Extended Data Fig. 1: Overview of MIRA topic model architecture.

a, The MIRA topic model uses a variational autoencoder (VAE) approach to learn stochastic mappings between observations in X-space, gene-counts or peak-counts in a cell, which are high-dimensional and noisy, and a simpler latent Z-space or topic space, which exists on the simplex basis with a Dirichlet prior. (bottom right) The generative model relates the observations X to the estimated composition 𝞺 over features (genes or peaks), sampling a negative binomial distribution for RNA counts and a multinomial distribution for ATAC peaks. (top right) The composition over features is given by the topic matrix 𝜷 encoding topic-feature associations and the latent topics Z of a cell, which are sampled from the distribution q_φ(Z|X), the variational approximation of p_𝜗(Z|X). (top left) The distribution of Z is parameterized by 𝞵 and 𝞼², outputs from the encoder neural network given the X-space observations as inputs. (bottom left) The encoder neural network for RNA data performs deviance residual featurization of counts which are passed through feed-forward layers. The ATAC data encoder passes binarized peak accessibility features through a deep averaging network. (Illustration adapted from Kingma and Welling, Foundations and Trends in Machine Learning, 2019). b, Ratio of probability of medulla fate commitment versus cortex commitment of each cell in the hair follicle, arranged by pseudotime. MIRA defines branch points between cell states where probabilities of differentiating into one terminal state diverges from another. c, MIRA joint representation UMAP colored by ratio of probability of medulla fate commitment within the ORS, matrix, medulla, and cortex populations. Differentiation in the hair follicle proceeds from ORS to progenitor matrix cells, which then specify into the medulla or cortex fate. (IRS cells indicated in black are not included in this trajectory).