arXiv subjects

Qi Ye

Publications and source records attributed to Qi Ye.

88 records · Page 5Linked to original sources

arXiv2021

Few-shot learning with improved local representations via bias rectify module

Recent approaches based on metric learning have achieved great progress in few-shot learning. However, most of them are limited to image-level representation manners, which fail to properly deal with the intra-class variations and spatial knowledge and thus produce undesirable performance. In this paper we propose a Deep Bias Rectify Network (DBRN) to fully exploit the spatial information that exists in the structure of the feature representations. We first employ a bias rectify module to alleviate the adverse impact caused by the intra-class variations. bias rectify module is able to focus on the features that are more discriminative for classification by given different weights. To make full use of the training data, we design a prototype augment mechanism that can make the prototypes generated from the support set to be more representative. To validate the effectiveness of our method, we conducted extensive experiments on various popular few-shot classification benchmarks and our methods can outperform state-of-the-art methods.

cs.CV↗

arXiv2021

Optimal Retirement Time and Consumption with the Variation in Habitual Persistence

In this paper,we study the individual's optimal retirement time and optimal consumption under habitual persistence. Because the individual feels equally satisfied with a lower habitual level and is more reluctant to change the habitual level after retirement, we assume that both the level and the sensitivity of the habitual consumption decline at the time of retirement. We establish the concise form of the habitual evolutions, and obtain the optimal retirement time and consumption policy based on martingale and duality methods. The optimal consumption experiences a sharp decline at retirement, but the excess consumption raises because of the reduced sensitivity of the habitual level. This result contributes to explain the "retirement consumption puzzle". Particularly, the optimal retirement and consumption policies are balanced between the wealth effect and the habitual effect. Larger wealth increases consumption, and larger growth inertia (sensitivity) of the habitual level decreases consumption and brings forward the retirement time.

q-fin.MF↗

arXiv2020

The Phong Surface: Efficient 3D Model Fitting using Lifted Optimization

Realtime perceptual and interaction capabilities in mixed reality require a range of 3D tracking problems to be solved at low latency on resource-constrained hardware such as head-mounted devices. Indeed, for devices such as HoloLens 2 where the CPU and GPU are left available for applications, multiple tracking subsystems are required to run on a continuous, real-time basis while sharing a single Digital Signal Processor. To solve model-fitting problems for HoloLens 2 hand tracking, where the computational budget is approximately 100 times smaller than an iPhone 7, we introduce a new surface model: the `Phong surface'. Using ideas from computer graphics, the Phong surface describes the same 3D shape as a triangulated mesh model, but with continuous surface normals which enable the use of lifting-based optimization, providing significant efficiency gains over ICP-based methods. We show that Phong surfaces retain the convergence benefits of smoother surface models, while triangle meshes do not.

cs.CV↗

arXiv2019

A Note on Lower Digits Extraction Polynomial for Bootstrapping

Bootstrapping is a crucial but computationally expensive step for realizing Fully Homomorphic Encryption (FHE). Recently, Chen and Han (Eurocrypt 2018) introduced a family of low-degree polynomials to extract the lowest digit with respect to a certain congruence, which helps improve the bootstrapping for both FV and BGV schemes. In this note, we present the following relevant findings about the work of Chen and Han (referred to as CH18): 1. We provide a simpler construction of the low-degree polynomials that serve the same purpose and match the asymptotic bound achieved in CH18; 2. We show the optimality and limit of our approach by solving a minimal polynomial degree problem; 3. We consider the problem of extracting other low-order digits using polynomials, and provide negative results.

cs.CR↗

arXiv2018

Occlusion-aware Hand Pose Estimation Using Hierarchical Mixture Density Network

Learning and predicting the pose parameters of a 3D hand model given an image, such as locations of hand joints, is challenging due to large viewpoint changes and articulations, and severe self-occlusions exhibited particularly in egocentric views. Both feature learning and prediction modeling have been investigated to tackle the problem. Though effective, most existing discriminative methods yield a single deterministic estimation of target poses. Due to their single-value mapping intrinsic, they fail to adequately handle self-occlusion problems, where occluded joints present multiple modes. In this paper, we tackle the self-occlusion issue and provide a complete description of observed poses given an input depth image by a novel method called hierarchical mixture density networks (HMDN). The proposed method leverages the state-of-the-art hand pose estimators based on Convolutional Neural Networks to facilitate feature learning, while it models the multiple modes in a two-level hierarchy to reconcile single-valued and multi-valued mapping in its output. The whole framework with a mixture of two differentiable density functions is naturally end-to-end trainable. In the experiments, HMDN produces interpretable and diverse candidate samples, and significantly outperforms the state-of-the-art methods on two benchmarks with occlusions, and performs comparably on another benchmark free of occlusions.

cs.CV↗

arXiv2017

BigHand2.2M Benchmark: Hand Pose Dataset and State of the Art Analysis

In this paper we introduce a large-scale hand pose dataset, collected using a novel capture method. Existing datasets are either generated synthetically or captured using depth sensors: synthetic datasets exhibit a certain level of appearance difference from real depth images, and real datasets are limited in quantity and coverage, mainly due to the difficulty to annotate them. We propose a tracking system with six 6D magnetic sensors and inverse kinematics to automatically obtain 21-joints hand pose annotations of depth maps captured with minimal restriction on the range of motion. The capture protocol aims to fully cover the natural hand pose space. As shown in embedding plots, the new dataset exhibits a significantly wider and denser range of hand poses compared to existing benchmarks. Current state-of-the-art methods are evaluated on the dataset, and we demonstrate significant improvements in cross-benchmark performance. We also show significant improvements in egocentric hand pose estimation with a CNN trained on the new dataset.

cs.CV↗

arXiv2017

Kernel-based Approximation Methods for Generalized Interpolations: A Deterministic or Stochastic Problem?

In this article, we solve a deterministically generalized interpolation problem by a stochastic approach. We introduce a kernel-based probability measure on a Banach space by a covariance kernel which is defined on the dual space of the Banach space. The kernel-based probability measure provides a numerical tool to construct and analyze the kernel-based estimators conditioned on non-noise data or noisy data including algorithms and error analysis. Same as meshfree methods, we can also obtain the kernel-based approximate solutions of elliptic partial differential equations by the kernel-based probability measure.

math.NA↗

arXiv2017

The 2017 Hands in the Million Challenge on 3D Hand Pose Estimation

We present the 2017 Hands in the Million Challenge, a public competition designed for the evaluation of the task of 3D hand pose estimation. The goal of this challenge is to assess how far is the state of the art in terms of solving the problem of 3D hand pose estimation as well as detect major failure and strength modes of both systems and evaluation metrics that can help to identify future research directions. The challenge follows up the recent publication of BigHand2.2M and First-Person Hand Action datasets, which have been designed to exhaustively cover multiple hand, viewpoint, hand articulation, and occlusion. The challenge consists of a standardized dataset, an evaluation protocol for two different tasks, and a public competition. In this document we describe the different aspects of the challenge and, jointly with the results of the participants, it will be presented at the 3rd International Workshop on Observing and Understanding Hands in Action, HANDS 2017, with ICCV 2017.

cs.CV↗

arXiv2017

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First we verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, we develop a new concept of generalized Mercer kernels to construct $p$-norm RKBSs for $1\leq p\leq\infty$. The $p$-norm RKBSs preserve the same simple format as the Mercer representation of RKHSs. Moreover, the $p$-norm RKBSs are isometrically equivalent to the standard $p$-norm spaces of countable sequences. Hence, the $p$-norm RKBSs possess more geometrical structures than RKHSs including sparsity. The generalized Mercer kernels also cover many well-known kernels, for example, min kernels, Gaussian kernels, and power series kernels. Finally, we propose to solve the support vector machines in the $p$-norm RKBSs, which are to minimize the regularized empirical risks over the $p$-norm RKBSs. We show that the infinite dimensional support vector machines in the $p$-norm RKBSs can be equivalently transferred to finite dimensional convex optimization problems such that we obtain the finite dimensional representations of the support vector machine solutions for practical applications. In particular, we verify that some special support vector machines in the $1$-norm RKBSs are equivalent to the classical $1$-norm sparse regressions. This gives fundamental supports of a novel learning tool called sparse learning methods to be investigated in our next research project.

math.FA↗

arXiv2016

Spatial Attention Deep Net with Partial PSO for Hierarchical Hybrid Hand Pose Estimation

Discriminative methods often generate hand poses kinematically implausible, then generative methods are used to correct (or verify) these results in a hybrid method. Estimating 3D hand pose in a hierarchy, where the high-dimensional output space is decomposed into smaller ones, has been shown effective. Existing hierarchical methods mainly focus on the decomposition of the output space while the input space remains almost the same along the hierarchy. In this paper, a hybrid hand pose estimation method is proposed by applying the kinematic hierarchy strategy to the input space (as well as the output space) of the discriminative method by a spatial attention mechanism and to the optimization of the generative method by hierarchical Particle Swarm Optimization (PSO). The spatial attention mechanism integrates cascaded and hierarchical regression into a CNN framework by transforming both the input(and feature space) and the output space, which greatly reduces the viewpoint and articulation variations. Between the levels in the hierarchy, the hierarchical PSO forces the kinematic constraints to the results of the CNNs. The experimental results show that our method significantly outperforms four state-of-the-art methods and three baselines on three public benchmarks.

cs.CV↗

arXiv2015

Kernel-based Methods for Stochastic Partial Differential Equations

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend the kernel-based methods for the deterministic data to the stochastic data. The main idea is to endow the Sobolev spaces with the probability measures induced by the positive definite kernels such that the Gaussian random variables can be well-defined on the Sobolev spaces. The constructions of these Gaussian random variables provide the kernel-based approximate solutions of the stochastic models. In the numerical examples of the stochastic Poisson and heat equations, we show that the approximate probability distributions are well-posed for various kinds of kernels such as the compactly supported kernels (Wendland functions) and the Sobolev-spline kernels (Matérn functions).

math.NA↗

arXiv2013

Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions

In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of semi-inner-products, we can obtain the explicit representations of the dual (normalized-duality-mapping) elements of support vector machine solutions. In addition, we can introduce the reproduction property in a generalized native space by Fourier transform techniques such that it becomes a reproducing kernel Banach space, which can be even embedded into Sobolev spaces, and its reproducing kernel is set up by the related positive definite function. The representations of the optimal solutions of support vector machines (regularized empirical risks) in these reproducing kernel Banach spaces are formulated explicitly in terms of positive definite functions, and their finite numbers of coefficients can be computed by fixed point iteration. We also give some typical examples of reproducing kernel Banach spaces induced by Matérn functions (Sobolev splines) so that their support vector machine solutions are well computable as the classical algorithms. Moreover, each of their reproducing bases includes information from multiple training data points. The concept of reproducing kernel Banach spaces offers us a new numerical tool for solving support vector machines.

stat.ML↗

arXiv2013

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Matérn kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.

math.NA↗

arXiv2012

Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method

In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations (SPDEs). Using an implicit time stepping scheme, we transform stochastic parabolic equations into stochastic elliptic equations. Our main attention is concentrated on the numerical solution of the elliptic equations at each time step. The estimator of the solution of the elliptic equations is given as a linear combination of reproducing kernels derived from the differential and boundary operators of the SPDE centered at collocation points to be chosen by the user. The random expansion coefficients are computed by solving a random system of linear equations. Numerical experiments demonstrate the feasibility of the method.

math.NA↗

arXiv2011

Reproducing Kernels of Sobolev Spaces via a Green Kernel Approach with Differential Operators and Boundary Operators

We introduce a vector differential operator $\mathbf{P}$ and a vector boundary operator $\mathbf{B}$ to derive a reproducing kernel along with its associated Hilbert space which is shown to be embedded in a classical Sobolev space. This reproducing kernel is a Green kernel of differential operator $L:=\mathbf{P}^{\ast T}\mathbf{P}$ with homogeneous or nonhomogeneous boundary conditions given by $\mathbf{B}$, where we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. We represent the inner product of the reproducing-kernel Hilbert space in terms of the operators $\mathbf{P}$ and $\mathbf{B}$. In addition, we find relationships for the eigenfunctions and eigenvalues of the reproducing kernel and the operators with homogeneous or nonhomogeneous boundary conditions. These eigenfunctions and eigenvalues are used to compute a series expansion of the reproducing kernel and an orthonormal basis of the reproducing-kernel Hilbert space. Our theoretical results provide perhaps a more intuitive way of understanding what kind of functions are well approximated by the reproducing kernel-based interpolant to a given multivariate data sample.

math.NA↗

arXiv2011

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Differential Operators

In this paper we introduce a generalization of the classical $\Leb_2(\Rd)$-based Sobolev spaces with the help of a vector differential operator $\mathbf{P}$ which consists of finitely or countably many differential operators $P_n$ which themselves are linear combinations of distributional derivatives. We find that certain proper full-space Green functions $G$ with respect to $L=\mathbf{P}^{\ast T}\mathbf{P}$ are positive definite functions. Here we ensure that the vector distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. We then provide sufficient conditions under which our generalized Sobolev space will become a reproducing-kernel Hilbert space whose reproducing kernel can be computed via the associated Green function $G$. As an application of this theoretical framework we use $G$ to construct multivariate minimum-norm interpolants $s_{f,X}$ to data sampled from a generalized Sobolev function $f$ on $X$. Among other examples we show the reproducing-kernel Hilbert space of the Gaussian function is equivalent to a generalized Sobolev space.

math.NA↗