Widely used deep latent variable models (DLVMs), in particular Variational Autoencoders (VAEs), employ overly simplistic priors on the latent space. To achieve strong clustering performance, existing methods that replace the standard normal prior with a Gaussian mixture model (GMM) require defining the number of clusters to be close to the number of expected ground truth classes a-priori and are susceptible to poor initializations. We leverage VampPrior concepts (Tomczak and Welling, 2018) to fit a Bayesian GMM prior, resulting in the VampPrior Mixture Model (VMM), a novel prior for DLVMs. In a VAE, the VMM attains highly competitive clustering performance on benchmark datasets. Integrating the VMM into scVI (Lopez et al., 2018), a popular scRNA-seq integration method, significantly improves its performance and automatically arranges cells into clusters with similar biological characteristics.

The success of machine learning models relies heavily on effectively representing high-dimensional data. However, ensuring data representations capture human-understandable concepts remains difficult, often requiring the incorporation of prior knowledge and decomposition of data into multiple subspaces. Traditional linear methods fall short in modeling more than one space, while more expressive deep learning approaches lack interpretability. Here, we introduce Supervised Independent Subspace Principal Component Analysis ($\texttt{sisPCA}$), a PCA extension designed for multi-subspace learning. Leveraging the Hilbert-Schmidt Independence Criterion (HSIC), $\texttt{sisPCA}$ incorporates supervision and simultaneously ensures subspace disentanglement. We demonstrate $\texttt{sisPCA}$'s connections with autoencoders and regularized linear regression and showcase its ability to identify and separate hidden data structures through extensive applications, including breast cancer diagnosis from image features, learning aging-associated DNA methylation changes, and single-cell analysis of malaria infection. Our results reveal distinct functional pathways associated with malaria colonization, underscoring the essentiality of explainable representation in high-dimensional data analysis.

Heteroscedastic regression models a Gaussian variable’s mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing network parameters via log likelihood gradients can yield suboptimal mean and uncalibrated variance estimates. Current solutions side-step this optimization problem with surrogate objectives or Bayesian treatments. Instead, we make two simple modifications to optimization. Notably, their combination produces a heteroscedastic model with mean estimates that are provably as accurate as those from its homoscedastic counterpart (i.e. fitting the mean under squared error loss). For a wide variety of network and task complexities, we find that mean estimates from existing heteroscedastic solutions can be significantly less accurate than those from an equivalently expressive mean-only model. Our approach provably retains the accuracy of an equally flexible mean-only model while also offering best-in-class variance calibration. Lastly, we show how to leverage our method to recover the underlying heteroscedastic noise variance.

MOTIVATION: Linkage disequilibrium (LD) matrices derived from large populations are widely used in population genetics in fine-mapping, LD score regression, and linear mixed models for Genome-wide Association Studies (GWAS). However, these matrices can reach large sizes when they are derived from millions of individuals; hence, moving, sharing and extracting granular information from this large amount of data can be cumbersome. RESULTS: We sought to address the need for compressing and easily querying large LD matrices by developing LDmat. LDmat is a standalone tool to compress large LD matrices in an HDF5 file format and query these compressed matrices. It can extract submatrices corresponding to a sub-region of the genome, a list of select loci, and loci within a minor allele frequency range. LDmat can also rebuild the original file formats from the compressed files. AVAILABILITY AND IMPLEMENTATION: LDmat is implemented in python, and can be installed on Unix systems with the command 'pip install ldmat'. It can also be accessed through https://github.com/G2Lab/ldmat and https://pypi.org/project/ldmat/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Multi-task deep learning (DL) models can accurately predict diverse genomic marks from sequence, but whether these models learn the causal relationships between genomic marks is unknown. Here, we describe Deep Mendelian Randomization (DeepMR), a method for estimating causal relationships between genomic marks learned by genomic DL models. By combining Mendelian randomization with in silico mutagenesis, DeepMR obtains local (locus specific) and global estimates of (an assumed) linear causal relationship between marks. In a simulation designed to test recovery of pairwise causal relations between transcription factors (TFs), DeepMR gives accurate and unbiased estimates of the 'true' global causal effect, but its coverage decays in the presence of sequence-dependent confounding. We then apply DeepMR to examine the global relationships learned by a state-of-the-art DL model, BPNet, between TFs involved in reprogramming. DeepMR's causal effect estimates validate previously hypothesized relationships between TFs and suggest new relationships for future investigation.

We construct a new distribution for the simplex using the Kumaraswamy distribution and an ordered stick-breaking process. We explore and develop the theoretical properties of this new distribution and prove that it exhibits symmetry (exchangeability) under the same conditions as the well-known Dirichlet. Like the Dirichlet, the new distribution is adept at capturing sparsity but, unlike the Dirichlet, has an exact and closed form reparameterization--making it well suited for deep variational Bayesian modeling. We demonstrate the distribution's utility in a variety of semi-supervised auto-encoding tasks. In all cases, the resulting models achieve competitive performance commensurate with their simplicity, use of explicit probability models, and abstinence from adversarial training.

Drug screening studies typically involve assaying the sensitivity of a range of cancer cell lines across an array of anti-cancer therapeutics. Alongside these sensitivity measurements high dimensional molecular characterizations of the cell lines are typically available, including gene expression, copy number variation and genomic mutations. We propose a sparse multitask regression model which learns discriminative latent characteristics that predict drug sensitivity and are associated with specific molecular features. We use ideas from Bayesian nonparametrics to automatically infer the appropriate number of these latent characteristics. The resulting analysis couples high predictive performance with interpretability since each latent characteristic involves a typically small set of drugs, cell lines and genomic features. Our model uncovers a number of drug-gene sensitivity associations missed by single gene analyses. We functionally validate one such novel association: that increased expression of the cell-cycle regulator C/EBPδ decreases sensitivity to the histone deacetylase (HDAC) inhibitor panobinostat.

We propose a Bayesian nonparametric prior over feature allocations for sequential data, the birth-death feature allocation process (BDFP). The BDFP models the evolution of the feature allocation of a set of N objects across a covariate (e.g.~time) by creating and deleting features. A BDFP is exchangeable, projective, stationary and reversible, and its equilibrium distribution is given by the Indian buffet process (IBP). We show that the Beta process on an extended space is the de Finetti mixing distribution underlying the BDFP. Finally, we present the finite approximation of the BDFP, the Beta Event Process (BEP), that permits simplified inference. The utility of the BDFP as a prior is demonstrated on real world dynamic genomics and social network data.

Stochastic variational inference (SVI) is emerging as the most promising candidate for scaling inference in Bayesian probabilistic models to large datasets. However, the performance of these methods has been assessed primarily in the context of Bayesian topic models, particularly latent Dirichlet allocation (LDA). Deriving several new algorithms, and using synthetic, image and genomic datasets, we investigate whether the understanding gleaned from LDA applies in the setting of sparse latent factor models, specifically beta process factor analysis (BPFA). We demonstrate that the big picture is consistent: using Gibbs sampling within SVI to maintain certain posterior dependencies is extremely effective. However, we also show that different posterior dependencies are important in BPFA relative to LDA.

In this paper we introduce the Pitman Yor Diffusion Tree (PYDT), a Bayesian non-parametric prior over tree structures which generalises the Dirichlet Diffusion Tree [30] and removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model including showing its construction as the continuum limit of a nested Chinese restaurant process model. We then present two alternative MCMC samplers which allow us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.

Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes then depends only on their cluster assignment. Currently available models can be classified by whether clusters are disjoint or are allowed to overlap. These models can explain a "flat" clustering structure. Hierarchical Bayesian models provide a natural approach to capture more complex dependencies. We propose a model in which objects are characterised by a latent feature vector. Each feature is itself partitioned into disjoint groups (subclusters), corresponding to a second layer of hierarchy. In experimental comparisons, the model achieves significantly improved predictive performance on social and biological link prediction tasks. The results indicate that models with a single layer hierarchy over-simplify real networks.

We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. The generative process for the tree is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet and Pitman-Yor diffusion trees (Neal, 2003b; Knowles & Ghahramani, 2011), both of which define tree structures over clusters of the particles. With the beta diffusion tree, however, multiple copies of a particle may exist and diffuse to multiple locations in the continuous space, resulting in (a random number of) possibly overlapping clusters of the objects. We demonstrate how to build a hierarchically-clustered factor analysis model with the beta diffusion tree and how to perform inference over the random tree structures with a Markov chain Monte Carlo algorithm. We conclude with several numerical experiments on missing data problems with data sets of gene expression arrays, international development statistics, and intranational socioeconomic measurements.

We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Markov chain. The resulting prior over infinite transition matrices is closely related to the hierarchical Dirichlet process but enforces reversibility. A reinforcement scheme has recently been proposed with similar properties, but the de Finetti measure is not well characterised. We take the alternative approach of explicitly constructing the mixing measure, which allows more straightforward and efficient inference at the cost of no longer having a closed form predictive distribution. We use our process to construct a reversible infinite HMM which we apply to two real datasets, one from epigenomics and one ion channel recording.

Factor analysis models effectively summarise the covariance structure of high dimensional data, but the solutions are typically hard to interpret. This motivates attempting to find a disjoint partition, i.e. a clustering, of observed variables so that variables in a cluster are highly correlated. We introduce a Bayesian non-parametric approach to this problem, and demonstrate advantages over heuristic methods proposed to date.

Variational Message Passing (VMP) is an algorithmic implementation of the Variational Bayes (VB) method which applies only in the special case of conjugate exponential family models. We propose an extension to VMP, which we refer to as Non-conjugate Variational Message Passing (NCVMP) which aims to alleviate this restriction while maintaining modularity, allowing choice in how expectations are calculated, and integrating into an existing message-passing framework: Infer.NET. We demonstrate NCVMP on logistic binary and multinomial regression. In the multinomial case we introduce a novel variational bound for the softmax factor which is tighter than other commonly used bounds whilst maintaining computational tractability.

Nonparametric Bayesian models provide a framework for flexible probabilistic modelling of complex datasets. Unfortunately, Bayesian inference methods often require high-dimensional averages and can be slow to compute, especially with the potentially unbounded representations associated with nonparametric models. We address the challenge of scaling nonparametric Bayesian inference to the increasingly large datasets found in real-world applications, focusing on the case of parallelising inference in the Indian Buffet Process (IBP). Our approach divides a large data set between multiple processors. The processors use message passing to compute likelihoods in an asynchronous, distributed fashion and to propagate statistics about the global Bayesian posterior. This novel MCMC sampler is the first parallel inference scheme for IBP-based models, scaling to datasets orders of magnitude larger than had previously been possible.