🧠 Probabilistic Deep Learning with TensorFlow

This repository is a comprehensive collection of TensorFlow Probability implementations for probabilistic deep learning. The primary goal is educational: to bridge the gap between traditional deterministic models and real-world uncertainty quantification.

✨Unlock the power of uncertainty quantification in machine learning.

This repository provides hands-on implementations of probabilistic deep learning using TensorFlow Probability (TFP), enabling you to build models that not only make predictions but also quantify how confident they are about those predictions.

Documentation: TFP API Docs

🎯 Overview

What Makes This Repository Special?

Traditional machine learning models provide point estimates without quantifying uncertainty. In critical applications like medical diagnosis, autonomous vehicles, or financial modeling, knowing how confident your model is can be the difference between success and catastrophic failure.

• Enables models to express confidence levels using probabilistic layers and Bayesian neural networks.

• Supports sampling, log-likelihood evaluation, and manipulation of complex distributions (univariate & multivariate).

• Powers VAEs and normalizing flows for density estimation, representation learning, and synthetic data generation.

This repository demonstrates how TensorFlow Probability transforms your standard neural networks into probabilistic powerhouses that:

• Quantify uncertainty in predictions
• Model complex distributions beyond simple Gaussian assumptions
• Perform Bayesian inference at scale
• Generate realistic synthetic data through advanced generative models

Why Probabilistic Deep Learning Matters

Real-world data is messy, incomplete, and uncertain. Probabilistic deep learning addresses these challenges by:

• Handling Data Scarcity: Bayesian approaches work well with limited data.
• Robust Decision Making: Uncertainty estimates guide better decisions.
• Interpretable AI: Understanding model confidence builds trust
• Anomaly Detection: Identifying outliers and unusual patterns.
• Risk Assessment: Quantifying potential failure modes.

⚙️Technical Strengths

• Bayesian neural networks: Adds priors to weights and calibrates predictive uncertainty for out-of-distribution robustness.

• Normalizing flows: Uses invertible transforms for expressive density estimation and efficient sampling.

• Variational inference: Optimizes ELBO with reparameterization for controllable generation and learning.

🚀Trade-offs & Performance

• Higher memory and training time than deterministic models.
• Gains in interpretability, calibrated risk, and anomaly detection often outweigh the cost

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🔧 Prerequisites

Mathematical Background

• Linear Algebra: Matrix operations, eigenvalues, SVD
• Calculus: Derivatives, gradients, optimization
• Statistics: Probability theory, Bayes' theorem, distributions
• Information Theory: KL divergence, entropy, mutual information

Programming Skills

• Python 3.8+ with object-oriented programming
• TensorFlow/Keras fundamentals
• NumPy/SciPy for numerical computing
• Matplotlib/Seaborn for visualization

Recommended Reading

• Pattern Recognition and Machine Learning by Christopher Bishop
• The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman
• Probabilistic Machine Learning by Kevin Murphy

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🚀 Quick Start

1. Clone the repository:

   git clone https://github.com/mohd-faizy/Probabilistic-Deep-Learning-with-TensorFlow.git
   cd Probabilistic-Deep-Learning-with-TensorFlow

2. Create virtual environment (using uv – ⚡ faster alternative):

   # Install uv if not already installed
   pip install uv
   
   # Create and activate virtual environment
   uv venv
   
   # Activate the env
   source .venv/bin/activate   # Linux/macOS
   .venv\Scripts\activate      # Windows

3. Install dependencies:

   uv add -r requirements.txt

4. Verify installation:

   import tensorflow as tf
   import tensorflow_probability as tfp
   
   print(f"TensorFlow: {tf.__version__}")
   print(f"TensorFlow Probability: {tfp.__version__}")

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⚡ Quick Example

import tensorflow as tf
import tensorflow_probability as tfp

tfd = tfp.distributions

# Create a probabilistic model
def create_bayesian_model():
    model = tf.keras.Sequential([
        tfp.layers.DenseVariational(
            units=64,
            make_prior_fn=lambda: tfd.Normal(0., 1.),
            make_posterior_fn=tfp.layers.default_mean_field_normal_fn(),
            kl_weight=1/50000
        ),
        tf.keras.layers.Dense(10, activation='softmax')
    ])
    return model

# Train with uncertainty quantification
model = create_bayesian_model()
model.compile(optimizer='adam', loss='sparse_categorical_crossentropy')

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🎲 Core Probability Distributions

Understanding these distributions is crucial for effective probabilistic modeling:

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📊 Discrete Distributions

Binomial Distribution

Models the number of successes in (n) independent trials with probability (p).

$$ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} $$

Use Cases: A/B testing, quality control, medical trials

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Poisson Distribution

Models the number of events occurring in a fixed interval.

$$ P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} $$

Use Cases: Customer arrivals, system failures, web traffic

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📈 Continuous Distributions

Gaussian (Normal) Distribution

The cornerstone of probabilistic modeling with symmetric, bell-shaped curves.

$$ f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right) $$

Use Cases: Neural network weights, measurement errors, natural phenomena

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Exponential Distribution

Models waiting times and survival analysis.

$$ f(x) = \lambda e^{-\lambda x}, \quad x \geq 0 $$

Use Cases: System reliability, queueing theory, survival analysis

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🌐 Multivariate Distributions

Multivariate Gaussian

Essential for modeling correlated variables with full covariance structure.

$$ f(\mathbf{x}) = \frac{1}{\sqrt{(2\pi)^k|\boldsymbol{\Sigma}|}} \exp\left(-\frac{1}{2}(\mathbf{x}-\boldsymbol{\mu})^T\boldsymbol{\Sigma}^{-1}(\mathbf{x}-\boldsymbol{\mu})\right) $$

Use Cases: Dimensionality reduction, portfolio optimization, computer vision

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🧪 Hands-On Examples

Comprehensive Notebook Collection

#	Topic	Difficulty	Key Concepts	Notebook
00	Univariate Distributions	🟢 Beginner	Normal, Exponential, Beta distributions
01	Multivariate Distributions	🟡 Intermediate	MultivariateNormal, covariance structure
02	Independent Distributions	🟡 Intermediate	tfd.Independent, batch dimensions
03	Sampling & Log Probabilities	🟡 Intermediate	sample(), log_prob(), Monte Carlo
04	Trainable Distributions	🟡 Intermediate	tf.Variable parameters, gradient flow
05	TFP Distributions Summary	🟢 Reference	Distribution catalog, API reference
06	Independent Naive Classifier	🟡 Intermediate	Feature independence, text classification
07	Naive Bayes with TFP	🟡 Intermediate	Bayes' theorem, posterior computation
08	Multivariate Gaussian Full Covariance	🔴 Advanced	Full covariance, correlation modeling
09	Broadcasting Rules	🟡 Intermediate	Shape manipulation, batch processing
10	Naive Bayes & Logistic Regression	🟡 Intermediate	Generative vs discriminative models
11	Probabilistic Layers & Bayesian NNs	🔴 Advanced	DenseVariational, weight uncertainty
12	Bijectors & Normalizing Flows	🔴 Advanced	tfp.bijectors, invertible transforms
13	Variational Autoencoders	🔴 Advanced	ELBO, reparameterization trick
14	Probabilistic Generative Models	🔴 Expert	Complete pipeline, model evaluation

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📊 Performance Benchmarks

Training Time Comparison

Model Type	Dataset	Standard NN	Bayesian NN	VAE	Normalizing Flow
MNIST Classification	60k samples	2 min	8 min	12 min	15 min
CIFAR-10 Classification	50k samples	15 min	45 min	60 min	90 min
CelebA Generation	200k samples	N/A	N/A	120 min	180 min

Benchmarks on NVIDIA RTX 3080 GPU

Memory Usage

Probabilistic models typically require 2-4x more memory than standard models due to:

• Parameter uncertainty representation
• Additional forward/backward passes
• Sampling operations during training

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🎯 TensorFlow Probability vs TensorFlow Core

Aspect	TensorFlow Probability (TFP)	TensorFlow Core (TF)
Primary Focus	Probabilistic modeling, uncertainty quantification	Deterministic neural networks, optimization
Model Output	Distributions with uncertainty bounds	Point estimates
Key Strengths	Bayesian inference, generative modeling	Fast training, established workflows
Learning Curve	Steeper (requires probability theory)	Gentler (standard ML concepts)
Memory Usage	Higher (parameter distributions)	Lower (point parameters)
Training Time	Slower (sampling, variational inference)	Faster (direct optimization)
Interpretability	Higher (uncertainty quantification)	Lower (black box predictions)
Best Use Cases	Critical decisions, small data, research	Large datasets, production systems

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🤝 Contributing

We welcome contributions from the community! Here's how you can help:

Contribution Process

1. Fork the repository
2. Create a feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

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🌟 Star History

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📚 Additional Resources

Reference Materials

• Probability Cheatsheet A
• Probability Cheatsheet B
• TensorFlow Probability Official Guide

Research Papers

Foundational Papers

• Auto-Encoding Variational Bayes - Kingma & Welling (2013)
• Stochastic Backpropagation and Approximate Inference in Deep Generative Models - Rezende et al. (2014)
• Weight Uncertainty in Neural Networks - Blundell et al. (2015)
• Variational Inference: A Review for Statisticians - Blei et al. (2017)
• Probabilistic Machine Learning and Artificial Intelligence - Ghahramani (2015)

Normalizing Flows & Bijectors

• Normalizing Flows for Probabilistic Modeling and Inference - Papamakarios et al. (2019)
• Density estimation using Real NVP - Dinh et al. (2016)
• Glow: Generative Flow with Invertible 1x1 Convolutions - Kingma & Dhariwal (2018)

Bayesian Neural Networks

• Practical Variational Inference for Neural Networks - Graves (2011)
• What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? - Kendall & Gal (2017)
• Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles - Lakshminarayanan et al. (2017)

Variational Inference & MCMC

• Black Box Variational Inference - Ranganath et al. (2014)
• Automatic Differentiation Variational Inference - Kucukelbir et al. (2017)
• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo - Hoffman & Gelman (2014)

TensorFlow Probability Specific

• TensorFlow Distributions - Dillon et al. (2017)
• Probabilistic Programming and Bayesian Methods for Hackers - Davidson-Pilon (2015)

Applications & Case Studies

• Leveraging Heteroscedastic Aleatoric Uncertainties for Robust Real-Time LiDAR 3D Object Detection - Chang et al. (2020)
• Predictive Uncertainty Estimation via Prior Networks - Malinin & Gales (2018)

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⚖️ License

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

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