Bayesian Linear Regression
Budget: $10 – $30 USD
please look at the jupyter note to see the existing code and the required data to run it and more details about the project.
this project focuses on implementing some of the simple requisite calculations and manipulations for applying Bayesian linear regression models.
project include:
computing the posterior distribution,
computing the marginal likelihood,
evaluating and choosing regularisation parameters,
obtaining posterior mean models,
calculating error-bars (the predictive variance),
... some presentation of results.
The data will be derived from a synthetic, noisy, sine wave and our model will be a linearly-weighted set of "Gaussian" (RBF) basis functions.
There are 3 principal tasks (detailed below)
Fit various Gaussian RBF-based linear models to the training data using penalised least-squares (OLS), and visualise the results.
compute the train, validation and test set errors, plus the marginal likelihood, over a range of λλ (or αα ) values,
Identify the best posterior mean model, visualise it along with its error-bars (predictive variance), and consider how those error-bars might be usefully exploited.
this project focuses on implementing some of the simple requisite calculations and manipulations for applying Bayesian linear regression models.
project include:
computing the posterior distribution,
computing the marginal likelihood,
evaluating and choosing regularisation parameters,
obtaining posterior mean models,
calculating error-bars (the predictive variance),
... some presentation of results.
The data will be derived from a synthetic, noisy, sine wave and our model will be a linearly-weighted set of "Gaussian" (RBF) basis functions.
There are 3 principal tasks (detailed below)
Fit various Gaussian RBF-based linear models to the training data using penalised least-squares (OLS), and visualise the results.
compute the train, validation and test set errors, plus the marginal likelihood, over a range of λλ (or αα ) values,
Identify the best posterior mean model, visualise it along with its error-bars (predictive variance), and consider how those error-bars might be usefully exploited.