Probabilistic prediction

As explained in Bayesian Optimization in Action

A probabilistic prediction is a prediction represented by a probability distribution rather than a single point value.

Probabilistic prediction represents an outcome with a probability distribution rather than a single point value. This distribution expresses predictive uncertainty, helping Bayesian optimization balance risk and reward when choosing what to evaluate next. section 1.2.1

The distinction from point prediction is practical:

• A ridge regressor predicts one value at each test point; for example, it predicts 2.2 at test point 2. section 1.2.1
• A Gaussian process produces a probability distribution at each test point, revealing how uncertain the prediction is. section 1.2.1
• This uncertainty supports better risk–reward tradeoffs than predictions that provide no uncertainty measure. section 1.2.1

Figure 1.3 Non-Bayesian models, such as ridge regressors, make pointwise estimates, while GPs produce probability distributions as predictions. GPs thus offer a calibrated quantification of uncertainty, which is an important factor when making high-risk decisions.

Compare pointwise estimates with Gaussian-process distributions and their calibrated uncertainty visually. section 1.2.1

How Bayesian Optimization in Action covers it

How deep it goes

Defines distribution-valued predictions and contrasts them with point estimates, without developing Gaussian-process internals.

Examples

Uses a regression dataset, a ridge prediction of 2.2 at test point 2, and a visual comparison with Gaussian-process predictions.

What you can do after

Evaluate model predictions by distinguishing single-valued estimates from uncertainty-aware probability distributions.

How it connects

Connects Gaussian processes with Bayesian optimization, ridge regression, support vector machines, decision trees, and neural networks.

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