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Chong Zhang

Publications and source records attributed to Chong Zhang.

175 records · Page 10Linked to original sources
arXiv2017

On Reject and Refine Options in Multicategory Classification

In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In recent years, there has been much development for binary classification with a reject option. Yet, little progress has been made for the multicategory case. In this article, we propose margin-based multicategory classification methods with a reject option. In addition, and more importantly, we introduce a new and unique refine option for the multicategory problem, where the class of an observation is predicted to be from a set of class labels, whose cardinality is not necessarily one. The main advantage of both options lies in their capacity of identifying error-prone observations. Moreover, the refine option can provide more constructive information for classification by effectively ruling out implausible classes. Efficient implementations have been developed for the proposed methods. On the theoretical side, we offer a novel statistical learning theory and show a fast convergence rate of the excess $\ell$-risk of our methods with emphasis on diverging dimensionality and number of classes. The results can be further improved under a low noise assumption. A set of comprehensive simulation and real data studies has shown the usefulness of the new learning tools compared to regular multicategory classifiers. Detailed proofs of theorems and extended numerical results are included in the supplemental materials available online.

stat.ML↗
arXiv2016

Efficient Pose and Cell Segmentation using Column Generation

We study the problems of multi-person pose segmentation in natural images and instance segmentation in biological images with crowded cells. We formulate these distinct tasks as integer programs where variables correspond to poses/cells. To optimize, we propose a generic relaxation scheme for solving these combinatorial problems using a column generation formulation where the program for generating a column is solved via exact optimization of very small scale integer programs. This results in efficient exploration of the spaces of poses and cells.

cs.CV↗
arXiv2016

An active efficient coding model of the optokinetic nystagmus

Optokinetic nystagmus (OKN) is an involuntary eye movement responsible for stabilizing retinal images in the presence of relative motion between an observer and the environment. Fully understanding the development of optokinetic nystagmus requires a neurally plausible computational model that accounts for the neural development and the behavior. To date, work in this area has been limited. We propose a neurally plausible framework for the joint development of disparity and motion tuning in the visual cortex, the optokinetic and vergence eye movements. This framework models the joint emergence of both perception and behavior, and accounts for the importance of the development of normal vergence control and binocular vision in achieving normal monocular OKN (mOKN) behaviors. Because the model includes behavior, we can simulate the same perturbations as performed in past experiments, such as artificially induced strabismus. The proposed model agrees both qualitatively and quantitatively with a number of findings from the literature on both binocular vision as well as the optokinetic reflex. Finally, our model also makes quantitative predictions about the OKN behavior using the same methods used to characterize the OKN in the experimental literature.

q-bio.NC↗
arXiv2016

A note on local periods for supercuspidal representations

Let $G$ be a $p$-adic reductive group and $H$ a unimodular spherical subgroup of $G$. Let $π$ be a unitary supercuspidal representation of $G$. In this note, under a mild assumption, we show that local periods in $Hom_H(π,\mathbb{C})$ can be constructed by integrating the matrix coefficients of $π$ over $H$.

math.RT↗
arXiv2015

Local periods for discrete series representations

Let $(G,H)$ be a symmetric pair over a $p$-adic field and $π$ a discrete series representation of $G$. In this paper, for some type of symmetric pairs $(G,H)$, we show that local periods in $Hom_H(π,\mathbb{C})$ can be constructed by integrating the matrix coefficients of $π$ over $H$.

math.RT↗
arXiv2014

On linear periods

Let $π'$ be a cuspidal automorphic representation of $GL_{2n}$, which is assumed to be the Jacquet-Langlands transfer from a cuspidal automorphic representation $π$ of $GL_{2m}(D)$, where $D$ is a division algebra so that $GL_{2m}(D)$ is an inner form of $GL_{2n}$. In this paper, we consider the relation between linear periods on $π$ and $π'$. We conjecture that the non-vanishing of the linear period on $π$ would imply the non-vanishing of that on $π'$. We illustrate an approach using a relative trace formula towards this conjecture, and prove the existence of smooth transfer over non-archimedean local fields.

math.RT↗
arXiv2014

The explicit solution and precise distribution of CKLS model under Girsanov transform

We study the relation between CKLS model and CIR model. We prove that under a suitable transformation, any CKLS model of order $\frac{1}{2}<γ<1$ or $γ> 1$ corresponds to a CIR model under a new probability space. Moreover, we get the explicit solution and the precise distribution of the CKLS model at any time $t$ under the new probability measure. We also give the moment estimation of CKLS model.

math.PR↗
arXiv2014

Polynomial and exponential stability of $θ$-EM approximations to a class of stochastic differential equations

Both the mean square polynomial stability and exponential stability of $θ$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\leθ\le 1$ by using an auxiliary function $F$ (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions.

math.NA↗
arXiv2014

Vortex-state-mediated Josephson effect

The Josephson effect is a kind of macroscopic quantum phenomenon that supercurrent flows through a Josephson junction without any voltage applied. We predict a novel vortex-state-mediated Josephson effect in an SNS Josephson junction supporting vortices. The vortex-state-mediated supercurrent is enhanced or reduced significantly in magnitude depending on the junction length, and exhibits several steps with the number of effective propagating channels in current-phase evolution at zero temperature. At finite temperatures, these supercurrent steps persist in the short junction limit, and develop into sawtooth oscillations if the junction length becomes comparable to the coherence length $ξ=\hbar v_F/Δ$ of the superconductor, and in later case a supercurrent reversal can be observed. These findings may provide a smoking-gun signature of vortex bound states in superconductors and promise possible applications in future Josephson devices.

cond-mat.supr-con↗
arXiv2014

Intrinsically Motivated Learning of Visual Motion Perception and Smooth Pursuit

We extend the framework of efficient coding, which has been used to model the development of sensory processing in isolation, to model the development of the perception/action cycle. Our extension combines sparse coding and reinforcement learning so that sensory processing and behavior co-develop to optimize a shared intrinsic motivational signal: the fidelity of the neural encoding of the sensory input under resource constraints. Applying this framework to a model system consisting of an active eye behaving in a time varying environment, we find that this generic principle leads to the simultaneous development of both smooth pursuit behavior and model neurons whose properties are similar to those of primary visual cortical neurons selective for different directions of visual motion. We suggest that this general principle may form the basis for a unified and integrated explanation of many perception/action loops.

cs.CV↗