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Qing Liu

Publications and source records attributed to Qing Liu.

At least 217 records · Page 12Linked to original sources
arXiv2019

Minimax adaptive wavelet estimator for the anisotropic functional deconvolution model with unknown kernel

In the present paper, we consider the estimation of a periodic two-dimensional function $f(\cdot,\cdot)$ based on observations from its noisy convolution, and convolution kernel $g(\cdot,\cdot)$ unknown. We derive the minimax lower bounds for the mean squared error assuming that $f$ belongs to certain Besov space and the kernel function $g$ satisfies some smoothness properties. We construct an adaptive hard-thresholding wavelet estimator that is asymptotically near-optimal within a logarithmic factor in a wide range of Besov balls. The proposed estimation algorithm implements a truncation to estimate the wavelet coefficients, in addition to the conventional hard-thresholds. A limited simulations study confirms theoretical claims of the paper.

math.ST↗
arXiv2019

Dynamics on the Morse Boundary

Let $X$ be a proper geodesic metric space and let $G$ be a group of isometries of $X$ which acts geometrically. Cordes constructed the Morse boundary of $X$ which generalizes the contracting boundary for CAT(0) spaces and the visual boundary for hyperbolic spaces. We characterize Morse elements in $G$ by their fixed points on the Morse boundary $\partial_MX$. The dynamics on the Morse boundary is very similar to that of a $δ$-hyperbolic space. In particular, we show that the action of $G$ on $\partial_MX$ is minimal if $G$ is not virtually cyclic. We also get a uniform convergence result on the Morse boundary which gives us a weak north-south dynamics for a Morse isometry. This generalizes the work of Murray in the case of the contracting boundary of a CAT(0) space.

math.GT↗
arXiv2019

Parabolic Minkowski convolutions of viscosity solutions to fully nonlinear equations

This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains. As a consequence, we can for instance obtain parabolic power concavity of solutions to a general class of parabolic equations. Our results apply to the Pucci operator, the normalized $q$-Laplacians with $1<q\leq\infty$, the Finsler Laplacian and more general quasilinear operators.

math.AP↗
arXiv2019

DDNet: Cartesian-polar Dual-domain Network for the Joint Optic Disc and Cup Segmentation

Existing joint optic disc and cup segmentation approaches are developed either in Cartesian or polar coordinate system. However, due to the subtle optic cup, the contextual information exploited from the single domain even by the prevailing CNNs is still insufficient. In this paper, we propose a novel segmentation approach, named Cartesian-polar dual-domain network (DDNet), which for the first time considers the complementary of the Cartesian domain and the polar domain. We propose a two-branch of domain feature encoder and learn translation equivariant representations on rectilinear grid from Cartesian domain and rotation equivariant representations on polar grid from polar domain parallelly. To fuse the features on two different grids, we propose a dual-domain fusion module. This module builds the correspondence between two grids by the differentiable polar transform layer and learns the feature importance across two domains in element-wise to enhance the expressive capability. Finally, the decoder aggregates the fused features from low-level to high-level and makes dense predictions. We validate the state-of-the-art segmentation performances of our DDNet on the public dataset ORIGA. According to the segmentation masks, we estimate the commonly used clinical measure for glaucoma, i.e., the vertical cup-to-disc ratio. The low cup-to-disc ratio estimation error demonstrates the potential application in glaucoma screening.

cs.CV↗
arXiv2019

Landmark Proportional Subdistribution Hazards Models for Dynamic Prediction of Cumulative Incidence Functions

An individualized risk prediction model that dynamically updates the probability of a clinical event from a specific cause is valuable for physicians to be able to optimize personalized treatment strategies in real-time by incorporating all available information collected over the follow-up. However, this is more complex and challenging when competing risks are present, because it requires simultaneously updating the overall survival and the cumulative incidence functions (CIFs) while adjusting for the time-dependent covariates and time-varying covariate effects. In this study, we developed a landmark proportional subdistribution hazards (PSH) model and a more comprehensive supermodel by extending the landmark method to the Fine-Gray model. The performance of our models was assessed via simulations and through analysis of data from a multicenter clinical trial for breast cancer patients. Our proposed models have appealing advantages over other dynamic prediction models for data with competing risks. First, our models are robust against violations of the PSH assumption and can directly predict the conditional CIFs bypassing the estimation of overall survival and greatly simplify the prediction procedure. Second, our landmark PSH supermodel enables researchers to make predictions at a set of landmark points in one step. Third, the proposed models can easily incorporate various types of time-dependent information using existing standard software without computational burden.

stat.ME↗
arXiv2018

Advancing the State of the Art in Open Domain Dialog Systems through the Alexa Prize

Building open domain conversational systems that allow users to have engaging conversations on topics of their choice is a challenging task. Alexa Prize was launched in 2016 to tackle the problem of achieving natural, sustained, coherent and engaging open-domain dialogs. In the second iteration of the competition in 2018, university teams advanced the state of the art by using context in dialog models, leveraging knowledge graphs for language understanding, handling complex utterances, building statistical and hierarchical dialog managers, and leveraging model-driven signals from user responses. The 2018 competition also included the provision of a suite of tools and models to the competitors including the CoBot (conversational bot) toolkit, topic and dialog act detection models, conversation evaluators, and a sensitive content detection model so that the competing teams could focus on building knowledge-rich, coherent and engaging multi-turn dialog systems. This paper outlines the advances developed by the university teams as well as the Alexa Prize team to achieve the common goal of advancing the science of Conversational AI. We address several key open-ended problems such as conversational speech recognition, open domain natural language understanding, commonsense reasoning, statistical dialog management, and dialog evaluation. These collaborative efforts have driven improved experiences by Alexa users to an average rating of 3.61, the median duration of 2 mins 18 seconds, and average turns to 14.6, increases of 14%, 92%, 54% respectively since the launch of the 2018 competition. For conversational speech recognition, we have improved our relative Word Error Rate by 55% and our relative Entity Error Rate by 34% since the launch of the Alexa Prize. Socialbots improved in quality significantly more rapidly in 2018, in part due to the release of the CoBot toolkit.

cs.CL↗
arXiv2018

Anisotropic functional deconvolution with long-memory noise: the case of a multi-parameter fractional Wiener sheet

We look into the minimax results for the anisotropic two-dimensional functional deconvolution model with the two-parameter fractional Gaussian noise. We derive the lower bounds for the $L^p$-risk, $1 \leq p < \infty$, and taking advantage of the Riesz poly-potential, we apply a wavelet-vaguelette expansion to de-correlate the anisotropic fractional Gaussian noise. We construct an adaptive wavelet hard-thresholding estimator that attains asymptotically quasi-optimal convergence rates in a wide range of Besov balls. Such convergence rates depend on a delicate balance between the parameters of the Besov balls, the degree of ill-posedness of the convolution operator and the parameters of the fractional Gaussian noise. A limited simulations study confirms theoretical claims of the paper. The proposed approach is extended to the general $r$-dimensional case, with $r> 2$, and the corresponding convergence rates do not suffer from the curse of dimensionality.

math.ST↗
arXiv2018

An Efficient and Truthful Pricing Mechanism for Team Formation in Crowdsourcing Markets

In a crowdsourcing market, a requester is looking to form a team of workers to perform a complex task that requires a variety of skills. Candidate workers advertise their certified skills and bid prices for their participation. We design four incentive mechanisms for selecting workers to form a valid team (that can complete the task) and determining each individual worker's payment. We examine profitability, individual rationality, computational efficiency, and truthfulness for each of the four mechanisms. Our analysis shows that TruTeam, one of the four mechanisms, is superior to the others, particularly due to its computational efficiency and truthfulness. Our extensive simulations confirm the analysis and demonstrate that TruTeam is an efficient and truthful pricing mechanism for team formation in crowdsourcing markets.

cs.GT↗
arXiv2018

Optimal stochastic modelling with unitary quantum dynamics

Identifying and extracting the past information relevant to the future behaviour of stochastic processes is a central task in the quantitative sciences. Quantum models offer a promising approach to this, allowing for accurate simulation of future trajectories whilst using less past information than any classical counterpart. Here we introduce a class of phase-enhanced quantum models, representing the most general means of causal simulation with a unitary quantum circuit. We show that the resulting constructions can display advantages over previous state-of-art methods - both in the amount of information they need to store about the past, and in the minimal memory dimension they require to store this information. Moreover, we find that these two features are generally competing factors in optimisation - leading to an ambiguity in what constitutes the optimal model - a phenomenon that does not manifest classically. Our results thus simultaneously offer new quantum advantages for stochastic simulation, and illustrate further qualitative differences in behaviour between classical and quantum notions of complexity.

quant-ph↗
arXiv2018

What determines the local metallicity of galaxies: global stellar mass, local stellar mass surface density or star formation rate?

The metallicity and its relationship with other galactic properties is a fundamental probe of the evolution of galaxies. In this work, we select about 750,000 star-forming spatial pixels from 1122 blue galaxies in the MaNGA survey to investigate the global stellar mass - local stellar mass surface density - gas-phase metallicity ($M_*$ - $Σ_*$ - $Z$ ) relation. At a fixed $M_*$, the metallicity increases steeply with increasing $Σ_*$. Similarly, at a fixed $Σ_*$, the metallicity increases strongly with increasing $M_*$ at low mass end, while this trend becomes less obvious at high mass end. We find the metallicity to be more strongly correlated to $Σ_*$ than to $M_*$. Furthermore, we construct a tight (0.07 dex scatter) $M_*$ - $Σ_*$ - $Z$ relation, which reduces the scatter in the $Σ_*$ - $Z$ relation by about 30$\%$ for galaxies with $7.8 < {\rm log}(M_*/M_\odot) < 11.0$, while the reduction of scatter is much weaker for high-mass galaxies. This result suggests that, especially for low-mass galaxies, the $M_*$ - $Σ_*$ - $Z$ relation is largely more fundamental than the $M_*$ - $Z$ and $Σ_*$ - $Z$ relations, meaning that both $M_*$ and $Σ_*$ play important roles in shaping the local metallicity. We also find that the local metallicity is probably independent on the local star formation rate surface density at a fixed $M_*$ and $Σ_*$. Our results are consistent with the scenario that the local metallicities in galaxies are shaped by the combination of the local stars formed in the history and the metal loss caused by galactic winds.

astro-ph.GA↗
arXiv2018

Corrigendum to Néron models, Lie algebras, and reduction of curves of genus one [LLR1] and The Brauer group of a surface [LLR2]

Let X be a proper smooth and connected surface over a finite field. We proved in [LLR2] that the order of the Brauer group Br(X) of X is a perfect square if it is finite. Our proof is based in part on a result of Gordon [Gor], which we used in [LLR1] to establish a key formula. Thomas Geisser noted that the formula in [LLR1] is incorrect, due to an omission in [Gor], and provides a corrected formula. We explain in this corrigendum how to modify the work of Gordon to establish a correct formula. The corrected formula can be used to prove the result in [LLR2] without further modifications.

math.AG↗
arXiv2018

Elevation or Suppression? The Resolved Star Formation Main Sequence of Galaxies with Two Different Assembly Modes

We investigate the spatially-resolved star formation main sequence in star-forming galaxies (SFGs) using Integral Field Spectroscopic (IFS) observations from the Mapping Nearby Galaxies at the Apache Point Observatory (MaNGA) survey. We demonstrate that the correlation between the stellar mass surface density ($Σ_*$) and star formation rate surface density ($Σ_{\mathrm{SFR}}$) holds down to sub-galactic scale, leading to the Sub-Galactic Main Sequence (SGMS). By dividing galaxies into two populations based on their recent mass assembly modes, we find the resolved main sequence in galaxies with 'outside-in' mode is steeper than that in galaxies with 'inside-out' mode. This is also confirmed on a galaxy-by-galaxy level, where we find the distributions of SGMS slopes for individual galaxies are clearly separated for the two populations. When normalizing and stacking the SGMS of individual galaxies on one panel for the two populations, we find the inner regions of galaxies with 'inside-out' mode statistically exhibit a suppression in star formation, with a less significant trend in the outer regions of galaxies with 'outside-in' mode. In contrast, the inner regions of galaxies with 'outside-in' mode and the outer regions of galaxies with 'inside-out' mode follow a slightly sub-linear scaling relation with a slope $\sim$0.9, which is in good agreement with previous findings, suggesting that they are experiencing a universal regulation without influences of additional physical processes.

astro-ph.GA↗
arXiv2018

Limit theory for an AR(1) model with intercept and a possible infinite variance

In this paper, we derive the limit distribution of the least squares estimator for an AR(1) model with a non-zero intercept and a possible infinite variance. It turns out that the estimator has a quite different limit for the cases of $|ρ| < 1$, $|ρ| > 1$, and $ρ= 1 + \frac{c}{n^α}$ for some constant $c \in R$ and $α\in (0, 1]$, and whether or not the variance of the model errors is infinite also has a great impact on both the convergence rate and the limit distribution of the estimator.

math.ST↗
arXiv2018

Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean

Median absolute deviation (hereafter MAD) is known as a robust alternative to the ordinary variance. It has been widely utilized to induce robust statistical inferential procedures. In this paper, we investigate the strong and weak Bahadur representations of its bootstrap counterpart. As a useful application, we utilize the results to derive the weak Bahadur representation of the bootstrap sample projection depth weighted mean---a quite important location estimator depending on MAD.

math.ST↗
arXiv2018

Few-shot Learning by Exploiting Visual Concepts within CNNs

Convolutional neural networks (CNNs) are one of the driving forces for the advancement of computer vision. Despite their promising performances on many tasks, CNNs still face major obstacles on the road to achieving ideal machine intelligence. One is that CNNs are complex and hard to interpret. Another is that standard CNNs require large amounts of annotated data, which is sometimes hard to obtain, and it is desirable to learn to recognize objects from few examples. In this work, we address these limitations of CNNs by developing novel, flexible, and interpretable models for few-shot learning. Our models are based on the idea of encoding objects in terms of visual concepts (VCs), which are interpretable visual cues represented by the feature vectors within CNNs. We first adapt the learning of VCs to the few-shot setting, and then uncover two key properties of feature encoding using VCs, which we call category sensitivity and spatial pattern. Motivated by these properties, we present two intuitive models for the problem of few-shot learning. Experiments show that our models achieve competitive performances, while being more flexible and interpretable than alternative state-of-the-art few-shot learning methods. We conclude that using VCs helps expose the natural capability of CNNs for few-shot learning.

cs.CV↗
arXiv2018

Conversational AI: The Science Behind the Alexa Prize

Conversational agents are exploding in popularity. However, much work remains in the area of social conversation as well as free-form conversation over a broad range of domains and topics. To advance the state of the art in conversational AI, Amazon launched the Alexa Prize, a 2.5-million-dollar university competition where sixteen selected university teams were challenged to build conversational agents, known as socialbots, to converse coherently and engagingly with humans on popular topics such as Sports, Politics, Entertainment, Fashion and Technology for 20 minutes. The Alexa Prize offers the academic community a unique opportunity to perform research with a live system used by millions of users. The competition provided university teams with real user conversational data at scale, along with the user-provided ratings and feedback augmented with annotations by the Alexa team. This enabled teams to effectively iterate and make improvements throughout the competition while being evaluated in real-time through live user interactions. To build their socialbots, university teams combined state-of-the-art techniques with novel strategies in the areas of Natural Language Understanding, Context Modeling, Dialog Management, Response Generation, and Knowledge Acquisition. To support the efforts of participating teams, the Alexa Prize team made significant scientific and engineering investments to build and improve Conversational Speech Recognition, Topic Tracking, Dialog Evaluation, Voice User Experience, and tools for traffic management and scalability. This paper outlines the advances created by the university teams as well as the Alexa Prize team to achieve the common goal of solving the problem of Conversational AI.

cs.AI↗
arXiv2018

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

Since its introduction 30 years ago, the lattice Boltzmann (LB) method has achieved great success in simulating fluid flows and modeling physics in fluids. Owing to its kinetic nature, the LB method has the capability to incorporate the essential microscopic or mesoscopic physics, and it is particularly successful in modeling transport phenomena involving complex boundaries and interfacial dynamics. The LB method can be considered to be an efficient numerical tool for fluid flow and heat transfer in porous media. Moreover, since the LB method is inherently transient, it is especially useful for investigating transient solid-liquid phase-change processes wherein the interfacial behaviors are very important. In this article, a comprehensive review of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media at both the pore scale and representative elementary volume (REV) scale. The review first introduces the fundamentals of the LB method for fluid flow and heat transfer. Then the REV-scale LB method for fluid flow and single-phase heat transfer in porous media, and the LB method for solid-liquid phase-change heat transfer, are described. Some applications of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media are provided. In addition, applications of the LB method to predict effective thermal conductivity of porous materials are also provided. Finally, further developments of the LB method in the related areas are discussed.

physics.comp-ph↗