Uncertainty Estimation and Bayesian Approaches¶
Preface¶
The goal of Bayesian methods is to maintain the posterior distribution \(p(\mathbf{w |} \mathcal{D})\). These weights can be the parameters for a prediction function or for generative models.
In MAP, we use the point estimate \(\arg\!\max_{\mathbf{w}} p(\mathbf{w} | \mathcal{D})\). Bayesian methods are able to capture more information; the uncertainty we have in out weights. If the distribution is wide, high variance, then we are uncertain about the credibility of our weights producing a good prediction.
With more data, the posterior concentrates and in the limit we once again obtain a point estimate (absolute certainty).
We will talk about Bayesian Linear Regression and Gaussian Processes.
Bayesian Linear Regression¶
Uncertainty in Predictions via Bayesian Inference¶
Uncertainty in Predictions via Bayesian Inference
Nonlinear Uncertainty Estimation¶
Estimating Uncertainty for Nonlinear Models