Probabilistic ML - 25 - Revision

2025-08-05 · Source: Tübingen Machine Learning - YouTube · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Software Development & Engineering · Depth: Advanced, extended

Summary

This lecture provides a comprehensive revision of probabilistic machine learning concepts, emphasizing foundational ideas from the past 24 sessions. It begins with the laws of probability and Bayes' Theorem, highlighting their universal application in inference. The discussion then moves to the intractability of general probabilistic models and introduces Gaussian distributions as a key tool for tractability, showing how Gaussian inference maps to linear algebra. The lecture covers parametric regression, kernel machines, Gaussian processes, and marginal likelihood estimation, explaining how these frameworks are used for learning functions. It addresses computational complexity, particularly for large datasets, leading to the introduction of Markov chains and Kalman filters for online learning and time series analysis. The second half transitions to approximate non-Gaussian methods, detailing exponential families, their conjugate priors, and the properties derived from their log partition functions. Finally, it explores the Laplace approximation as a universal tool for constructing Gaussian posteriors, including its application to deep neural networks, and briefly touches on sampling methods, generative models like diffusion and flow matching, and variational inference, including the EM algorithm and mean-field approaches.

Key takeaway

For AI Engineers and Machine Learning Researchers grappling with model uncertainty and computational tractability, understanding the core principles of probabilistic inference is crucial. You should prioritize Gaussian and exponential family models where applicable, as they offer structured, efficient inference. When exact inference is intractable, consider the Laplace approximation for its universality and computational efficiency, even for deep neural networks, to gain insights into model behavior and uncertainty quantification.

Key insights

Probabilistic inference, though often intractable, provides a foundational framework for machine learning through structured approximations.

Principles

• Bayes' Theorem is fundamental for inference.
• Gaussian models simplify inference to linear algebra.
• Exponential families enable efficient inference via conjugate priors.

Method

The Laplace approximation constructs Gaussian posteriors by finding a mode of the log-posterior and performing a second-order Taylor expansion, leveraging automatic differentiation and optimization.

In practice

• Design smart kernels for Gaussian process models.
• Use Laplace approximation to analyze deep neural network uncertainty.
• Employ iterative algorithms for variational inference in complex models.

Topics

• Bayesian Inference
• Gaussian Models
• Gaussian Processes
• Approximate Inference
• Deep Learning Uncertainty

Best for: AI Student, Machine Learning Engineer, AI Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Tübingen Machine Learning - YouTube.