Modelling Pipeline#

Our current modelling pipeline has three steps.

class gigalens.inference.ModellingSequenceInterface(phys_model, prob_model, sim_config)[source]#

Defines the three steps in modelling:

  1. Multi-starts gradient descent to find the maximum a posteriori (MAP) estimate. See Martí [Marti03], György and Kocsis [GyorgyK11].

  2. Variational inference (VI) using the MAP as a starting point. See Hoffman et al. [HBWP13], Blei et al. [BKM17]. Note that the implementation of variational inference is stochastic variational inference, so VI and SVI are interchangeable.

  3. Hamiltonian Monte Carlo (HMC) using the inverse of the VI covariance matrix as the mass matrix \(M\). See Duane et al. [DKPR87], Neal [Neal11].

Parameters

  • phys_model (PhysicalModel) – The physical model of the lensing system that we want to fit

  • prob_model (ProbabilisticModel) – The probabilistic model of the data we are fitting

  • sim_config (SimulatorConfig) – Parameters for image simulation (e.g., pixel scale)

abstract MAP(optimizer, start, n_samples, num_steps, seed)[source]#

Finds maximum a posteriori (MAP) estimates for the parameters. See Section 2.3 in our paper.

Parameters

  • optimizer – An optimizer object with which to run MAP. Adam or variants thereof are recommended, using a decaying learning rate

  • start (Optional[Any]) – Samples from which to start optimization. If none are provided, optimization will be started by sampling directly from the prior

  • n_samples (int) – Number of samples with which to run multi-starts gradient descent

  • num_steps (int) – Number of gradient descent steps

  • seed (Optional[Any]) – A random seed (only necessary if start is not specified)

Returns

The unconstrained parameters of all n_samples samples after running num_steps of optimization.

abstract SVI(optimizer, start, n_vi, num_steps, init_scales, seed)[source]#

Runs stochastic variational inference (SVI) to characterize the posterior scales. Currently, only multi-variate Gaussian ansatz is supported. Note that the implementation of variational inference is stochastic variational inference, so VI and SVI are interchangeable. This is roughly equivalent to taking the Hessian of the log posterior at the MAP. However, in our experience, the Hessian can become unstable in high dimensions (in cases of very small eigenvalues). See Section 2.4 in our paper.

Parameters

  • optimizer – An optimizer with which to minimize the ELBO loss. Adam or variants thereof are recommended, using slow learning rate warm-up.

  • start – Initial guess for posterior mean. Must be shape (1,d), where d is the number of parameters. Convention is that it is in unconstrained parameter space.

  • n_vi (int) – Number of samples with which to approximate the ELBO loss

  • num_steps (int) – Number of optimization steps

  • init_scales (float or np.array) – Initial VI standard deviation guess

  • seed (Any) – A random seed for drawing samples from the posterior ansatz

Returns

The fitter posterior in unconstrained space

abstract HMC(q_z, init_eps, init_l, n_hmc, num_burnin_steps, num_results, max_leapfrog_steps, seed)[source]#

Runs Hamiltonian Monte Carlo (HMC) to draw posterior samples. See Section 2.5 in our paper.

Parameters

  • q_z – Fitted posterior from SVI. Used to calculate the mass matrix \(M\) for preconditioned HMC. Convention is that q_z is an approximation of the unconstrained posterior.

  • init_eps (float) – Initial step size \(\epsilon\)

  • init_l (int) – Initial number of leapfrog steps \(L\)

  • n_hmc (int) – Number of HMC chains to run in parallel

  • num_burnin_steps (int) – Number of burn-in steps

  • num_results (int) – Number of samples to draw from each chain (after burning in)

  • max_leapfrog_steps (int) – Maximum number of leapfrog steps if \(L\) is tuned automatically

  • seed (Any) – A random seed

Returns

Posterior chains in unconstrained space