Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior. This approach results in a superior latent representation and allows each encoding to preserve information better from its uncompressed original features. In extensive experiments on multiple benchmark datasets and two challenging real-world datasets, we show improved learned latent representations and imputation of missing data modalities compared to existing methods.

We present a fully Bayesian autoencoder model that treats both local latent variables and global decoder parameters in a Bayesian fashion. This approach allows for flexible priors and posterior approximations while keeping the inference costs low. To achieve this, we introduce an amortized MCMC approach by utilizing an implicit stochastic network to learn sampling from the posterior over local latent variables. Furthermore, we extend the model by incorporating a Sparse Gaussian Process prior over the latent space, allowing for a fully Bayesian treatment of inducing points and kernel hyperparameters and leading to improved scalability. Additionally, we enable Deep Gaussian Process priors on the latent space and the handling of missing data. We evaluate our model on a range of experiments focusing on dynamic representation learning and generative modeling, demonstrating the strong performance of our approach in comparison to existing methods that combine Gaussian Processes and autoencoders.

It is well known that the Fisher information induces a Riemannian geometry on parametric families of probability density functions. Following recent work, we consider the nonparametric generalization of the Fisher geometry. The resulting nonparametric Fisher geometry is shown to be equivalent to a familiar, albeit infinite-dimensional, geometric object—the sphere. By shifting focus away from density functions and toward square-root density functions, one may calculate theoretical quantities of interest with ease. More importantly, the sphere of square-root densities is much more computationally tractable. As discussed here, this insight leads to a novel Bayesian nonparametric density estimation model.

Dynamic functional connectivity, as measured by the time-varying covariance of neurological signals, is believed to play an important role in many aspects of cognition. While many methods have been proposed, reliably establishing the presence and characteristics of brain connectivity is challenging due to the high dimensionality and noisiness of neuroimaging data. We present a latent factor Gaussian process model which addresses these challenges by learning a parsimonious representation of connectivity dynamics. The proposed model naturally allows for inference and visualization of the time-varying connectivity. As an illustration of the scientific utility of the model, application to a data set of rat local field potential activity recorded during a complex non-spatial memory task provides evidence of stimuli differentiation.

MOTIVATION: Circadian rhythms date back to the origins of life, are found in virtually every species and every cell, and play fundamental roles in functions ranging from metabolism to cognition. Modern high-throughput technologies allow the measurement of concentrations of transcripts, metabolites and other species along the circadian cycle creating novel computational challenges and opportunities, including the problems of inferring whether a given species oscillate in circadian fashion or not, and inferring the time at which a set of measurements was taken. RESULTS: We first curate several large synthetic and biological time series datasets containing labels for both periodic and aperiodic signals. We then use deep learning methods to develop and train BIO_CYCLE, a system to robustly estimate which signals are periodic in high-throughput circadian experiments, producing estimates of amplitudes, periods, phases, as well as several statistical significance measures. Using the curated data, BIO_CYCLE is compared to other approaches and shown to achieve state-of-the-art performance across multiple metrics. We then use deep learning methods to develop and train BIO_CLOCK to robustly estimate the time at which a particular single-time-point transcriptomic experiment was carried. In most cases, BIO_CLOCK can reliably predict time, within approximately 1 h, using the expression levels of only a small number of core clock genes. BIO_CLOCK is shown to work reasonably well across tissue types, and often with only small degradation across conditions. BIO_CLOCK is used to annotate most mouse experiments found in the GEO database with an inferred time stamp. AVAILABILITY AND IMPLEMENTATION: All data and software are publicly available on the CircadiOmics web portal: circadiomics.igb.uci.edu/ CONTACTS: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bioinformatics (2016) 32(12), i8–i17 doi: 10.1093/bioinformatics/btw243 The authors wish to correct the following errors in the above article: In Section 2.1.2, Arabdiposis should read Arabidopsis, in Sections 2.1.2 and 4.4.1, Cyr1 should read Cry1, and in Section 3.1.5, V ;> ;V(i) should read V(i) ;> ;V. The authors apologize for these errors.

MOTIVATION: The field of phylodynamics focuses on the problem of reconstructing population size dynamics over time using current genetic samples taken from the population of interest. This technique has been extensively used in many areas of biology but is particularly useful for studying the spread of quickly evolving infectious diseases agents, e.g. influenza virus. Phylodynamic inference uses a coalescent model that defines a probability density for the genealogy of randomly sampled individuals from the population. When we assume that such a genealogy is known, the coalescent model, equipped with a Gaussian process prior on population size trajectory, allows for nonparametric Bayesian estimation of population size dynamics. Although this approach is quite powerful, large datasets collected during infectious disease surveillance challenge the state-of-the-art of Bayesian phylodynamics and demand inferential methods with relatively low computational cost. RESULTS: To satisfy this demand, we provide a computationally efficient Bayesian inference framework based on Hamiltonian Monte Carlo for coalescent process models. Moreover, we show that by splitting the Hamiltonian function, we can further improve the efficiency of this approach. Using several simulated and real datasets, we show that our method provides accurate estimates of population size dynamics and is substantially faster than alternative methods based on elliptical slice sampler and Metropolis-adjusted Langevin algorithm. AVAILABILITY AND IMPLEMENTATION: The R code for all simulation studies and real data analysis conducted in this article are publicly available at http://www.ics.uci.edu/∼slan/lanzi/CODES.html and in the R package phylodyn available at https://github.com/mdkarcher/phylodyn. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create \emph{wormholes} connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to rediscovering those previously identified, we employ a novel mode searching algorithm that explores a \emph{residual energy} function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function.

Probabilistic inference on a big data scale is becoming increasingly relevant to both the machine learning and statistics communities. Here we introduce the first fully distributed MCMC algorithm based on stochastic gradients. We argue that stochastic gradient MCMC algorithms are particularly suited for distributed inference because individual chains can draw minibatches from their local pool of data for a flexible amount of time before jumping to or syncing with other chains. This greatly reduces communication overhead and allows adaptive load balancing. Our experiments for LDA on Wikipedia and Pubmed show that relative to the state of the art in distributed MCMC we reduce compute time from 27 hours to half an hour in order to reach the same perplexity level.

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit models, many copula models, and Latent Dirichlet Allocation (LDA) models. Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. For such problems, we propose a novel Markov Chain Monte Carlo (MCMC) method that provides a general and computationally efficient framework for handling boundary conditions. Our method first maps the D-dimensional constrained domain of parameters to the unit ball \bf B_0^D(1), then augments it to the D-dimensional sphere \bf S^D such that the original boundary corresponds to the equator of \bf S^D. This way, our method handles the constraints implicitly by moving freely on sphere generating proposals that remain within boundaries when mapped back to the original space. To improve the computational efficiency of our algorithm, we divide the dynamics into several parts such that the resulting split dynamics has a partial analytical solution as a geodesic flow on the sphere. We apply our method to several examples including truncated Gaussian, Bayesian Lasso, Bayesian bridge regression, and a copula model for identifying synchrony among multiple neurons. Our results show that the proposed method can provide a natural and efficient framework for handling several types of constraints on target distributions.

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their cofiring (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1s (spike) and 0s (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows. The nonparametric component (i.e., the gaussian process model) provides a flexible framework for modeling the underlying firing rates, and the parametric component (i.e., the copula model) allows us to make inferences regarding both contemporaneous and lagged relationships among neurons. Using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of a dependence structure among variables. Our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high-dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas.

BACKGROUND: We investigate whether annotation of gene function can be improved using a classification scheme that is aware that functional classes are organized in a hierarchy. The classifiers look at phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL) model, a hierarchical model based on a set of nested MNL models, and an MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs) from the E. coli genome. RESULTS: The results from all three models show substantial improvement over previous methods, which were based on the C5 decision tree algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining the three sources of information in this dataset, our new approach to combining data sources produces a higher accuracy rate than applying our models to each data source alone. CONCLUSION: Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information.