Gaussian Processes

ExpQuad(input_dim, lengthscales[, active_dims]) The exponentiated quadratic kernel.
RatQuad(input_dim, lengthscales, alpha[, ...]) The rational quadratic kernel.
Matern32(input_dim, lengthscales[, active_dims]) The Matern kernel with nu = 3/2.
Matern52(input_dim, lengthscales[, active_dims]) The Matern kernel with nu = 5/2.
Exponential(input_dim, lengthscales[, ...]) The Exponential kernel.
Cosine(input_dim, lengthscales[, active_dims]) The cosine kernel.
Linear(input_dim, c[, active_dims]) The linear kernel.
Polynomial(input_dim, c, d, offset[, ...]) The polynomial covariance function.
WarpedInput(input_dim, cov_func, warp_func) Warp the inputs of any covariance function using an arbitrary function defined using Theano.
Gibbs(input_dim, lengthscale_func[, args, ...]) Use an arbitrary lengthscale function defined using Theano.
class pymc3.gp.cov.ExpQuad(input_dim, lengthscales, active_dims=None)

The exponentiated quadratic kernel. Also refered to as the squared exponential, or radial basis function kernel.

\[k(x, x') = \mathrm{exp}\left[ -\frac{(x - x')^2}{2 \ell^2} \right]\]
class pymc3.gp.cov.RatQuad(input_dim, lengthscales, alpha, active_dims=None)

The rational quadratic kernel.

\[k(x, x') = \left(1 + \frac{(x - x')^2}{2\alpha\ell^2} \right)^{-\alpha}\]
class pymc3.gp.cov.Exponential(input_dim, lengthscales, active_dims=None)

The Exponential kernel.

\[k(x, x') = \mathrm{exp}\left[ -\frac{||x - x'||}{2\ell^2} \right]\]
class pymc3.gp.cov.Matern52(input_dim, lengthscales, active_dims=None)

The Matern kernel with nu = 5/2.

\[k(x, x') = \left(1 + \frac{\sqrt{5(x - x')^2}}{\ell} + \frac{5(x-x')^2}{3\ell^2}\right) \mathrm{exp}\left[ - \frac{\sqrt{5(x - x')^2}}{\ell} \right]\]
class pymc3.gp.cov.Matern32(input_dim, lengthscales, active_dims=None)

The Matern kernel with nu = 3/2.

\[k(x, x') = \left(1 + \frac{\sqrt{3(x - x')^2}}{\ell}\right)\mathrm{exp}\left[ - \frac{\sqrt{3(x - x')^2}}{\ell} \right]\]
class pymc3.gp.cov.Linear(input_dim, c, active_dims=None)

The linear kernel.

\[k(x, x') = (x - c)(x' - c)\]
class pymc3.gp.cov.Polynomial(input_dim, c, d, offset, active_dims=None)

The polynomial covariance function.

\[k(x, x') = [(x - c)(x' - c) + \mathrm{offset}]^{d}\]
class pymc3.gp.cov.Cosine(input_dim, lengthscales, active_dims=None)

The cosine kernel.

\[k(x, x') = \mathrm{cos}\left( \frac{||x - x'||}{ \ell^2} \right)\]
class pymc3.gp.cov.WarpedInput(input_dim, cov_func, warp_func, args=None, active_dims=None)

Warp the inputs of any covariance function using an arbitrary function defined using Theano.

\[k_{\mathrm{warped}}(x, x') = k(w(x), w(x'))\]
Parameters:
  • cov_func (Covariance) –
  • warp_func (callable) – Theano function of X and additional optional arguments.
  • args (optional, tuple or list of scalars or PyMC3 variables) – Additional inputs (besides X or Z) to warp_func.
class pymc3.gp.cov.Gibbs(input_dim, lengthscale_func, args=None, active_dims=None)

Use an arbitrary lengthscale function defined using Theano. Operates on a single input dimension.

\[k_{\mathrm{gibbs}}(x, x') = \sqrt{\frac{2\ell(x)\ell(x')}{\ell^2(x) + \ell^2(x')}} \mathrm{exp}\left[ -\frac{(x - x')^2}{\ell(x)^2 + \ell^2(x')} \right]\]
Parameters:
  • lengthscale_func (callable) – Theano function of X and additional optional arguments.
  • args (optional, tuple or list of scalars or PyMC3 variables) – Additional inputs (besides X or Z) to warp_func.