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Optimization-based models have been used to predict cellular behavior for over 25 years. The constraints in these models are derived from genome annotations, measured macromolecular composition of cells, and by measuring the cell's growth rate and metabolism in different conditions. The cellular goal (the optimization problem that the cell is trying to solve) can be challenging to derive experimentally for many organisms, including human or mammalian cells, which have complex metabolic capabilities and are not well understood. Existing approaches to learning goals from data include (a) estimating a linear objective function, or (b) estimating linear constraints that model complex biochemical reactions and constrain the cell's operation. The latter approach is important because often the known reactions are not enough to explain observations; therefore, there is a need to extend automatically the model complexity by learning new reactions. However, this leads to nonconvex optimization problems, and existing tools cannot scale to realistically large metabolic models. Hence, constraint estimation is still used sparingly despite its benefits for modeling cell metabolism, which is important for developing novel antimicrobials against pathogens, discovering cancer drug targets, and producing value-added chemicals. Here, we develop the first approach to estimating constraint reactions from data that can scale to realistically large metabolic models. Previous tools were used on problems having less than 75 reactions and 60 metabolites, which limits real-life-size applications. We perform extensive experiments using 75 large-scale metabolic network models for different organisms (including bacteria, yeasts, and mammals) and show that our algorithm can recover cellular constraint reactions. The recovered constraints enable accurate prediction of metabolic states in hundreds of growth environments not seen in training data, and we recover useful cellular goals even when some measurements are missing. 

Several algorithms build on the perfect phylogeny model to infer evolutionary trees. This problem is particularly hard when evolutionary trees are inferred from the fraction of genomes that have mutations in different positions, across different samples. Existing algorithms might do extensive searches over the space of possible trees. At the center of these algorithms is a projection problem that assigns a fitness cost to phylogenetic trees. In order to perform a wide search over the space of the trees, it is critical to solve this projection problem fast. In this paper, we use Moreau's decomposition for proximal operators, and a tree reduction scheme, to develop a new algorithm to compute this projection. Our algorithm terminates with an exact solution in a finite number of steps, and is extremely fast. In particular, it can search over all evolutionary trees with fewer than 11 nodes, a size relevant for several biological problems (more than 2 billion trees) in about 2 hours. 

The framework of Integral Quadratic Constraints (IQC) introduced by Lessard et al. (2014) reduces the com- putation of upper bounds on the convergence rate of several optimization algorithms to semi-definite programming (SDP). In particular, this technique was applied to Nesterov’s accelerated method (NAM). For quadratic functions, this SDP was explicitly solved leading to a new bound on the convergence rate of NAM, and for arbitrary strongly convex functions it was shown numerically that IQC can improve bounds from Nesterov (2004). Unfortunately, an explicit analytic solution to the SDP was not provided. In this paper, we provide such an analytical solution, obtaining a new general and explicit upper bound on the convergence rate of NAM, which we further optimize over its parameters. To the best of our knowledge, this is the best, and explicit, upper bound on the convergence rate of NAM for strongly convex functions. 

The framework of Integral Quadratic Constraints (IQC) introduced by Lessard et al. (2014) reduces the com- putation of upper bounds on the convergence rate of several optimization algorithms to semi-definite programming (SDP). In particular, this technique was applied to Nesterov’s accelerated method (NAM). For quadratic functions, this SDP was explicitly solved leading to a new bound on the convergence rate of NAM, and for arbitrary strongly convex functions it was shown numerically that IQC can improve bounds from Nesterov (2004). Unfortunately, an explicit analytic solution to the SDP was not provided. In this paper, we provide such an analytical solution, obtaining a new general and explicit upper bound on the convergence rate of NAM, which we further optimize over its parameters. To the best of our knowledge, this is the best, and explicit, upper bound on the convergence rate of NAM for strongly convex functions. 

Important data mining problems such as nearestneighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in diverse areas, including, e.g., image processing and social networks. Unfortunately, popular distance scores used in these applications, that scale over large graphs, are not metrics and thus come with no guarantees. Classic graph distances such as, e.g., the chemical and the CKS distance are arguably natural and intuitive, and are indeed also metrics, but they are intractable: as such, their computation does not scale to large graphs. We define a broad family of graph distances, that includes both the chemical and the CKS distance, and prove that these are all metrics. Crucially, we show that our family includes metrics that are tractable. Moreover, we extend these distances by incorporating auxiliary node attributes, which is important in practice, while maintaining both the metric property and tractability.