Learning Theory of Distribution Regression with Neural Networks

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution regression are probability measures. Then we often need to perform a second-stage sampling process to approximate the actual information of the distribution. On the other hand, the classical neural network structure requires the input variable to be a vector. When the input samples are probability distributions, the traditional deep neural network method cannot be directly used and the difficulty arises for distribution regression. A well-defined neural network structure for distribution inputs is intensively desirable. There is no mathematical model and theoretical analysis on neural network realization of distribution regression. To overcome technical difficulties and address this issue, we establish a novel fully connected neural network framework to realize an approximation theory of functionals defined on the space of Borel probability measures. Furthermore, based on the established functional approximation results, in the hypothesis space induced by the novel FNN structure with distribution inputs, almost optimal learning rates for the proposed distribution regression model up to logarithmic terms are derived via a novel two-stage error decomposition technique

Di-μ-chlorido-bis­[chlorido(N,N-di­methyl­ethylenediamine-κ2 N,N′)zinc(II)]

The centrosymmetric dinuclear title compound, [Zn2Cl4(C4H12N2)2], is isostructural with its previously reported CuII analogue [Phelps, Goodman & Hodgson (1976 ▶). Inorg. Chem. 15, 2266–2270]. In the title compound, each of the ZnII ions is coordinated by two N atoms from a chelating N,N-dimethyl­ethylenediamine ligand, two bridging Cl atoms and one terminal Cl atom. The coordination environment is distorted square-pyramidal. The Zn—Cl bond distances of the two bridging Cl atoms are distinctly different: the equatorial Cl atom exbibits a Zn—Cl distance of 2.318 (1) Å and the axial Cl atom exbibits a Zn—Cl distance of 2.747 (2) Å, which is significantly longer. The mol­ecule can thus be seen as a dimer of two nearly square-planar monomeric units which are related to each other by an inversion center located in the middle of the dimer. Within one monomeric unit, the Zn atom, the two N atoms and the two Cl atoms are almost coplanar, with a mean deviation of only 0.05 (1) Å from the associated least-squares plane. The Zn⋯Zn distance within the dimer is 3.472 (3) Å. N—H⋯Cl and C—H⋯Cl hydrogen-bond inter­actions connect neighboring mol­ecules with each other

(E)-2-[(2-Amino-4,5-dibromo­phen­yl)imino­meth­yl]-6-methoxy­phenol

The title compound, C14H12Br2N2O2, was prepared from the condensation of 4,5-dibromo-1,2-phenyl­enediamine and 2-hydr­oxy-3-methoxy­benzaldehyde in methanol. The N=C double bond shows a trans conformation and the dihedral angle between the aromatic ring planes is 5.9 (4)°. In the crystal structure, there are intra­molecular O—H⋯N and N—H⋯N and inter­molecular N—H⋯O hydrogen bonds, the latter resulting in inversion dimers

A Fully Data-Driven Approach for Realistic Traffic Signal Control Using Offline Reinforcement Learning

The optimization of traffic signal control (TSC) is critical for an efficient transportation system. In recent years, reinforcement learning (RL) techniques have emerged as a popular approach for TSC and show promising results for highly adaptive control. However, existing RL-based methods suffer from notably poor real-world applicability and hardly have any successful deployments. The reasons for such failures are mostly due to the reliance on over-idealized traffic simulators for policy optimization, as well as using unrealistic fine-grained state observations and reward signals that are not directly obtainable from real-world sensors. In this paper, we propose a fully Data-Driven and simulator-free framework for realistic Traffic Signal Control (D2TSC). Specifically, we combine well-established traffic flow theory with machine learning to construct a reward inference model to infer the reward signals from coarse-grained traffic data. With the inferred rewards, we further propose a sample-efficient offline RL method to enable direct signal control policy learning from historical offline datasets of real-world intersections. To evaluate our approach, we collect historical traffic data from a real-world intersection, and develop a highly customized simulation environment that strictly follows real data characteristics. We demonstrate through extensive experiments that our approach achieves superior performance over conventional and offline RL baselines, and also enjoys much better real-world applicability.Comment: 15 pages, 6 figure

Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm

The official published version can be found at the link below.This paper presents a novel particle swarm optimization (PSO) algorithm based on Markov chains and competitive penalized method. Such an algorithm is developed to solve global optimization problems with applications in identifying unknown parameters of a class of genetic regulatory networks (GRNs). By using an evolutionary factor, a new switching PSO (SPSO) algorithm is first proposed and analyzed, where the velocity updating equation jumps from one mode to another according to a Markov chain, and acceleration coefficients are dependent on mode switching. Furthermore, a leader competitive penalized multi-learning approach (LCPMLA) is introduced to improve the global search ability and refine the convergent solutions. The LCPMLA can automatically choose search strategy using a learning and penalizing mechanism. The presented SPSO algorithm is compared with some well-known PSO algorithms in the experiments. It is shown that the SPSO algorithm has faster local convergence speed, higher accuracy and algorithm reliability, resulting in better balance between the global and local searching of the algorithm, and thus generating good performance. Finally, we utilize the presented SPSO algorithm to identify not only the unknown parameters but also the coupling topology and time-delay of a class of GRNs.This research was partially supported by the National Natural Science Foundation of PR China (Grant No. 60874113), the Research Fund for the Doctoral Program of Higher Education (Grant No. 200802550007), the Key Creative Project of Shanghai Education Community (Grant No. 09ZZ66), the Key Foundation Project of Shanghai (Grant No. 09JC1400700), the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant No. GR/S27658/01, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, an International Joint Project sponsored by the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Controller design for synchronization of an array of delayed neural networks using a controllable

This is the post-print version of the Article - Copyright @ 2011 ElsevierIn this paper, a controllable probabilistic particle swarm optimization (CPPSO) algorithm is introduced based on Bernoulli stochastic variables and a competitive penalized method. The CPPSO algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller, which is used in the synchronization of an array of delayed neural networks (DNNs). The learning strategies occur in a random way governed by Bernoulli stochastic variables. The expectations of Bernoulli stochastic variables are automatically updated by the search environment. The proposed method not only keeps the diversity of the swarm, but also maintains the rapid convergence of the CPPSO algorithm according to the competitive penalized mechanism. In addition, the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value. The efficiency of the proposed CPPSO algorithm is demonstrated by comparing it with some well-known PSO algorithms on benchmark test functions with and without rotations. In the end, the proposed CPPSO algorithm is used to design the controller for the synchronization of an array of continuous-time delayed neural networks.This research was partially supported by the National Natural Science Foundation of PR China (Grant No 60874113), the Research Fund for the Doctoral Program of Higher Education (Grant No 200802550007), the Key Creative Project of Shanghai Education Community (Grant No 09ZZ66), the Key Foundation Project of Shanghai(Grant No 09JC1400700), the Engineering and Physical Sciences Research Council EPSRC of the U.K. under Grant No. GR/S27658/01, an International Joint Project sponsored by the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany