regression

The code in the following cell defines the PyTorch model architecture. It creates a flexible neural network with the following characteristics:

  • Configurable architecture: Adjustable number and size of hidden layers.
  • Activation functions: ReLU for hidden layers, linear for output.
  • Regularization: Optional dropout to prevent overfitting.
  • Layer normalization: To stabilize training and accelerate convergence.

To demonstrate different approaches, the following cells show how to create the neural network first using a standard PyTorch module and then using a PyTorch Lightning module.

class RegressionNN(nn.Module):
    """
    A flexible feedforward neural network for regression tasks.
    
    Attributes:
        input_dim (int): Number of input features.
        hidden_dims (List[int]): List of hidden layer dimensions.
        dropout_rate (float): Dropout probability for regularization.
        use_layer_norm (bool): Whether to use layer normalization.
    """
    
    def __init__(
        self,
        input_dim: int,
        hidden_dims: List[int] = [64, 32],
        dropout_rate: float = 0.1,
        use_layer_norm: bool = True
    ):
        """
        Initialize the neural network.
        
        Args:
            input_dim (int): Number of input features.
            hidden_dims (List[int]): List of hidden layer dimensions.
            dropout_rate (float): Dropout probability for regularization.
            use_layer_norm (bool): Whether to use layer normalization.
        """
        super().__init__()
        
        self.input_dim = input_dim
        self.hidden_dims = hidden_dims
        self.dropout_rate = dropout_rate
        self.use_layer_norm = use_layer_norm
        
        # Build layers dynamically based on hidden_dims
        layers = []
        
        # Input layer
        prev_dim = input_dim
        
        # Hidden layers
        for dim in hidden_dims:
            layers.append(nn.Linear(prev_dim, dim))
            
            if use_layer_norm:
                layers.append(nn.LayerNorm(dim))
                
            layers.append(nn.ReLU())
            
            if dropout_rate > 0:
                layers.append(nn.Dropout(dropout_rate))
                
            prev_dim = dim
        
        # Output layer (single output for regression)
        layers.append(nn.Linear(prev_dim, 1))
        
        # Combine all layers
        self.model = nn.Sequential(*layers)
    
    def forward(self, x):
        """Forward pass through the network."""
        return self.model(x).squeeze()
    
    def get_params(self) -> Dict[str, Any]:
        """Return model parameters as a dictionary for MLflow logging."""
        return {
            "input_dim": self.input_dim,
            "hidden_dims": self.hidden_dims,
            "dropout_rate": self.dropout_rate,
            "use_layer_norm": self.use_layer_norm
        }
class RegressionLightningModule(pl.LightningModule):
    """
    PyTorch Lightning module for regression tasks.
    
    This class wraps the RegressionNN model and adds training, validation,
    and testing logic using the PyTorch Lightning framework.
    """
    
    def __init__(
        self,
        input_dim: int,
        hidden_dims: List[int] = [64, 32],
        dropout_rate: float = 0.1,
        use_layer_norm: bool = True,
        learning_rate: float = 1e-3,
        weight_decay: float = 1e-5
    ):
        """
        Initialize the Lightning module.
        
        Args:
            input_dim (int): Number of input features.
            hidden_dims (List[int]): List of hidden layer dimensions.
            dropout_rate (float): Dropout probability for regularization.
            use_layer_norm (bool): Whether to use layer normalization.
            learning_rate (float): Learning rate for the optimizer.
            weight_decay (float): Weight decay for L2 regularization.
        """
        super().__init__()
        
        # Save hyperparameters
        self.save_hyperparameters()
        
        # Create the model
        self.model = RegressionNN(
            input_dim=input_dim,
            hidden_dims=hidden_dims,
            dropout_rate=dropout_rate,
            use_layer_norm=use_layer_norm
        )
        
        # Loss function
        self.loss_fn = nn.MSELoss()
    
    def forward(self, x):
        """Forward pass through the network."""
        return self.model(x)
    
    def configure_optimizers(self):
        """Configure the optimizer for training."""
        optimizer = torch.optim.Adam(
            self.parameters(),
            lr=self.hparams.learning_rate,
            weight_decay=self.hparams.weight_decay
        )
        return optimizer
    
    def training_step(self, batch, batch_idx):
        """Perform a training step."""
        x, y = batch
        y_pred = self(x)
        loss = self.loss_fn(y_pred, y)
        self.log('train_loss', loss, prog_bar=True)
        return loss
    
    def validation_step(self, batch, batch_idx):
        """Perform a validation step."""
        x, y = batch
        y_pred = self(x)
        loss = self.loss_fn(y_pred, y)
        self.log('val_loss', loss, prog_bar=True)
        
        # Calculate additional metrics
        rmse = torch.sqrt(loss)
        mae = torch.mean(torch.abs(y_pred - y))
        
        self.log('val_rmse', rmse, prog_bar=True)
        self.log('val_mae', mae, prog_bar=True)
        
        return loss
    
    def test_step(self, batch, batch_idx):
        """Perform a test step."""
        x, y = batch
        y_pred = self(x)
        loss = self.loss_fn(y_pred, y)
        
        # Calculate metrics for test set
        rmse = torch.sqrt(loss)
        mae = torch.mean(torch.abs(y_pred - y))
        
        self.log('test_loss', loss)
        self.log('test_rmse', rmse)
        self.log('test_mae', mae)
        
        return loss
    
    def get_params(self) -> Dict[str, Any]:
        """Return model parameters as a dictionary for MLflow logging."""
        return {
            "input_dim": self.hparams.input_dim,
            "hidden_dims": self.hparams.hidden_dims,
            "dropout_rate": self.hparams.dropout_rate,
            "use_layer_norm": self.hparams.use_layer_norm,
            "learning_rate": self.hparams.learning_rate,
            "weight_decay": self.hparams.weight_decay
        }
def prepare_dataloader(
    X_train, y_train, X_val, y_val, X_test, y_test, batch_size: int = 32
):
    """
    Create PyTorch DataLoaders for training, validation, and testing.
    
    Args:
        X_train, y_train: Training data and labels.
        X_val, y_val: Validation data and labels.
        X_test, y_test: Test data and labels.
        batch_size (int): Batch size for the DataLoaders.
        
    Returns:
        Tuple of (train_loader, val_loader, test_loader, scaler)
    """
    # Initialize a scaler
    scaler = StandardScaler()
    
    # Fit and transform the training data
    X_train_scaled = scaler.fit_transform(X_train)
    X_val_scaled = scaler.transform(X_val)
    X_test_scaled = scaler.transform(X_test)
    
    # Convert to PyTorch tensors - explicitly set dtype to float32
    X_train_tensor = torch.tensor(X_train_scaled, dtype=torch.float32)
    y_train_tensor = torch.tensor(y_train.values, dtype=torch.float32)
    
    X_val_tensor = torch.tensor(X_val_scaled, dtype=torch.float32)
    y_val_tensor = torch.tensor(y_val.values, dtype=torch.float32)
    
    X_test_tensor = torch.tensor(X_test_scaled, dtype=torch.float32)
    y_test_tensor = torch.tensor(y_test.values, dtype=torch.float32)
    
    # Create TensorDatasets
    train_dataset = TensorDataset(X_train_tensor, y_train_tensor)
    val_dataset = TensorDataset(X_val_tensor, y_val_tensor)
    test_dataset = TensorDataset(X_test_tensor, y_test_tensor)
    
    # Create DataLoaders
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    val_loader = DataLoader(val_dataset, batch_size=batch_size)
    test_loader = DataLoader(test_dataset, batch_size=batch_size)
    
    return train_loader, val_loader, test_loader, scaler

4. Standard modeling workflow

The code in the next cell implements a standard PyTorch modeling workflow with MLflow integration, using the following steps:

  1. Generate and explore synthetic data.
  2. Split the data into training, validation, and test sets.
  3. Scale the data and create PyTorch DataLoaders.
  4. Define and train a neural network model.
  5. Evaluate the model's performance.
  6. Log metrics, parameters, and artifacts to MLflow.

This standard workflow provides a baseline model. You can then use hyperparameter tuning to improve the model.

# Create the regression dataset
n_samples = 1000
n_features = 10
X, y = create_regression_data(n_samples=n_samples, n_features=n_features, nonlinear=True)

# Create EDA plots
dist_plot = plot_feature_distributions(X, y)
corr_plot = plot_correlation_heatmap(X, y)
scatter_plot = plot_feature_target_relationships(X, y)
corr_with_target = X.corrwith(y).abs().sort_values(ascending=False)
top_features = corr_with_target.head(4).index.tolist()
pairwise_plot = plot_pairwise_relationships(X, y, top_features)
outlier_plot = plot_outliers(X)

# Split the data into train, validation, and test sets
X_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size=0.3, random_state=42)
X_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size=0.5, random_state=42)

# Prepare DataLoaders
batch_size = 32
train_loader, val_loader, test_loader, scaler = prepare_dataloader(
    X_train, y_train, X_val, y_val, X_test, y_test, batch_size=batch_size)

# Define model parameters
input_dim = X_train.shape[1]
hidden_dims = [64, 32]
dropout_rate = 0.1
use_layer_norm = True
learning_rate = 1e-3
weight_decay = 1e-5

# Create the PyTorch Lightning model
model = RegressionLightningModule(
    input_dim=input_dim,
    hidden_dims=hidden_dims,
    dropout_rate=dropout_rate,
    use_layer_norm=use_layer_norm,
    learning_rate=learning_rate,
    weight_decay=weight_decay
)

# Define early stopping and model checkpoint callbacks
early_stopping = EarlyStopping(
    monitor='val_loss',
    patience=10,
    mode='min'
)

checkpoint_callback = ModelCheckpoint(
    monitor='val_loss',
    dirpath='./checkpoints',
    filename='pytorch-regression-{epoch:02d}-{val_loss:.4f}',
    save_top_k=1,
    mode='min'
)

# Define trainer
trainer = pl.Trainer(
    max_epochs=100,
    callbacks=[early_stopping, checkpoint_callback],
    enable_progress_bar=True,
    log_every_n_steps=5
)

# Train the model
trainer.fit(model, train_loader, val_loader)

# Test the model
test_results = trainer.test(model, test_loader)

# Make predictions on the test set for evaluation
model.eval()
test_preds = []
true_values = []

with torch.no_grad():
    for batch in test_loader:
        x, y = batch
        y_pred = model(x)
        test_preds.extend(y_pred.numpy())
        true_values.extend(y.numpy())

test_preds = np.array(test_preds)
true_values = np.array(true_values)

# Calculate metrics
rmse = np.sqrt(mean_squared_error(true_values, test_preds))
mae = mean_absolute_error(true_values, test_preds)
r2 = r2_score(true_values, test_preds)

# Create residual plot
residual_plot = plot_residuals(pd.Series(true_values), test_preds)

5. Log the model using MLflow

When you log a model using MLflow on Databricks, important artifacts and metadata are captured. This ensures that your model is not only reproducible but also ready for deployment with all necessary dependencies and clear API contracts. For details on what is logged, see the MLflow documentation.

The code in the next cell starts an MLflow run using with mlflow.start_run():. This initializes the MLflow context manager for the run and encloses the run in a code block. When the code block ends, all logged metrics, parameters, and artifacts are saved, and the MLflow run is automatically terminated.

# Log the model and training results with MLflow
with mlflow.start_run() as run:
    # Create MLflow client for batch logging
    mlflow_client = MlflowClient()
    run_id = run.info.run_id
    
    # Extract metrics
    final_train_loss = trainer.callback_metrics.get("train_loss").item() if "train_loss" in trainer.callback_metrics else None
    final_val_loss = trainer.callback_metrics.get("val_loss").item() if "val_loss" in trainer.callback_metrics else None
    
    # Extract parameters for logging
    model_params = model.get_params()
     
    # Create a list to store all metrics for batch logging
    all_metrics = []
    
    # Add each metric to the list
    if final_train_loss is not None:
        all_metrics.append(Metric(key="train_loss", value=final_train_loss, timestamp=0, step=0))
    if final_val_loss is not None:
        all_metrics.append(Metric(key="val_loss", value=final_val_loss, timestamp=0, step=0))
    
    # Add test metrics
    all_metrics.append(Metric(key="test_rmse", value=rmse, timestamp=0, step=0))
    all_metrics.append(Metric(key="test_mae", value=mae, timestamp=0, step=0))
    all_metrics.append(Metric(key="test_r2", value=r2, timestamp=0, step=0))
    
    # Collect all parameters to log
    # Note: The code uses log_params for model_params since there could be many parameters,
    # but converts the individual param calls to batch
    from mlflow.entities import Param
    all_params = [
        Param(key="batch_size", value=str(batch_size)),
        Param(key="early_stopping_patience", value=str(early_stopping.patience)),
        Param(key="max_epochs", value=str(trainer.max_epochs)),
        Param(key="actual_epochs", value=str(trainer.current_epoch))
    ]
    
    # Generate a model signature using the infer signature utility in MLflow
    input_example = X_train.iloc[[0]].values.astype(np.float32)  # Ensure float32 type
    input_example_scaled = scaler.transform(input_example).astype(np.float32)
    
    model.eval()
    with torch.no_grad():
        # Ensure tensor is float32
        tensor_input = torch.tensor(input_example_scaled, dtype=torch.float32)
        signature_preds = model(tensor_input)
    
    # Ensure prediction is also float32
    signature = infer_signature(input_example, signature_preds.numpy().reshape(-1).astype(np.float32))
    
    # Log model parameters first (since these could be numerous)
    mlflow.log_params(model_params)
    
    # Log all metrics and remaining parameters in a single batch operation
    mlflow_client.log_batch(
        run_id=run_id,
        metrics=all_metrics,
        params=all_params
    )
    
    # Log the model to MLflow and register the model to Unity Catalog
    model_info = mlflow.pytorch.log_model(
        model,
        artifact_path="model",
        input_example=input_example,
        signature=signature,
        registered_model_name="demo.pytorch_regression_model",
    )
    
    # Log feature analysis plots
    mlflow.log_figure(dist_plot, "feature_distributions.png")
    mlflow.log_figure(corr_plot, "correlation_heatmap.png")
    mlflow.log_figure(scatter_plot, "feature_target_relationships.png")
    mlflow.log_figure(pairwise_plot, "pairwise_relationships.png")
    mlflow.log_figure(outlier_plot, "outlier_detection.png")
    mlflow.log_figure(residual_plot, "residual_plot.png")
    
    # Run MLflow evaluation to generate additional metrics without having to implement them
    evaluation_data = X_test.copy()
    evaluation_data["label"] = y_test
    
    # Skip mlflow.evaluate for now to avoid type mismatch issues
    # Instead, log the metrics directly
    print(f"Model logged: {model_info.model_uri}")
    print(f"Test RMSE: {rmse:.4f}")
    print(f"Test MAE: {mae:.4f}")
    print(f"Test R²: {r2:.4f}")

6. Hyperparameter tuning

This section shows how to automate hyperparameter tuning using Optuna and nested runs in MLflow. In this way you can explore a range of parameter configurations and capture all of the experimental details.

The code in the next cell does the following:

  1. Uses the create_regression_data function defined previously to generate a synthetic regression dataset.

  2. Splits the dataset into separate training and test datasets, and saves a copy of the test dataset for evaluation.

  3. Creates an objective function for the hyperparameter tuning process. The objective function defines the search space for hyperparameters of the PyTorch model, such as the number of layers, hidden dimensions, dropout rate, learning rate, and regularization parameters. Optuna dynamically samples these values, ensuring that each trial tests a different combination of parameters.

  4. Initiates a nested MLflow run inside the objective function. This nested run automatically captures and logs all details specific to the current hyperparameter trial. By isolating each trial in its own nested run, you can keep a well-organized record of each configuration and its corresponding performance metrics. The nested run logs the following:

    • The specific hyperparameters used for that trial.
    • The performance metric (in this case, validation loss) computed on the test set.
    • The trained model instance is also stored as part of the trial’s metadata. This makes it easy to retrieve the best-performing model later.

    The code does not record each model to MLflow. While doing hyperparameter tuning, each iteration is not guaranteed to be particularly good, so there is no reason to record the model artifact for each one.

  5. Create a parent MLflow run. This run initiates an Optuna study designed to identify the optimal set of hyperparameters (the set that produces the lowest validation loss). Optuna runs a series of trials where each trial uses a unique combination of hyperparameters. During each trial, the nested MLflow run captures all the experiment details, so you can later track and compare the performance of each model configuration.

  6. The study identifies the best trial based on the lowest validation loss. The code extracts the best model and the optimal parameter values. The code uses infer_signature to save a model signature, which specifies the expected input and output schemas and is important for consistent deployment and integration with systems like Unity Catalog. Finally, the best model is logged and registered to Unity Catalog. Additional artifacts such as EDA plots and feature importance charts are also recorded.

# Create a custom pruning callback as a fallback
class PyTorchLightningPruningCallback(pl.Callback):
    """PyTorch Lightning callback to prune unpromising trials.
    
    This is a simplified version for use when the optuna-integration package isn't available.
    """
    
    def __init__(self, trial, monitor):
        super().__init__()
        self._trial = trial
        self.monitor = monitor
        
    def on_validation_end(self, trainer, pl_module):
        # Report the validation metric to Optuna
        metrics = trainer.callback_metrics
        current_score = metrics.get(self.monitor)
        
        if current_score is not None:
            self._trial.report(current_score.item(), trainer.current_epoch)
            
            # If trial should be pruned based on current value,
            # stop the training
            if self._trial.should_prune():
                message = "Trial was pruned at epoch {}.".format(trainer.current_epoch)
                raise optuna.TrialPruned(message)

# Generate a larger dataset for hyperparameter tuning
n_samples = 2000
n_features = 10

X, y = create_regression_data(n_samples=n_samples, n_features=n_features, nonlinear=True)

# Split the data
X_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size=0.3, random_state=42)
X_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size=0.5, random_state=42)

# Prepare the evaluation data
evaluation_data = X_test.copy()
evaluation_data["label"] = y_test

# Create the data loaders
batch_size = 32
train_loader, val_loader, test_loader, scaler = prepare_dataloader(
    X_train, y_train, X_val, y_val, X_test, y_test, batch_size=batch_size)

def objective(trial):
    """Optuna objective function to minimize validation loss."""
    
    # Define the hyperparameter search space
    n_layers = trial.suggest_int("n_layers", 1, 3)
    
    # Create hidden dimensions based on number of layers
    hidden_dims = []
    for i in range(n_layers):
        hidden_dims.append(trial.suggest_int(f"hidden_dim_{i}", 16, 128))
    
    # Other hyperparameters
    dropout_rate = trial.suggest_float("dropout_rate", 0.0, 0.5)
    learning_rate = trial.suggest_float("learning_rate", 1e-4, 1e-2, log=True)
    weight_decay = trial.suggest_float("weight_decay", 1e-6, 1e-3, log=True)
    use_layer_norm = trial.suggest_categorical("use_layer_norm", [True, False])
    
    # Start a nested MLflow run for this trial
    with mlflow.start_run(nested=True) as child_run:
        # Create MLflow client for batch logging
        mlflow_client = MlflowClient()
        run_id = child_run.info.run_id
        
        # Prepare parameters for batch logging
        params_list = []
        param_dict = {
            "n_layers": n_layers,
            "hidden_dims": str(hidden_dims),  # Convert list to string
            "dropout_rate": dropout_rate,
            "learning_rate": learning_rate,
            "weight_decay": weight_decay,
            "use_layer_norm": use_layer_norm,
            "batch_size": batch_size
        }
        
        # Convert parameters to Param objects
        for key, value in param_dict.items():
            params_list.append(Param(key, str(value)))
        
        # Create the model with these hyperparameters
        model = RegressionLightningModule(
            input_dim=X_train.shape[1],
            hidden_dims=hidden_dims,
            dropout_rate=dropout_rate,
            use_layer_norm=use_layer_norm,
            learning_rate=learning_rate,
            weight_decay=weight_decay
        )
        
        # Callbacks
        early_stopping = EarlyStopping(
            monitor='val_loss',
            patience=5,
            mode='min'
        )
        
        pruning_callback = PyTorchLightningPruningCallback(
            trial, monitor="val_loss"
        )
        
        # Define trainer with early stopping and pruning
        trainer = pl.Trainer(
            max_epochs=50,
            callbacks=[early_stopping, pruning_callback],
            enable_progress_bar=False,
            log_every_n_steps=10
        )
        
        # Train and validate the model
        trainer.fit(model, train_loader, val_loader)
        
        # Get the best validation loss
        best_val_loss = trainer.callback_metrics.get("val_loss").item()
        val_rmse = np.sqrt(best_val_loss)
        
        # Prepare metrics for batch logging
        current_time = int(time.time() * 1000)  # Current time in milliseconds
        metrics_list = [
            Metric("val_loss", best_val_loss, current_time, 0),
            Metric("val_rmse", val_rmse, current_time, 0)
        ]
        
        # Use log_batch through the client for efficient logging
        mlflow_client.log_batch(run_id, metrics=metrics_list, params=params_list)
        
    # Store the model in the trial's user attributes
    trial.set_user_attr("model", model)
    
    # Return the value to minimize (validation loss)
    return best_val_loss

best_model_version = None
# The parent run stores the best iteration from the hyperparameter tuning execution
with mlflow.start_run() as run:
    # Create MLflow client for batch logging
    mlflow_client = MlflowClient()
    run_id = run.info.run_id
    
    study = optuna.create_study(direction="minimize")
    study.optimize(objective, n_trials=20)

    best_trial = study.best_trial
    best_model = best_trial.user_attrs["model"]
    
    # Test the best model
    trainer = pl.Trainer(
        enable_progress_bar=True,
        log_every_n_steps=5
    )
    test_results = trainer.test(best_model, test_loader)
    
    # Make predictions on the test set for evaluation
    best_model.eval()
    test_preds = []
    true_values = []
    
    with torch.no_grad():
        for batch in test_loader:
            x, y = batch
            y_pred = best_model(x)
            test_preds.extend(y_pred.numpy())
            true_values.extend(y.numpy())
    
    test_preds = np.array(test_preds)
    true_values = np.array(true_values)
    
    # Calculate metrics
    rmse = np.sqrt(mean_squared_error(true_values, test_preds))
    mae = mean_absolute_error(true_values, test_preds)
    r2 = r2_score(true_values, test_preds)
    
    # Prepare parameters for batch logging
    best_params_list = []
    for key, value in best_trial.params.items():
        best_params_list.append(Param(f"best_{key}", str(value)))
    
    # Prepare metrics for batch logging
    current_time = int(time.time() * 1000)  # Current time in milliseconds
    metrics_list = [
        Metric("best_val_loss", best_trial.value, current_time, 0),
        Metric("test_rmse", rmse, current_time, 0),
        Metric("test_mae", mae, current_time, 0),
        Metric("test_r2", r2, current_time, 0)
    ]
    
    # Log metrics and parameters in a single batch call
    mlflow_client.log_batch(run_id, metrics=metrics_list, params=best_params_list)

    # Generate model signature - ensure consistent float32 types
    input_example = X_train.iloc[[0]].values.astype(np.float32)
    input_example_scaled = scaler.transform(input_example).astype(np.float32)
    
    best_model.eval()
    with torch.no_grad():
        tensor_input = torch.tensor(input_example_scaled, dtype=torch.float32)
        signature_preds = best_model(tensor_input)
    
    signature = infer_signature(input_example, signature_preds.numpy().reshape(-1).astype(np.float32))

    # Log and register the PyTorch model
    model_info = mlflow.pytorch.log_model(
        best_model,
        artifact_path="model",
        input_example=input_example,
        signature=signature,
        registered_model_name="demo.pytorch_regression_optimized",
    )
    
    # Create residual plot
    residual_plot = plot_residuals(pd.Series(true_values), test_preds)
    
    # Log figures (no batch equivalent for figures)
    mlflow.log_figure(dist_plot, "feature_distributions.png")
    mlflow.log_figure(corr_plot, "correlation_heatmap.png")
    mlflow.log_figure(scatter_plot, "feature_target_relationships.png")
    mlflow.log_figure(pairwise_plot, "pairwise_relationships.png")
    mlflow.log_figure(outlier_plot, "outlier_detection.png")
    mlflow.log_figure(residual_plot, "residual_plot.png")

    # Skip mlflow.evaluate for now to avoid type mismatch issues
    # Instead, log the metrics directly
    print(f"Best model logged: {model_info.model_uri}")
    print(f"Best parameters: {best_trial.params}")
    print(f"Test RMSE: {rmse:.4f}")
    print(f"Test MAE: {mae:.4f}")
    print(f"Test R²: {r2:.4f}")

    best_model_version = model_info.registered_model_version
from mlflow import MlflowClient

# Initialize MLflow client
client = MlflowClient()

# Set a human-readable alias for the best model version
# This makes it easier to reference specific model versions programmatically
client.set_registered_model_alias("demo.pytorch_regression_optimized", "best", int(best_model_version))

7. Pre-deployment validation

MLflow provides the mlflow.models.predict utility to simulate a production-like environment and validate that your model is configured correctly.

# Reference the model by its alias
model_uri = "models:/demo.pytorch_regression_optimized@best"

# Validate the model's deployment readiness
mlflow.models.predict(model_uri=model_uri, input_data=X_test, env_manager="local")

8. Load the registered model and make predictions

The code in this section shows how to load the registered model from MLflow and use it to make predictions locally. This is useful for testing or for batch inference scenarios.

# Convert the data type of X_test to float32
X_test = X_test.astype('float32')

# Load the model using the pyfunc interface (recommended for deployment)
loaded_model = mlflow.pyfunc.load_model(model_uri=model_uri)

# Make predictions with the loaded model
predictions = loaded_model.predict(X_test)

print(f"Shape of predictions: {predictions.shape}")
print(f"First 5 predictions: {predictions[:5]}")
print(f"First 5 actual values: {y_test.values[:5]}")

9. Batch prediction using Spark UDF in MLflow

For large-scale predictions, you can convert the model to a Spark UDF and apply it to a Spark DataFrame, enabling distributed inference.

from pyspark.sql.functions import array, col

# Convert the test data to a Spark DataFrame
X_spark = spark.createDataFrame(X_test)

# Create an array of all feature columns
# This step is necessary because:
# 1. The PyTorch model expects an input tensor with shape [-1, 13]
# 2. The model_udf needs to receive each row as a single array of 13 values
# 3. Without this array transformation, 13 separate columns would be passed to the model
#    which wouldn't match the expected tensor structure
X_spark_with_array = X_spark.withColumn(
    "features_array", 
    array(*[col(c) for c in X_spark.columns])
)

# Create a Spark UDF from the registered model
model_udf = mlflow.pyfunc.spark_udf(spark, model_uri=model_uri)

# Apply MLflow UDF to the array column
# Pass the single array column to the model, which matches the expected tensor format
X_spark_with_predictions = X_spark_with_array.withColumn(
    "prediction", 
    model_udf("features_array")
)

display(X_spark_with_predictions.limit(5))
;