Learning mixed graphical models with separate sparsity parameters and stability-based model selection.

BACKGROUND: Mixed graphical models (MGMs) are graphical models learned over a combination of continuous and discrete variables. Mixed variable types are common in biomedical datasets. MGMs consist of a parameterized joint probability density, which implies a network structure over these heterogeneous variables. The network structure reveals direct associations between the variables and the joint probability density allows one to ask arbitrary probabilistic questions on the data. This information can be used for feature selection, classification and other important tasks. RESULTS: We studied the properties of MGM learning and applications of MGMs to high-dimensional data (biological and simulated). Our results show that MGMs reliably uncover the underlying graph structure, and when used for classification, their performance is comparable to popular discriminative methods (lasso regression and support vector machines). We also show that imposing separate sparsity penalties for edges connecting different types of variables significantly improves edge recovery performance. To choose these sparsity parameters, we propose a new efficient model selection method, named Stable Edge-specific Penalty Selection (StEPS). StEPS is an expansion of an earlier method, StARS, to mixed variable types. In terms of edge recovery, StEPS selected MGMs outperform those models selected using standard techniques, including AIC, BIC and cross-validation. In addition, we use a heuristic search that is linear in size of the sparsity value search space as opposed to the cubic grid search required by other model selection methods. We applied our method to clinical and mRNA expression data from the Lung Genomics Research Consortium (LGRC) and the learned MGM correctly recovered connections between the diagnosis of obstructive or interstitial lung disease, two diagnostic breathing tests, and cigarette smoking history. Our model also suggested biologically relevant mRNA markers that are linked to these three clinical variables. CONCLUSIONS: MGMs are able to accurately recover dependencies between sets of continuous and discrete variables in both simulated and biomedical datasets. Separation of sparsity penalties by edge type is essential for accurate network edge recovery. Furthermore, our stability based method for model selection determines sparsity parameters faster and more accurately (in terms of edge recovery) than other model selection methods. With the ongoing availability of comprehensive clinical and biomedical datasets, MGMs are expected to become a valuable tool for investigating disease mechanisms and answering an array of critical healthcare questions.

Unbiased Rare Event Sampling in Spatial Stochastic Systems Biology Models Using a Weighted Ensemble of Trajectories.

The long-term goal of connecting scales in biological simulation can be facilitated by scale-agnostic methods. We demonstrate that the weighted ensemble (WE) strategy, initially developed for molecular simulations, applies effectively to spatially resolved cell-scale simulations. The WE approach runs an ensemble of parallel trajectories with assigned weights and uses a statistical resampling strategy of replicating and pruning trajectories to focus computational effort on difficult-to-sample regions. The method can also generate unbiased estimates of non-equilibrium and equilibrium observables, sometimes with significantly less aggregate computing time than would be possible using standard parallelization. Here, we use WE to orchestrate particle-based kinetic Monte Carlo simulations, which include spatial geometry (e.g., of organelles, plasma membrane) and biochemical interactions among mobile molecular species. We study a series of models exhibiting spatial, temporal and biochemical complexity and show that although WE has important limitations, it can achieve performance significantly exceeding standard parallel simulation--by orders of magnitude for some observables.

Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories.

We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study, WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent "brute-force" calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over "brute-force" in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ~10(12) to ~10(18) for characterizing rare states in a distribution, and ~10(2) to ~10(4) for finding mean first passage times.