BACKGROUND: Supervised learning from high-throughput sequencing data presents many challenges. For one, the curse of dimensionality often leads to overfitting as well as issues with scalability. This can bring about inaccurate models or those that require extensive compute time and resources. Additionally, variant calls may not be the optimal encoding for a given learning task, which also contributes to poor predictive capabilities. To address these issues, we present HARVESTMAN, a method that takes advantage of hierarchical relationships among the possible biological interpretations and representations of genomic variants to perform automatic feature learning, feature selection, and model building. RESULTS: We demonstrate that HARVESTMAN scales to thousands of genomes comprising more than 84 million variants by processing phase 3 data from the 1000 Genomes Project, one of the largest publicly available collection of whole genome sequences. Using breast cancer data from The Cancer Genome Atlas, we show that HARVESTMAN selects a rich combination of representations that are adapted to the learning task, and performs better than a binary representation of SNPs alone. We compare HARVESTMAN to existing feature selection methods and demonstrate that our method is more parsimonious-it selects smaller and less redundant feature subsets while maintaining accuracy of the resulting classifier. CONCLUSION: HARVESTMAN is a hierarchical feature selection approach for supervised model building from variant call data. By building a knowledge graph over genomic variants and solving an integer linear program , HARVESTMAN automatically and optimally finds the right encoding for genomic variants. Compared to other hierarchical feature selection methods, HARVESTMAN is faster and selects features more parsimoniously.

We introduce a new scalable approximation for Gaussian processes with provable guarantees which holds simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse spectrum Gaussian processes (SSGPs). In particular, our analysis shows that under a certain data disentangling condition, an SSGP's prediction and model evidence (for training) can well-approximate those of a full GP with low sample complexity. We also develop a new auto-encoding algorithm that finds a latent space to disentangle latent input coordinates into well-separated clusters, which is amenable to our sample complexity analysis. We validate our proposed method on several benchmarks with promising results supporting our theoretical analysis.

This paper presents a novel Collective Online Learning of Gaussian Processes (COOL-GP) framework for enabling a massive number of GP inference agents to simultaneously perform (a) efficient online updates of their GP models using their local streaming data with varying correlation structures and (b) decentralized fusion of their resulting online GP models with different learned hyperparameter settings and inducing inputs. To realize this, we exploit the notion of a common encoding structure to encapsulate the local streaming data gathered by any GP inference agent into summary statistics based on our proposed representation, which is amenable to both an efficient online update via an importance sampling trick as well as multi-agent model fusion via decentralized message passing that can exploit sparse connectivity among agents for improving efficiency and enhance the robustness of our framework against transmission loss. We provide a rigorous theoretical analysis of the approximation loss arising from our proposed representation to achieve efficient online updates and model fusion. Empirical evaluations show that COOL-GP is highly effective in model fusion, resilient to information disparity between agents, robust to transmission loss, and can scale to thousands of agents.

Model fusion is a fundamental problem in collec-tive machine learning (ML) where independentexperts with heterogeneous learning architecturesare required to combine expertise to improve pre-dictive performance. This is particularly chal-lenging in information-sensitive domains whereexperts do not have access to each other’s internalarchitecture and local data. This paper presentsthe first collective model fusion framework formultiple experts with heterogeneous black-box ar-chitectures. The proposed method will enable thisby addressing the key issues of how black-boxexperts interact to understand the predictive be-haviors of one another; how these understandingscan be represented and shared efficiently amongthemselves; and how the shared understandingscan be combined to generate high-quality consen-sus prediction. The performance of the resultingframework is analyzed theoretically and demon-strated empirically on several datasets.

This paper presents a novel decentralized high-dimensional Bayesian optimization (DEC-HBO) algorithm that, in contrast to existing HBO algorithms, can exploit the interdependent effects of various input components on the output of the unknown objective function f for boosting the BO performance and still preserve scalability in the number of input dimensions without requiring prior knowledge or the existence of a low (effective) dimension of the input space. To realize this, we propose a sparse yet rich factor graph representation of f to be exploited for designing an acquisition function that can be similarly represented by a sparse factor graph and hence be efficiently optimized in a decentralized manner using distributed message passing. Despite richly characterizing the interdependent effects of the input components on the output of f with a factor graph, DEC-HBO can still guarantee no-regret performance asymptotically. Empirical evaluation on synthetic and real-world experiments (e.g., sparse Gaussian process model with 1811 hyperparameters) shows that DEC-HBO outperforms the state-of-the-art HBO algorithms.

While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that exploit the sparse spectral representation of a GP kernel. This paper presents such an effort to advance the state of the art of sparse spectrum GP models to achieve competitive predictive performance for massive datasets. Our generalized framework of stochastic variational Bayesian sparse spectrum GP (sVBSSGP) models addresses their shortcomings by adopting a Bayesian treatment of the spectral frequencies to avoid overfitting, modeling these frequencies jointly in its variational distribution to enable their interaction a posteriori, and exploiting local data for boosting the predictive performance. However, such structural improvements result in a variational lower bound that is intractable to be optimized. To resolve this, we exploit a variational parameterization trick to make it amenable to stochastic optimization. Interestingly, the resulting stochastic gradient has a linearly decomposable structure that can be exploited to refine our stochastic optimization method to incur constant time per iteration while preserving its property of being an unbiased estimator of the exact gradient of the variational lower bound. Empirical evaluation on real-world datasets shows that sVBSSGP outperforms state-of-the-art stochastic implementations of sparse GP models.

This paper presents a novel distributed variational inference framework that unifies many parallel sparse Gaussian process regression (SGPR) models for scalable hyperparameter learning with big data. To achieve this, our framework exploits a structure of correlated noise process model that represents the observation noises as a finite realization of a high-order Gaussian Markov random process. By varying the Markov order and covariance function for the noise process model, different variational SGPR models result. This consequently allows the correlation structure of the noise process model to be characterized for which a particular variational SGPR model is optimal. We empirically evaluate the predictive performance and scalability of the distributed variational SGPR models unified by our framework on two real-world datasets.

This paper presents a novel unifying framework of anytime sparse Gaussian process regression (SGPR) models that can produce good predictive performance fast and improve their predictive performance over time. Our proposed unifying framework reverses the variational inference procedure to theoretically construct a non-trivial, concave functional that is maximized at the predictive distribution of any SGPR model of our choice. As a result, a stochastic natural gradient ascent method can be derived that involves iteratively following the stochastic natural gradient of the functional to improve its estimate of the predictive distribution of the chosen SGPR model and is guaranteed to achieve asymptotic convergence to it. Interestingly, we show that if the predictive distribution of the chosen SGPR model satisfies certain decomposability conditions, then the stochastic natural gradient is an unbiased estimator of the exact natural gradient and can be computed in constant time (i.e., independent of data size) at each iteration. We empirically evaluate the trade-off between the predictive performance vs. time efficiency of the anytime SGPR models on two real-world million-sized datasets.