Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems

Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

Interpretable Structure-Evolving LSTM

This paper develops a general framework for learning interpretable data representation via Long Short-Term Memory (LSTM) recurrent neural networks over hierarchal graph structures. Instead of learning LSTM models over the pre-fixed structures, we propose to further learn the intermediate interpretable multi-level graph structures in a progressive and stochastic way from data during the LSTM network optimization. We thus call this model the structure-evolving LSTM. In particular, starting with an initial element-level graph representation where each node is a small data element, the structure-evolving LSTM gradually evolves the multi-level graph representations by stochastically merging the graph nodes with high compatibilities along the stacked LSTM layers. In each LSTM layer, we estimate the compatibility of two connected nodes from their corresponding LSTM gate outputs, which is used to generate a merging probability. The candidate graph structures are accordingly generated where the nodes are grouped into cliques with their merging probabilities. We then produce the new graph structure with a Metropolis-Hasting algorithm, which alleviates the risk of getting stuck in local optimums by stochastic sampling with an acceptance probability. Once a graph structure is accepted, a higher-level graph is then constructed by taking the partitioned cliques as its nodes. During the evolving process, representation becomes more abstracted in higher-levels where redundant information is filtered out, allowing more efficient propagation of long-range data dependencies. We evaluate the effectiveness of structure-evolving LSTM in the application of semantic object parsing and demonstrate its advantage over state-of-the-art LSTM models on standard benchmarks.Comment: To appear in CVPR 2017 as a spotlight pape

Optimization of Trading Physics Models of Markets

We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive Simulated Annealing (ASA) is used for fitting parameters shared across these shells of dynamic and trading models

Evolving stochastic learning algorithm based on Tsallis entropic index

In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight, and applies a form of noise that is characterized by the nonextensive entropic index q, regulated by a weight decay term. The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values. This is achieved by introducing a formula that defines a time-dependent relationship between these two important learning parameters. Our experimental study verifies that there are indeed improvements in the convergence speed of this new evolving stochastic learning algorithm, which makes learning faster than using the original Hybrid Learning Scheme (HLS). In addition, experiments are conducted to explore the influence of the entropic index q and temperature T on the convergence speed and stability of the proposed method