Probabilistic model

As explained in Causal AI

Probabilistic modeling is the construction of models that represent uncertainty and data-generating processes with probability distributions.

A probabilistic model represents uncertainty and a data-generating process with probability distributions. It turns uncertain variables into quantities that support prediction, decisions, simulation, or inference. section 2.0 section 2.4

Build one by separating the question from its calculation. First pose the question; then write the probability or related quantity that answers it given the evidence; finally perform statistical inference to estimate that quantity. This workflow distinguishes the target from the procedure used to estimate it. section 1.5.1

Classifying an ambiguous handwritten digit

Given an MNIST image I that might depict 4 or 9, represent the question as P(D=4|I). Compare the conditional probabilities for candidate digits and choose the digit with the highest probability. The image supplies the evidence; the model supplies a distribution over labels rather than only an unexplained prediction. section 1.5 section 1.5.1

Distributions can be inspected visually: discrete outcomes use bars, continuous outcomes use curves, and conditional distributions show how the distribution of one variable changes with another. Conditional independence can reduce the number of variables that must be displayed or modeled together. section 2.1.8

For implementation, pgmpy provides graphical models that are comparatively easy to use and debug, while Pyro provides a more flexible probabilistic machine learning framework built on PyTorch's gradient-based learning. Inference algorithms such as variable elimination and importance sampling calculate conditional distributions from trained models. section 2.0 section 3.1.11

Figure 1.5 Is this an image of the digit 4 or 9? The canonical task of the MNIST dataset is to classify the digit label given the image.

Use the ambiguous MNIST image to connect evidence, conditional probability, and classification. section 1.5.1

How Causal AI covers it

How deep it goes

Explains the query-to-inference workflow, visualizes distributions, and implements inference, while stopping short of a mathematically exhaustive introduction.

Examples

Uses MNIST digit classification, distribution plots, transport-and-education inference, and a probabilistic enzyme model.

What it assumes

Assumes basic probability and statistics while introducing the modeling, inference, and causal concepts needed for probabilistic machine learning.

What you can do after

Apply it via pgmpy or Pyro to specify probabilistic models and infer conditional outcome distributions.

How it connects

Connects probability distributions to statistical inference, Bayesian inference, graphical models, causal models, and structural causal models.

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Also explained in

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  Time Series Forecasting Using Foundation ModelsA probabilistic model represents uncertainty by assigning probability distributions to possible data or prediction outcomes.

Compare how 2 books explain probabilistic model →

Related concepts

• TimeGPTincludes · TimeGPT is a proprietary foundation model designed for time-series forecasting and related time-series analysis.
• Moiraiincludes · Moirai is a foundation model designed for time-series forecasting across varied datasets.
• point forecastcontrasts with · A point forecast is a prediction that assigns a single value to each future observation without representing forecast uncertainty.
• language modelincludes · A language model is a computational model that represents patterns in linguistic tokens to estimate sequence probabilities and predict or generate language from context.
• Bayesian networkincludes · A Bayesian network is a probabilistic graphical model whose directed acyclic graph represents random variables and their conditional dependencies.
• Lag-Llamaincludes · Lag-Llama is a foundation model designed for probabilistic time-series forecasting using lagged series values and date-time features.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.