Importance sampling strategy for non-convex randomized block-coordinate descent

As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller ones. Coordinates to be optimized are usually selected randomly according to a given probability distribution. We introduce an importance sampling strategy that helps randomized coordinate descent algorithms to focus on blocks that are still far from convergence. The framework applies to problems composed of the sum of two possibly non-convex terms, one being separable and non-smooth. We have compared our algorithm to a full gradient proximal approach as well as to a randomized block coordinate algorithm that considers uniform sampling and cyclic block coordinate descent. Experimental evidences show the clear benefit of using an importance sampling strategy

Efficient generation of random derangements with the expected distribution of cycle lengths

We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random fixed-point-free involutions only, a.k.a. random perfect matchings on the complete graph. Our data indicate that the algorithms generate random samples with the expected distribution of cycle lengths, which we derive, and for relatively small samples, which can actually be very large in absolute numbers, we argue that they generate samples indistinguishable from the uniform distribution. Both algorithms are simple to understand and implement and possess a performance comparable to or better than those of currently known methods. Simulations suggest that the mixing time of the algorithm based on random restricted transpositions (in the total variance distance with respect to the distribution of cycle lengths) is $O(n^{a}\log{n}^{2})$ with $a \simeq \frac{1}{2}$ and $n$ the length of the derangement. We prove that the sequential importance sampling algorithm generates random derangements in $O(n)$ time with probability $O(1/n)$ of failing.Comment: This version corrected and updated; 14 pages, 2 algorithms, 2 tables, 4 figure

Optimizing significance testing of astronomical forcing in cyclostratigraphy

Peer reviewedPublisher PD

Enhanced sampling of multidimensional free-energy landscapes using adaptive biasing forces

We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with molecular dynamics to handle in a more effective fashion multidimensional reaction coordinates. The proposed approach is anticipated to be particularly useful for reaction coordinates, the components of which are weakly coupled, as illuminated in a mathematical analysis of the long-time convergence of the algorithm. The strength as well as the intrinsic limitation of the method are discussed and illustrated in two realistic test cases

An efficient Monte Carlo method for calculating ab initio transition state theory reaction rates in solution

In this article, we propose an efficient method for sampling the relevant state space in condensed phase reactions. In the present method, the reaction is described by solving the electronic Schr\"{o}dinger equation for the solute atoms in the presence of explicit solvent molecules. The sampling algorithm uses a molecular mechanics guiding potential in combination with simulated tempering ideas and allows thorough exploration of the solvent state space in the context of an ab initio calculation even when the dielectric relaxation time of the solvent is long. The method is applied to the study of the double proton transfer reaction that takes place between a molecule of acetic acid and a molecule of methanol in tetrahydrofuran. It is demonstrated that calculations of rates of chemical transformations occurring in solvents of medium polarity can be performed with an increase in the cpu time of factors ranging from 4 to 15 with respect to gas-phase calculations.Comment: 15 pages, 9 figures. To appear in J. Chem. Phy

Alternative proof and interpretations for a recent state-dependent importance sampling scheme

Recently, a state-dependent change of measure for simulating overflows in the two-node tandem queue was proposed by Dupuis et al. (Ann. Appl. Probab. 17(4):1306–1346, 2007), together with a proof of its asymptotic optimality. In the present paper, we present an alternative, shorter and simpler proof. As a side result, we obtain interpretations for several of the quantities involved in the change of measure in terms of likelihood ratios

Molecular model for the self-assembly of the cyclic lipodepsipeptide pseudodesmin A

Self-assembly of peptides into supramolecular structures represents an active field of research with potential applications ranging from material science to medicine. Their study typically involves the application of a large toolbox of spectroscopic and imaging techniques. However, quite often, the structural aspects remain underexposed. Besides, molecular modeling of the self-assembly process is usually difficult to handle, since a vast conformational space has to be sampled. Here, we have used an approach that combines short molecular dynamics simulations for peptide dimerization and NMR restraints to build a model of the supramolecular structure from the dimeric units. Experimental NMR data notably provide crucial information about the conformation of the monomeric units, the supramolecular assembly dimensions, and the orientation of the individual peptides within the assembly. This in silico/in vitro mixed approach enables us to define accurate atomistic models of supramolecular structures of the bacterial cyclic lipodepsipeptide pseudodesmin A