Writing

Part 6: Learning Parameters of a Markov Network

Part 6: Learning Parameters of a Markov Network

DJ Rich

The theory of Markov Network parameter learning is intuitive and instructive, but it exposes an intractable normalizer, forbidding the task from reducing to easier ones. Ultimately, the task is hard.

Part 4: Monte Carlo Methods

Part 4: Monte Carlo Methods

DJ Rich

Monte Carlo methods answer the inference task with a set of samples, sampled approximately from the target distribution. In total, they provide a supremely general toolset. However, to use them requires a skill for managing complexities of distributional convergence and autocorrelation.

Part 3: Variational Inference

Part 3: Variational Inference

DJ Rich

Variational Inference, a category of approximate inference algorithms, achieves efficiency by restricting inference to a computationally friendly set of distributions. Using tools from information theory, we may find the distribution that best approximates results of exact inference.

Part 2: Exact Inference

Part 2: Exact Inference

DJ Rich

Given a Probabilistic Graphical Model, exact inference algorithms exploit factorization and caching to answer questions about the system it represents.

Bias-Variance Trade-Off

Bias-Variance Trade-Off

DJ Rich

The bias-variance trade-off is a rare insight into the challenge of generalization.

Information Theory and Entropy

Information Theory and Entropy

DJ Rich

Entropy and its related concepts quantify the otherwise abstract concept of information. A tour reveals its relationship to information, binary encodings and uncertainty. Most intuitively, we're left with a simple analogy to 2D areas.

Generalized Linear Models

Generalized Linear Models

DJ Rich

A Generalized Linear Model, if viewed without knowledge of their motivation, can be a confusing tool. It's easier to understand if seen as a two knob generalization of linear regression.

Jensen's Inequality

Jensen's Inequality

DJ Rich

A visual makes Jensen's Inequality obvious and intuitive.