DEEM - Deep Ensemble Energy Models

DEEM is a Python library for unsupervised ensemble learning using deep energy-based models. It uniquely discovers latent true labels from diverse, noisy unsupervised sources by disentangling correlations and minimizing the energy of a joint inverse Restricted Boltzmann Machine (iRBM) distribution, without requiring any ground truth.

Abstract

Unsupervised ensemble learning emerged to address the challenge of combining multiple learners' predictions without access to ground truth labels or additional data. This paradigm is crucial in scenarios where evaluating individual classifier performance or understanding their strengths is challenging due to limited information. We propose a novel deep energy-based method for constructing an accurate meta-learner using only the predictions of individual learners, potentially capable of capturing complex dependence structures between them. Our approach requires no labeled data, learner features, or problem-specific information, and has theoretical guarantees for when learners are conditionally independent. We demonstrate superior performance across diverse ensemble scenarios, including challenging mixture of experts settings. Our experiments span standard ensemble datasets and curated datasets designed to test how the model fuses expertise from multiple sources. These results highlight the potential of unsupervised ensemble learning to harness collective intelligence, especially in data-scarce or privacy-sensitive environments.

Features

• 🚀 Simple 3-line API - Fit and predict in just a few lines of code
• 🔬 Unsupervised Learning - No labels required for training (though they can be used for evaluation)
• 🧮 Energy-Based Models - Uses RBMs to learn the joint distribution of classifier predictions
• 🎯 Transparent Hungarian Alignment - Automatic label permutation handling via align_to parameter
• ⚡ GPU Acceleration - Full PyTorch backend with CUDA support
• 🔧 Scikit-learn Compatible - Standard .fit(), .predict(), .score() interface
• 📊 Automatic Hyperparameters - Optional meta-learning for hyperparameter selection
• 🎚️ Weighted Initialization - Better classifiers get more influence (default ON)
• 📈 Soft Label Support - Works with probability distributions (3D tensors)

Installation

pip install deem

From Source

git clone https://github.com/shaham-lab/deem.git
cd rbm_python
pip install -e .

Quick Start

import numpy as np
from deem import DEEM

# Ensemble predictions from 15 classifiers on 100 samples with 3 classes
predictions = np.random.randint(0, 3, (100, 15))

# Train and predict in 3 lines!
model = DEEM()
model.fit(predictions)
consensus = model.predict(predictions)

With Evaluation (Transparent Label Alignment)

# If you have true labels, evaluate with automatic label alignment
model = DEEM(n_classes=3, epochs=50)
model.fit(train_predictions)

# Predict with transparent Hungarian alignment via align_to parameter
# Alignment is against MAJORITY VOTE, not true labels (unsupervised!)
consensus = model.predict(test_predictions, align_to=train_predictions)

# Or use score() which handles alignment automatically
accuracy = model.score(test_predictions, test_labels)
print(f"Consensus accuracy: {accuracy:.2%}")

With Soft Labels (Probability Distributions)

# Soft predictions: (n_samples, n_classes, n_classifiers)
# Each classifier outputs a probability distribution over classes
soft_predictions = np.random.rand(100, 3, 15)
soft_predictions = soft_predictions / soft_predictions.sum(axis=1, keepdims=True)

model = DEEM(n_classes=3)
model.fit(soft_predictions)  # Automatically detects 3D and enables oh_mode
consensus = model.predict(soft_predictions)

Custom Configuration

model = DEEM(
    n_classes=5,
    hidden_dim=1,           # Number of hidden units (keep at 1 for best results)
    learning_rate=0.01,
    epochs=100,
    batch_size=64,
    cd_k=10,                # Contrastive divergence steps
    deterministic=True,     # Use probabilities (more stable)
    use_weighted=True,      # Scale weights by classifier accuracy (default)
    device='cuda'           # Use GPU
)
model.fit(predictions)

Use Cases

1. Crowd Learning / Multi-Annotator Aggregation

Aggregate noisy labels from multiple human annotators:

# annotator_labels: (n_samples, n_annotators) with values 0 to k-1
model = DEEM(n_classes=k)
model.fit(annotator_labels)
consensus_labels = model.predict(annotator_labels)

2. Ensemble Model Aggregation

Combine predictions from multiple trained classifiers:

# Get predictions from multiple models
predictions = np.column_stack([
    model1.predict(X),
    model2.predict(X),
    model3.predict(X),
    # ... more models
])

# Learn optimal aggregation
ensemble = DEEM()
ensemble.fit(predictions)
final_predictions = ensemble.predict(predictions)

3. Missing Predictions

DEEM automatically handles cases where some classifiers don't provide predictions (use -1 for missing):

predictions = np.array([
    [0, 1, -1, 2, 1],  # Classifier 3 missing
    [1, 1, 1, -1, 1],  # Classifier 4 missing
    # ...
])
model = DEEM(n_classes=3)
model.fit(predictions)  # Missing values handled automatically

4. Weighted Initialization (Default ON)

By default, DEEM scales RBM weights by each classifier's agreement with majority vote. This gives better classifiers more influence:

# Weighted initialization is ON by default (recommended)
model = DEEM(n_classes=3)  # use_weighted=True by default
model.fit(predictions)

# Disable for ablation studies only
model = DEEM(n_classes=3, use_weighted=False)
model.fit(predictions)  # All classifiers treated equally

How It Works

DEEM uses Restricted Boltzmann Machines (RBMs) - energy-based models that learn the joint probability distribution over classifier predictions and hidden representations. The key insight is that multiple weak classifiers contain complementary information that can be combined through unsupervised learning.

Key Components

1. Energy Function: Models compatibility between visible (predictions) and hidden (consensus) states
2. Contrastive Divergence: Trains the RBM using GWG (Gibbs with Gradients) sampling
3. Hungarian Algorithm: Solves the label permutation problem during evaluation
4. Weighted Initialization: Scales weights by classifier quality (agreement with majority vote)
5. Buffer Initialization: Automatic sampler buffer initialization for better MCMC mixing

Architecture

Classifier Predictions → [Preprocessing] → RBM → Hidden Representation → Consensus Label
     (visible layer)       (optional)           (hidden layer)

What Happens Under the Hood

When you call model.fit(predictions):

1. Data Preparation: Filters samples with all missing values, infers n_classes
2. Buffer Initialization: First batch initializes MCMC sampler buffer (transparent)
3. Weighted Initialization: RBM weights scaled by classifier accuracy vs majority vote
4. Training: Contrastive divergence learns the energy function
5. Result: Model ready to predict consensus labels

When you call model.predict(data, align_to=reference):

1. Forward Pass: Compute hidden layer probabilities
2. Argmax: Get predicted class for each sample
3. Hungarian Alignment: Match predicted labels to majority vote of reference
4. Return: Aligned consensus predictions

API Reference

DEEM

Main class for ensemble aggregation.

Core Parameters:

• n_classes (int, optional): Number of classes. Auto-detected if not specified.
• hidden_dim (int, default=1): Number of hidden units. Keep at 1 for best results.
• cd_k (int, default=10): Contrastive divergence steps.
• deterministic (bool, default=True): Use probabilities instead of sampling.
• learning_rate (float, default=0.001): Learning rate for SGD.
• momentum (float, default=0.9): SGD momentum.
• epochs (int, default=100): Training epochs.
• batch_size (int, default=128): Batch size.
• device (str, default='auto'): Device ('cpu', 'cuda', or 'auto').
• random_state (int, optional): Random seed.

Phase 3 Parameters (New):

• use_weighted (bool, default=True): Scale weights by classifier accuracy vs majority vote.
  • Recommended: Keep True for production use.
  • Set to False only for ablation studies.
• auto_hyperparameters (bool, default=False): Auto-select hyperparameters based on data.
• model_dir (str, optional): Path to hyperparameter predictor models.

Preprocessing Parameters (Advanced):

• use_preprocessing (bool, default=False): Add Multinomial preprocessing layers.
• preprocessing_layers (int, default=1): Number of preprocessing layers.
• preprocessing_activation (str, default='sparsemax'): Activation function.
• preprocessing_init (str, default='identity'): Weight initialization method.

Sampler Parameters (Advanced):

• sampler_steps (int, default=5): MCMC sampling steps.
• sampler_oh_mode (bool, default=False): One-hot mode (auto-enabled for soft labels).

Methods:

• fit(predictions, labels=None, **kwargs): Train the model (unsupervised)
• predict(predictions, return_probs=False, align_to=None): Get consensus predictions
  • align_to: Reference data for Hungarian alignment (uses majority vote)
• score(predictions, true_labels): Compute accuracy with automatic alignment
• get_class_mapping(): Get the cached Hungarian class mapping
• reset_class_mapping(): Clear the cached mapping
• save(path): Save model to disk
• load(path): Load model from disk
• get_params(): Get parameters (sklearn compatibility)
• set_params(**params): Set parameters (sklearn compatibility)

Attributes (after fit):

• model_: The trained RBM model
• class_map_: Hungarian mapping (after alignment)
• n_classes_: Number of classes
• n_classifiers_: Number of classifiers
• history_: Training history
• is_fitted_: Whether model is trained

Advanced Features

Transparent Hungarian Alignment

The align_to parameter provides transparent control over label alignment:

# Align predictions to majority vote of training data
train_consensus = model.predict(train_preds, align_to=train_preds)

# Same alignment is cached and reused
test_consensus = model.predict(test_preds)  # Uses cached class_map_

# Force recomputation
model.reset_class_mapping()
new_consensus = model.predict(test_preds, align_to=test_preds)

# Get the mapping for inspection
mapping = model.get_class_mapping()
print(f"Predicted class 0 → Aligned class {mapping[0]}")

Important: Alignment is always against MAJORITY VOTE, not true labels. This preserves the unsupervised nature of the model.

Automatic Hyperparameter Selection

NEW: Hyperparameter prediction now works out-of-the-box! No need to specify model_dir.

# Simple - uses bundled trained models automatically
model = DEEM(
    n_classes=10,
    auto_hyperparameters=True  # That's it! 
)
model.fit(predictions, verbose=True)  # Shows auto-selected hyperparameters

# Still optionally override specific hyperparameters
model = DEEM(
    auto_hyperparameters=True,
    epochs=100,  # Override auto-selected epochs
    batch_size=512  # Override auto-selected batch size
)

# Use custom trained models (for experiments)
model = DEEM(
    auto_hyperparameters=True,
    model_dir='path/to/custom/models'  # Optional
)

What gets predicted automatically:

• batch_size: Training batch size
• epochs: Number of training epochs
• learning_rate: Optimizer learning rate
• init_method: Weight initialization (mv_rand, mv_lo, rand)
• num_layers: Number of preprocessing layers
• activation_func: Preprocessing activation function
• momentum: Optimizer momentum
• scheduler: Learning rate scheduler

The predictor uses dataset meta-features (n_samples, n_classifiers, token_density, etc.) to select optimal hyperparameters.

Soft Labels (Probability Distributions)

DEEM automatically detects and handles soft labels (3D tensors):

# soft_predictions: (n_samples, n_classes, n_classifiers)
# Each entry is a probability distribution over classes
soft_predictions = classifier_probabilities  # Shape: (100, 3, 15)

model = DEEM(n_classes=3)
model.fit(soft_predictions)  # Auto-detects 3D, enables oh_mode
consensus = model.predict(soft_predictions)

What happens automatically:

• Detects 3D tensor → enables one-hot sampler mode
• Infers n_classes from tensor shape (dim 1)
• Normalizes probabilities if needed

Save and Load Models

# Save trained model
model.save('my_ensemble.pt')

# Load later
model = DEEM()
model.load('my_ensemble.pt')
predictions = model.predict(new_data)

Preprocessing Layers (Advanced)

For complex datasets, add learnable preprocessing layers:

model = DEEM(
    n_classes=3,
    use_preprocessing=True,
    preprocessing_layers=1,
    preprocessing_activation='entmax',
    preprocessing_init='identity'
)
model.fit(predictions)

Disabling Weighted Initialization (Ablation Studies)

# Default behavior: classifiers weighted by accuracy vs majority vote
model = DEEM(n_classes=3, use_weighted=True)  # Default

# For ablation studies: disable weighting
model = DEEM(n_classes=3, use_weighted=False)
model.fit(predictions)  # All classifiers treated equally

Hyperparameters Reference

Core Training Parameters

Parameter	Type	Default	Description
n_classes	int, optional	None	Number of classes. Auto-inferred from data if not provided.
hidden_dim	int	1	Number of hidden units. Keep at 1 for best results.
learning_rate	float	0.001	Learning rate for optimizer.
epochs	int	50	Number of training epochs.
batch_size	int	128	Training batch size. Larger = faster, smaller = better mixing.
momentum	float	0.0	SGD momentum. Range: [0, 1].
device	str	'auto'	Device: 'auto', 'cpu', or 'cuda'. Auto selects GPU if available.

RBM Model Parameters

Parameter	Type	Default	Description
cd_k	int	10	Contrastive divergence steps. Higher = better but slower.
deterministic	bool	True	Use probabilities (True) vs sampling (False). Keep True for stability.
init_method	str	'mv_rand'	Weight init: 'mv_rand' (majority vote + random), 'mv_lo', or 'rand'.
use_weighted	bool	True	Scale weights by classifier accuracy vs majority vote. Recommended: True.

Sampler Parameters

Parameter	Type	Default	Description
sampler_steps	int	10	MCMC sampler steps. More steps = better samples but slower.
sampler_oh_mode	bool	False	One-hot mode for sampler. Auto-enabled for soft labels (3D tensors).

Preprocessing Parameters

Parameter	Type	Default	Description
use_preprocessing	bool	False	Enable learnable preprocessing layers before RBM.
preprocessing_layers	int	0	Number of Multinomial layers. Ignored if preprocessing_layer_widths specified.
preprocessing_layer_widths	list[int], optional	None	Custom layer widths, e.g., [20, 15, 10]. Overrides preprocessing_layers.
preprocessing_activation	str	'sparsemax'	Activation: 'sparsemax', 'entmax', 'softmax', 'relu', 'gelu', etc.
preprocessing_init	str	'identity'	Preprocessing init: 'identity', 'rand', 'mv'.
preprocessing_one_hot	bool	False	Use one-hot encoding in preprocessing.
preprocessing_use_softmax	bool	False	Apply softmax in preprocessing layers.
preprocessing_jitter	float	0.0	Jitter coefficient for preprocessing.

AutoML Parameters

Parameter	Type	Default	Description
auto_hyperparameters	bool	False	Enable automatic hyperparameter selection. Works out-of-the-box!
model_dir	str/Path, optional	None	Custom model directory. None = use bundled models.

Other Parameters

Parameter	Type	Default	Description
random_state	int, optional	None	Random seed for reproducibility.
kwargs	dict	{}	Additional kwargs passed to RBM model (e.g., custom init_method).

Soft Labels Guide

DEEM supports both hard labels (integers) and soft labels (probability distributions).

Hard Labels (Standard)

# Shape: (n_samples, n_classifiers)
# Each entry is an integer class label: 0, 1, 2, ..., k-1
hard_predictions = np.array([
    [0, 1, 0, 2, 0],  # Sample 1: classifiers predict 0, 1, 0, 2, 0
    [1, 1, 2, 1, 1],  # Sample 2: classifiers predict 1, 1, 2, 1, 1
    [2, 2, 2, 1, 2],  # Sample 3: classifiers predict 2, 2, 2, 1, 2
])

model = DEEM(n_classes=3)
model.fit(hard_predictions)

Soft Labels (Probability Distributions)

# Shape: (n_samples, n_classes, n_classifiers)
# Each entry is a probability distribution over classes
soft_predictions = np.array([
    # Sample 1 - 5 classifiers, each gives 3-class distribution
    [[0.7, 0.2, 0.1],  # Classifier 1: 70% class 0, 20% class 1, 10% class 2
     [0.1, 0.8, 0.1],  # Classifier 2: 10% class 0, 80% class 1, 10% class 2
     [0.6, 0.3, 0.1],  # Classifier 3: ...
     [0.2, 0.3, 0.5],  # Classifier 4: ...
     [0.8, 0.1, 0.1]], # Classifier 5: ...
    
    # Sample 2
    [[0.1, 0.7, 0.2],
     [0.2, 0.6, 0.2],
     [0.3, 0.4, 0.3],
     [0.1, 0.8, 0.1],
     [0.2, 0.7, 0.1]],
])
# Shape: (2, 3, 5) = (n_samples=2, n_classes=3, n_classifiers=5)

# DEEM automatically detects 3D tensors as soft labels!
model = DEEM()  # n_classes inferred from shape: 3
model.fit(soft_predictions)  # Auto-enables oh_mode=True
consensus = model.predict(soft_predictions)  # Returns hard labels: [0, 1, ...]

What happens automatically with soft labels:

1. ✅ 3D tensor detection: Checks if predictions.shape[0] == 3
2. ✅ Auto-infer n_classes: Extracts from predictions.shape[1]
3. ✅ Enable oh_mode: Sets sampler_oh_mode=True automatically
4. ✅ Proper preprocessing: Converts distributions to one-hot during sampling

Converting between formats:

# Soft → Hard (argmax)
hard_preds = soft_preds.argmax(axis=1)  # (N, K, D) → (N, D)

# Hard → Soft (one-hot)
from torch.nn.functional import one_hot
soft_preds = one_hot(torch.tensor(hard_preds), num_classes=3).numpy()
soft_preds = soft_preds.transpose(0, 2, 1)  # (N, D, K) → (N, K, D)

Preprocessing Guide

Preprocessing layers learn to transform classifier outputs before the RBM, useful for:

• Handling heterogeneous classifiers (different architectures)
• Learning calibration/alignment of classifier outputs
• Dimensionality transformation

Basic Preprocessing (Fixed Width)

# Add 2 preprocessing layers, each maintains same width (n_classifiers)
model = DEEM(
    n_classes=3,
    use_preprocessing=True,
    preprocessing_layers=2,  # Number of layers
    preprocessing_activation='entmax',  # Activation function
    preprocessing_init='identity',  # Initialize to identity transform
)
# Architecture: input(15) → Multinomial(15) → Multinomial(15) → RBM(15)

Custom Width Preprocessing

# Transform classifier dimension: 15 → 20 → 15 → 10
model = DEEM(
    n_classes=3,
    use_preprocessing=True,
    preprocessing_layer_widths=[20, 15, 10],  # Explicit widths
    preprocessing_activation='sparsemax',
)
# Architecture: input(15) → Multinomial(20) → Multinomial(15) → Multinomial(10) → RBM(10)

Activation Functions

Activation	Description	When to Use
sparsemax	Sparse softmax (default)	General purpose, encourages sparsity
entmax	Entmax-1.5	Adaptive sparsity, good for ensembles
softmax	Standard softmax	Dense distributions
relu	ReLU	Non-negative outputs
gelu	GELU	Smooth non-linearity

Initialization Methods

Init Method	Description	When to Use
identity	Identity transform (default)	Preserve input initially
rand	Random weights	Learn from scratch
mv	Majority vote statistics	Start near MV baseline

Example: YAML Config Equivalent

# Research code YAML config:
# model:
#   multinomial_net:
#     num_layers: 1
#     activation_func_name: 'entmax'
#     init_method: 'identity'
#     one_hot: False

# Python API equivalent:
model = DEEM(
    n_classes=3,
    use_preprocessing=True,
    preprocessing_layers=1,
    preprocessing_activation='entmax',
    preprocessing_init='identity',
    preprocessing_one_hot=False,
)

Troubleshooting

Model starts with low accuracy (~40%)

Problem: Model initialized with random weights instead of majority vote.

Solution: Check init_method:

model = DEEM(init_method='mv_rand')  # Should start near MV accuracy

If using auto_hyperparameters=True, this is handled automatically.

Double printing in Jupyter notebooks

Problem: Buffer/weighted init messages print twice with identical timestamps.

Solution: This is a Jupyter display quirk with %autoreload 2, not actual duplicate calls. The functionality works correctly. To avoid, disable autoreload or ignore the duplicate.

AutoML models not found

Problem: model_dir not found warning when using auto_hyperparameters=True.

Solution (v0.2.0+): Models are now bundled! Just upgrade:

pip install --upgrade deem

For older versions, download models separately or specify model_dir.

Soft labels not detected

Problem: 3D tensor not auto-detected as soft labels.

Check:

1. Shape must be (n_samples, n_classes, n_classifiers) - note the order!
2. Data type must be float (not int)
3. Values should sum to ~1.0 along axis 1 (probability distributions)

# Verify shape and normalization
print(f"Shape: {soft_preds.shape}")  # Should be (N, K, D)
print(f"Sum along axis 1: {soft_preds.sum(axis=1)}")  # Should be ~1.0

Out of memory on GPU

Problem: CUDA out of memory error.

Solutions:

1. Reduce batch_size: model = DEEM(batch_size=64)
2. Use CPU: model = DEEM(device='cpu')
3. Use smaller dataset subset for experimentation

Predictions don't match labels (wrong alignment)

Problem: Accuracy looks random (~33% for 3 classes).

Solution: Use align_to parameter or score() method:

# Wrong - no alignment
accuracy = (predictions == labels).mean()  # ❌ Random accuracy

# Correct - with alignment
accuracy = model.score(predictions, labels)  # ✅ Proper accuracy
# Or:
consensus = model.predict(predictions, align_to=train_predictions)
accuracy = (consensus == labels).mean()

Remember: Alignment is against MAJORITY VOTE, not true labels (unsupervised).

Training is slow

Solutions:

1. Use GPU: model = DEEM(device='cuda')
2. Increase batch_size: model = DEEM(batch_size=512)
3. Reduce cd_k: model = DEEM(cd_k=5) (default 10)
4. Reduce sampler_steps: model = DEEM(sampler_steps=5) (default 10)
5. Use fewer epochs: model = DEEM(epochs=20) (default 50)

Model not improving beyond majority vote

Check:

1. use_weighted=True (default, gives better classifiers more influence)
2. init_method='mv_rand' (starts near MV)
3. Sufficient epochs (try 50-100)
4. Dataset quality (are classifiers diverse and reasonably accurate?)

Note: DEEM is designed to match or slightly exceed majority vote. Large improvements (>5-10%) are rare and depend on dataset characteristics.

Requirements

Core Dependencies (installed automatically):

• Python >= 3.8
• PyTorch >= 1.9
• NumPy >= 1.19
• SciPy >= 1.7
• entmax >= 1.0
• scikit-learn >= 0.24 (for automatic hyperparameters)
• pandas >= 1.3 (for automatic hyperparameters)
• joblib >= 1.0 (for automatic hyperparameters)

Development (optional):

pip install deem[dev]  # Includes pytest, ruff

Authors

Maymona Albadri - @Rem4rkable

Citation

If you use DEEM in your research, please cite:

@software{deem2026,
  title={DEEM: Deep Ensemble Energy Models for Classifier Aggregation},
  author={Albadri, Maymona},
  year={2026},
  url={https://github.com/shaham-lab/deem}
}

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

Acknowledgments

• Based on research in energy-based models and crowd learning
• Built with PyTorch and inspired by scikit-learn's API design

Links

• GitHub: https://github.com/shaham-lab/deem
• Documentation: [Coming soon]
• Issues: https://github.com/shaham-lab/deem/issues

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