arXiv subjects

Chu Wang

Publications and source records attributed to Chu Wang.

67 records · Page 4Linked to original sources

arXiv2016

An Opinion Dynamics Model with Increasing Self-Confidence

We propose an opinion dynamics model in which agents gradually increase their own self-confidence while interacting with each other. The relations between the newly proposed model and existing works of social learning, inertial opinion dynamics, Bayesian inference, and stochastic multi-armed bandits are demonstrated. We prove the convergence of the system with the existence of a truth under fixed and periodically changing social networks, and obtain tight convergence bounds related to the spectral gap of the graph Laplacian and the maximum total degree centrality, respectively. In the case of randomly generated social networks, an almost-sure convergence result is obtained. The dynamics of the model with multiple truths or zero truth is also discussed.

math.OC↗

arXiv2016

Self-Sustaining Iterated Learning

An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve self-sustainability. Our work is in two parts. First, we characterize iterated learnability in geometric terms and show how a slight, steady increase in the lengths of the training sessions ensures self-sustainability for any discrete language class. In the second part, we tackle the nondiscrete case and investigate self-sustainability for iterated linear regression. We discuss the implications of our findings to issues of non-equilibrium dynamics in natural algorithms.

math.OC↗

arXiv2016

Inertial Hegselmann-Krause Systems

We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of HK systems with closed-minded agents, which settles a conjecture of long standing. This paper also introduces anchored HK systems and show their equivalence to the symmetric heterogeneous model.

eess.SY↗

arXiv2016

Computing optimal interfacial structure of modulated phases

We propose a general framework of computing interfacial structures between two modulated phases. Specifically we propose to use a computational box consisting of two half spaces, each occupied by a modulated phase with given position and orientation. The boundary conditions and basis functions are chosen to be commensurate with the bulk structures. It is observed that the ordered nature of modulated structures stabilizes the interface, which enables us to obtain optimal interfacial structures by searching local minima of the free energy landscape. The framework is applied to the Landau-Brazovskii model to investigate interfaces between modulated phases with different relative positions and orientations. Several types of novel complex interfacial structures are obtained from the calculations.

cond-mat.soft↗

arXiv2015

Noisy Hegselmann-Krause Systems: Phase Transition and the 2R-Conjecture

The classic Hegselmann-Krause (HK) model for opinion dynam- ics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of all the agents within a fixed distance R. In this work, we investigate the effects of noise in the continuous-time version of the model as described by its mean-field limiting Fokker-Planck equation. In the presence of a finite number of agents, the system exhibits a phase transition from order to disorder as the noise increases. The ordered phase features clusters whose width depends only on the noise level. We introduce an order parameter to track the phase transition and resolve the corresponding phase dia- gram. The system undergoes a phase transition for small R but none for larger R. Based on the stability analysis of the mean-field equation, we derive the existence of a forbidden zone for the disordered phase to emerge. We also provide a theoretical explanation for the well-known 2R conjecture, which states that, for a random initial distribution in a fixed interval, the final configuration consists of clusters separated by a distance of roughly 2R. Our theoretical analysis also confirms previous simulations and predicts properties of the noisy HK model in higher dimension.

math.OC↗

arXiv2015

Computing optimal interfacial structure of ordered phases

We propose a general framework of computing interfacial structure. If an ordered phase is involved, the interfacial structure can be obtained by simply minimizing the free energy with compatible boundary conditions. The framework is applied to Landau- Brazovskii model and works efficiently.

physics.comp-ph↗

arXiv2015

Well-Posedness of the Limiting Equation of a Noisy Consensus Model in Opinion Dynamics

This paper establishes the global well-posedness of the nonlinear Fokker-Planck equation for a noisy version of the Hegselmann-Krause model. The equation captures the mean-field behavior of a classic multiagent system for opinion dynamics. We prove the global existence, uniqueness, nonnegativity and regularity of the weak solution. We also exhibit a global stability condition, which delineates a forbidden region for consensus formation. This is the first nonlinear stability result derived for the Hegselmann-Krause model.

math.AP↗

arXiv2015

Functional Frank-Wolfe Boosting for General Loss Functions

Boosting is a generic learning method for classification and regression. Yet, as the number of base hypotheses becomes larger, boosting can lead to a deterioration of test performance. Overfitting is an important and ubiquitous phenomenon, especially in regression settings. To avoid overfitting, we consider using $l_1$ regularization. We propose a novel Frank-Wolfe type boosting algorithm (FWBoost) applied to general loss functions. By using exponential loss, the FWBoost algorithm can be rewritten as a variant of AdaBoost for binary classification. FWBoost algorithms have exactly the same form as existing boosting methods, in terms of making calls to a base learning algorithm with different weights update. This direct connection between boosting and Frank-Wolfe yields a new algorithm that is as practical as existing boosting methods but with new guarantees and rates of convergence. Experimental results show that the test performance of FWBoost is not degraded with larger rounds in boosting, which is consistent with the theoretical analysis.

stat.ML↗

arXiv2015

The Knowledge Gradient with Logistic Belief Models for Binary Classification

We consider sequential decision making problems for binary classification scenario in which the learner takes an active role in repeatedly selecting samples from the action pool and receives the binary label of the selected alternatives. Our problem is motivated by applications where observations are time consuming and/or expensive, resulting in small samples. The goal is to identify the best alternative with the highest response. We use Bayesian logistic regression to predict the response of each alternative. By formulating the problem as a Markov decision process, we develop a knowledge-gradient type policy to guide the experiment by maximizing the expected value of information of labeling each alternative and provide a finite-time analysis on the estimated error. Experiments on benchmark UCI datasets demonstrate the effectiveness of the proposed method.

stat.ML↗

arXiv2014

Lifts of Non-compact Convex Sets and Cone Factorizations

In this paper we generalize the factorization theorem of Gouveia, Parrilo and Thomas to a broader class of convex sets. Given a general convex set, we define a slack operator associated to the set and its polar according to whether the convex set is full dimensional, whether it is a translated cone and whether it contains lines. We strengthen the condition of a cone lift by requiring not only the convex set is the image of an affine slice of a given closed convex cone, but also its recession cone is the image of the linear slice of the closed convex cone. We show that the generalized lift of a convex set can also be characterized by the cone factorization of a properly defined slack operator.

math.OC↗

arXiv2014

A brain-wide association study of DISC1 genetic variants reveals a relationship with the structure and functional connectivity of the precuneus in schizophrenia

The Disrupted in Schizophrenia Gene 1 (DISC1) plays a role in both neural signalling and development and is associated with schizophrenia, although its links to altered brain structure and function in this disorder are not fully established. Here we have used structural and functional MRI to investigate links with six DISC1 single nucleotide polymorphisms (SNPs). We employed a brain-wide association analysis (BWAS) together with a Jacknife internal validation approach in 46 schizophrenia patients and 24 matched healthy control subjects. Results from structural MRI showed significant associations between all six DISC1 variants and gray matter volume in the precuneus, post-central gyrus and middle cingulate gyrus. Associations with specific SNPs were found for rs2738880 in the left precuneus and right post-central gyrus, and rs1535530 in the right precuneus and middle cingulate gyrus. Using regions showing structural associations as seeds a resting-state functional connectivity analysis revealed significant associations between all 6 SNPS and connectivity between the right precuneus and inferior frontal gyrus. The connection between the right precuneus and inferior frontal gyrus was also specifically associated with rs821617. Importantly schizophrenia patients showed positive correlations between the six DISC-1 SNPs associated gray matter volume in the left precuneus and right post-central gyrus and negative symptom severity. No correlations with illness duration were found. Our results provide the first evidence suggesting a key role for structural and functional connectivity associations between DISC1 polymorphisms and the precuneus in schizophrenia.

q-bio.NC↗

arXiv2014

Semidefinite representations of non-compact convex sets

We consider the problem of the semidefinite representation of a class of non-compact basic semialgebraic sets. We introduce the conditions of pointedness and closedness at infinity of a semialgebraic set and show that under these conditions our modified hierarchies of nested theta bodies and Lasserre's relaxations converge to the closure of the convex hull of $S$. Moreover, if the PP-BDR property is satisfied, our theta body and Lasserre's relaxation are exact when the order is large enough; if the PP-BDR property does not hold, our hierarchies convergent uniformly to the closure of the convex hull of $S$ restricted to every fixed ball centered at the origin. We illustrate through a set of examples that the conditions of pointedness and closedness are essential to ensure the convergence. Finally, we provide some strategies to deal with cases where the conditions of pointedness and closedness are violated.

math.OC↗

arXiv2012

A certificate for semidefinite relaxations in computing positive dimensional real varieties

For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal J generated by the kernel of a truncated moment matrix and nesting between I and its real radical ideal. We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algorithm. For a generic delta-regular coordinate system, we prove that the condition is satisfiable in a large enough order of moment relaxations.

math.OC↗