karltayeb / ipsc_gp_clustering

ipsc_gp_clustering

Assignments.py

Has assignment objects which keep track of gene and cell line level assignments.

pi [K] are cell line cluster mixture weights, the prior probability that a cell line belongs to a given cell line cluster Phi [N, K] are variational parameters for latent cell line assignment. Phi[n, k] gives the (approximate) posterior probability that cell line n belongs to cell line cluster k

psi [L] are gene cluster mixture weights, the prior probability that a gene belongs to a given gene cluster Lambda [G, L] are variational parameters for latent gene assignments. Phi[g, l] gives the (approximate) posterior probability that gene g belongs to gene cluster l

rho [2] a prior on whether a gene cluster is cell-line cluster specific or shared across cell line clusters. Gamma [L, 2] are variational parameters for whether each gene cluster has a shared or cell line specific trajectory. Gamma[l, 0] = 1 indicates that gene cluster trajectories are cell-line cluster specific. Each cell line cluster is free to learn its own expression trajectory for gene cluster l. Gamma[l, 1]=1 indicates that gene cluster l should share an expression trajectory in all cell line clusters.

Each assignment object has a few key functions:

• entropy() computes the entropy of that variational distributions, necessary for computing the evidence lower bound (ELBO)
• compute_weights() computes and expanded representation of assignment. expands Phi, Lambda, and Gamma to get probability that a sample from (cell_line, gene) pair belongs to one of K*L clusters
• update_assignments(m, X, Y) closed form updates for assignment variables. m is the gaussian process model, X, Y are inpute and observations respectively. computes expected likelihood of data under the model, plus prior, appropriately normalized. Also updates phi and psi.

MixtureSVGP.py

Gaussian process model implemented in GPFlow. The implementation is a simple extention of SVGP implemented in GPflow. We can think of this as K*L indpendent gaussian processes, where each (cell_line, gene) is weighted according to the probability that it comes from a particular (cell line cluster, gene cluster).

If we have N cell lines, G genes at T timepoints X is [NGT, D] where D is the dimensionality of your inpiut Y is [NGT, P] where P is the dimensionality of your output weight_idx [NGT] integer indexing of the observations such that all samples belonging to the same (cell_line, gene) share an index.

How to use

Input X, Y, weight_idx as above. We use gpflow's multioutput kernels to specify our model. Each output of the multioutput kernel corresponds to a (cell_line_cluster, gene_cluster) pair.

1. specify a kernel using gpflow multioutput kernel module.

2. specify a set of inducing points using gpflow multioutput feature module.

3. When initializing the model, be sure to specify num_latent, and if necessary minibatch size.

4. If data is only observed at a small number of input locations, and you are using a model with gaussian noise, we can speed up the computations for estimating the mean/variance by doing inference on a GP with the average observations as input. We can initialize a second model that we will feed a weighted average of our observations under the current assignment.

Learning proceeds as follows. We iteravely use the first model to estimate kernel parameters, and the mean-model to estimate trajectories.