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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Reducing local minima in fitness landscapes of parameter ...
Christoph Zimmer, Frank T. Bergmann, Sven Sahle · 2016-01-18 · via cs.DS updates on arXiv.org

Ordinary differential equations (ODE) are widely used for modeling in Systems Biology. As most commonly only some of the kinetic parameters are measurable or precisely known, parameter estimation techniques are applied to parametrize the model to experimental data. A main challenge for the parameter estimation is the complexity of the parameter space, especially its high dimensionality and local minima. Parameter estimation techniques consist of an objective function, measuring how well a certain parameter set describes the experimental data, and an optimization algorithm that optimizes this objective function. A lot of effort has been spent on developing highly sophisticated optimization algorithms to cope with the complexity in the parameter space, but surprisingly few articles address the influence of the objective function on the computational complexity in finding global optima. We extend a recently developed multiple shooting for stochastic systems (MSS) objective function for parameter estimation of stochastic models and apply it to parameter estimation of ODE models. This MSS objective function treats the intervals between measurement points separately. This separate treatment allows the ODE trajectory to stay closer to the data and we show that it reduces the complexity of the parameter space. We use examples from Systems Biology, namely a Lotka-Volterra model, a FitzHugh-Nagumo oscillator and a Calcium oscillation model, to demonstrate the power of the MSS approach for reducing the complexity and the number of local minima in the parameter space. The approach is fully implemented in the COPASI software package and, therefore, easily accessible for a wide community of researchers.