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Jie Zhong

Publications and source records attributed to Jie Zhong.

27 records · Page 2Linked to original sources
arXiv2020

A New Approach to Pinning Control of Boolean Networks

Boolean networks (BNs) are discrete-time systems where nodes are inter-connected (here we call such connection rule among nodes as network structure), and the dynamics of each gene node is determined by logical functions. In this paper, we propose a new approach on pinning control design for global stabilization of BNs based on BNs' network structure, named as network-structure-based distributed pinning control. By deleting the minimum number of edges, the network structure becomes acyclic. Then, an efficient distributed pinning control is designed to achieve global stabilization. Compared with existing literature, the design of pinning control is not based on the state transition matrix of BNs. Hence, the computational complexity in this paper is reduced from $O(2^n\times 2^n)$ to $O(2\times 2^K)$, where $n$ is the number of nodes and $K\leq n$ is the largest number of in-neighbors of nodes. In addition, without using state transition matrix, global state information is no longer needed, the design of pinning control is just based on neighbors' local information, which is easier to be implemented. The proposed method is well demonstrated by several biological networks with different sizes. The results are shown to be simple and concise, while the traditional pinning control can not be applied for BNs with such a large dimension.

eess.SY↗
arXiv2020

Pinning Stabilizer Design for Large-Scale Probabilistic Boolean Networks

This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate Boolean functions with probability distributions that govern the activation frequency of each Boolean function. Owing to the stochasticity, the uniform state feedback controller, independent of switching signal, might be out of work, and in this case, the non-uniform state feedback controller is required. Subsequently, a criterion is derived to determine whether uniform controllers is applicable to achieve stabilization. It is worth pointing out that the pinning control designed in this paper is based on the network structure, which only requires local in-neighbors' information, rather than global information (state transition matrix). Moreover, this pinning control strategy reduces the computational complexity from $O(2^{2n})$ to $O(n2^α)$, and thus it has the ability to handle some large-scale networks, especially the networks with sparse connections. Finally, the mammalian cell-cycle encountering a mutated phenotype is modelled by a PBN to demonstrate the obtained results.

eess.SY↗
arXiv2018

AutoML from Service Provider's Perspective: Multi-device, Multi-tenant Model Selection with GP-EI

AutoML has become a popular service that is provided by most leading cloud service providers today. In this paper, we focus on the AutoML problem from the \emph{service provider's perspective}, motivated by the following practical consideration: When an AutoML service needs to serve {\em multiple users} with {\em multiple devices} at the same time, how can we allocate these devices to users in an efficient way? We focus on GP-EI, one of the most popular algorithms for automatic model selection and hyperparameter tuning, used by systems such as Google Vizer. The technical contribution of this paper is the first multi-device, multi-tenant algorithm for GP-EI that is aware of \emph{multiple} computation devices and multiple users sharing the same set of computation devices. Theoretically, given $N$ users and $M$ devices, we obtain a regret bound of $O((\text{\bf {MIU}}(T,K) + M)\frac{N^2}{M})$, where $\text{\bf {MIU}}(T,K)$ refers to the maximal incremental uncertainty up to time $T$ for the covariance matrix $K$. Empirically, we evaluate our algorithm on two applications of automatic model selection, and show that our algorithm significantly outperforms the strategy of serving users independently. Moreover, when multiple computation devices are available, we achieve near-linear speedup when the number of users is much larger than the number of devices.

cs.LG↗
arXiv2017

Optimal Actuator Location of the Minimum Norm Controls for Stochastic Heat Equations

In this paper, we study the approximate controllability for the stochastic heat equation over measurable sets, and the optimal actuator location of the minimum norm controls. We formulate a relaxed optimization problem for both actuator location and its corresponding minimum norm control into a two-person zero sum game problem and develop a sufficient and necessary condition for the optimal solution via Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem.

math.OC↗
arXiv2017

Ease.ml: Towards Multi-tenant Resource Sharing for Machine Learning Workloads

We present ease.ml, a declarative machine learning service platform we built to support more than ten research groups outside the computer science departments at ETH Zurich for their machine learning needs. With ease.ml, a user defines the high-level schema of a machine learning application and submits the task via a Web interface. The system automatically deals with the rest, such as model selection and data movement. In this paper, we describe the ease.ml architecture and focus on a novel technical problem introduced by ease.ml regarding resource allocation. We ask, as a "service provider" that manages a shared cluster of machines among all our users running machine learning workloads, what is the resource allocation strategy that maximizes the global satisfaction of all our users? Resource allocation is a critical yet subtle issue in this multi-tenant scenario, as we have to balance between efficiency and fairness. We first formalize the problem that we call multi-tenant model selection, aiming for minimizing the total regret of all users running automatic model selection tasks. We then develop a novel algorithm that combines multi-armed bandits with Bayesian optimization and prove a regret bound under the multi-tenant setting. Finally, we report our evaluation of ease.ml on synthetic data and on one service we are providing to our users, namely, image classification with deep neural networks. Our experimental evaluation results show that our proposed solution can be up to 9.8x faster in achieving the same global quality for all users as the two popular heuristics used by our users before ease.ml.

cs.DB↗
arXiv2017

Asynchronous Parallel Empirical Variance Guided Algorithms for the Thresholding Bandit Problem

This paper considers the multi-armed thresholding bandit problem -- identifying all arms whose expected rewards are above a predefined threshold via as few pulls (or rounds) as possible -- proposed by Locatelli et al. [2016] recently. Although the proposed algorithm in Locatelli et al. [2016] achieves the optimal round complexity in a certain sense, there still remain unsolved issues. This paper proposes an asynchronous parallel thresholding algorithm and its parameter-free version to improve the efficiency and the applicability. On one hand, the proposed two algorithms use the empirical variance to guide the pull decision at each round, and significantly improve the round complexity of the "optimal" algorithm when all arms have bounded high order moments. The proposed algorithms can be proven to be optimal. On the other hand, most bandit algorithms assume that the reward can be observed immediately after the pull or the next decision would not be made before all rewards are observed. Our proposed asynchronous parallel algorithms allow making the choice of the next pull with unobserved rewards from earlier pulls, which avoids such an unrealistic assumption and significantly improves the identification process. Our theoretical analysis justifies the effectiveness and the efficiency of proposed asynchronous parallel algorithms.

stat.ML↗
arXiv2016

Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its Applications

This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an interesting relaxed optimal actuator location problem is formulated, and the existence of its solution is proved. Finally, the solution is characterized by a Nash equilibrium of the associated game problem.

math.OC↗
arXiv2005

Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system

Greenberger-Horne-Zeilinger (GHZ) theorem asserts that there is a set of mutually commuting nonlocal observables with a common eigenstate on which those observables assume values that refute the attempt to assign values only required to have them by the local realism of Einstein, Podolsky, and Rosen (EPR). It is known that for a three-qubit system there is only one form of the GHZ-Mermin-like argument with equivalence up to a local unitary transformation, which is exactly Mermin's version of the GHZ theorem. In this paper, however, for a four-qubit system which was originally studied by GHZ, we show that there are nine distinct forms of the GHZ-Mermin-like argument. The proof is obtained by using some geometric invariants to characterize the sets of mutually commuting nonlocal spin observables on the four-qubit system. It is proved that there are at most nine elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the four-qubit system, and each GHZ-Mermin-like argument involves a set of at least five mutually commuting four-qubit nonlocal spin observables with a GHZ state as a common eigenstate in GHZ's theorem. Therefore, we present a complete construction of the GHZ theorem for the four-qubit system.

quant-ph↗