arXiv subjects

Xuan Wu

Publications and source records attributed to Xuan Wu.

At least 73 records · Page 4Linked to original sources

arXiv2022

Intermediate Disorder regime for half-space directed polymers

We consider the convergence of partition functions and endpoint density for the half-space directed polymer model in dimension $1+1$ in the intermediate disorder regime as considered for the full space model by Alberts, Khanin and Quastel in [AKQ]. By scaling the inverse temperature like $βn^{-1/4}$, the point-to-point partition function converges to the chaos series for the solution to stochastic heat equation with Robin boundary condition and delta initial data. We also apply our convergence results to the exact-solvable log-gamma directed polymer model in a half-space.

math.PR↗

arXiv2022

Tightness of discrete Gibbsian line ensembles with exponential interaction Hamiltonians

In this paper we introduce a framework to prove tightness of a sequence of discrete Gibbsian line ensembles $\mathcal{L}^N = \{\mathcal{L}_k^N(x), k \in \mathbb{N}, x \in \frac{1}{N}\mathbb{Z}\}$, which is a collection of countable random curves. The sequence of discrete line ensembles $\mathcal{L}^N$ we consider enjoys a resampling invariance property, which we call $(H^N,H^{RW,N})$-Gibbs property. We also assume that $\mathcal{L}^N$ satisfies technical assumptions A1-A4 on $(H^N,H^{RW,N})$ and the assumption that the lowest labeled curve with a parabolic shift, $\mathcal{L}_1^N(x) + \frac{x^2}{2}$, converges weakly to a stationary process in the topology of uniform convergence on compact sets. Under these assumptions, we prove our main result Theorem 2.18 that $\mathcal{L}^N$ is tight as a line ensemble and that $H$-Brownian Gibbs property holds for all subsequential limit line ensembles with $H(x)= e^x$. As an application of Theorem 2.18, under weak noise scaling, we show that the scaled log-gamma line ensemble $\bar{\mathcal{L}}^N$ is tight, which is a sequence of discrete line ensembles associated with the inverse-gamma polymer model via the geometric RSK correspondence. The $H$-Brownian Gibbs property (with $H(x) = e^x$) of its subsequential limits also follows.

math.PR↗

arXiv2022

Convergence of the KPZ line ensemble

In this paper we study the KPZ line ensembles under the KPZ scaling. Based on their Gibbs property, we derive quantitative local fluctuation estimates for the scaled KPZ line ensembles. This allows us to show that the family of scaled KPZ line ensembles is tight. Together with the recent progress in [QS20], [Vir], and [DM], the tightness result yields the conjectural convergence of the scaled KPZ line ensembles to the Airy line ensemble.

math.PR↗

arXiv2021

Coresets for Clustering with Missing Values

We provide the first coreset for clustering points in $\mathbb{R}^d$ that have multiple missing values (coordinates). Previous coreset constructions only allow one missing coordinate. The challenge in this setting is that objective functions, like $k$-Means, are evaluated only on the set of available (non-missing) coordinates, which varies across points. Recall that an $ε$-coreset of a large dataset is a small proxy, usually a reweighted subset of points, that $(1+ε)$-approximates the clustering objective for every possible center set. Our coresets for $k$-Means and $k$-Median clustering have size $(jk)^{O(\min(j,k))} (ε^{-1} d \log n)^2$, where $n$ is the number of data points, $d$ is the dimension and $j$ is the maximum number of missing coordinates for each data point. We further design an algorithm to construct these coresets in near-linear time, and consequently improve a recent quadratic-time PTAS for $k$-Means with missing values [Eiben et al., SODA 2021] to near-linear time. We validate our coreset construction, which is based on importance sampling and is easy to implement, on various real data sets. Our coreset exhibits a flexible tradeoff between coreset size and accuracy, and generally outperforms the uniform-sampling baseline. Furthermore, it significantly speeds up a Lloyd's-style heuristic for $k$-Means with missing values.

cs.DS↗

arXiv2021

Neural Architecture Search based on Cartesian Genetic Programming Coding Method

Neural architecture search (NAS) is a hot topic in the field of automated machine learning and outperforms humans in designing neural architectures on quite a few machine learning tasks. Motivated by the natural representation form of neural networks by the Cartesian genetic programming (CGP), we propose an evolutionary approach of NAS based on CGP, called CGPNAS, to solve sentence classification task. To evolve the architectures under the framework of CGP, the operations such as convolution are identified as the types of function nodes of CGP, and the evolutionary operations are designed based on Evolutionary Strategy. The experimental results show that the searched architectures are comparable with the performance of human-designed architectures. We verify the ability of domain transfer of our evolved architectures. The transfer experimental results show that the accuracy deterioration is lower than 2-5%. Finally, the ablation study identifies the Attention function as the single key function node and the linear transformations along could keep the accuracy similar with the full evolved architectures, which is worthy of investigation in the future.

cs.NE↗

arXiv2021

Tightness of $(H, H^{RW})$-Gibbsian line ensembles

We develop a black-box theory, which can be used to show that a sequence of Gibbsian line ensembles is tight, provided that the one-point marginals of the lowest labeled curves of the ensembles are tight and globally approximate an inverted parabola. Our theory is applicable under certain technical assumptions on the nature of the Gibbs property and the underlying random walk measure. As a particular application of our general framework we show that a certain sequence of Gibbsian line ensembles, which naturally arises in the log-gamma polymer, is tight in the ubiquitous KPZ class $1/3: 2/3$ scaling, and also that all subsequential limits satisfy the Brownian Gibbs property, introduced by Corwin and Hammond in (Invent. Math. 195, 441-508, 2014). One of the core results proved in the paper, which underlies many of our arguments, is the construction of a continuous grand monotone coupling of Gibbsian line ensembles with respect to their boundary data (entrance and exit values, and bounding curves). Continuous means that the Gibbsian line ensemble measure varies continuously as one varies the boundary data, grand means that all uncountably many measures (one for each boundary data) are coupled to the same probability space, and monotone means that raising the values of the boundary data likewise raises the associated measure. Our continuous grand monotone coupling generalizes an analogous construction, which was recently implemented by Barraquand, Corwin and Dimitrov in (arXiv:2101.03045), from line ensembles with a single curve to ones with an arbitrary finite number of curves.

math.PR↗

arXiv2021

Determinantal structures for Bessel fields

A Bessel field $\mathcal{B}=\{\mathcal{B}(α,t), α\in\mathbb{N}_0, t\in\mathbb{R}\}$ is a two-variable random field such that for every $(α,t)$, $\mathcal{B}(α,t)$ has the law of a Bessel point process with index $α$. The Bessel fields arise as hard edge scaling limits of the Laguerre field, a natural extension of the classical Laguerre unitary ensemble. It is recently proved in [LW21] that for fixed $α$, $\{\mathcal{B}(α,t), t\in\mathbb{R}\}$ is a squared Bessel Gibbsian line ensemble. In this paper, we discover rich integrable structures for the Bessel fields: along a time-like or a space-like path, $\mathcal{B}$ is a determinantal point process with an explicit correlation kernel; for fixed $t$, $\{\mathcal{B}(α,t),α\in\mathbb{N}_0\}$ is an exponential Gibbsian line ensemble.

math.PR↗

arXiv2021

Enhanced Monte Carlo Estimation of the Fisher Information Matrix with Independent Perturbations for Complex Problems

The Fisher information matrix provides a way to measure the amount of information given observed data based on parameters of interest. Many applications of the FIM exist in statistical modeling, system identification, and parameter estimation. We sometimes use the Monte Carlo-based method to estimate the FIM because its analytical form is often impossible or difficult to be computed in real-world models. In this paper, we review the basic method based on simultaneous perturbations and present an enhanced resampling-based method with independent simultaneous perturbations to estimate the Fisher information matrix. We conduct theoretical and numerical analysis to show its accuracy via variance reduction from $O(1/N)$ to $O(1/(nN))$, where $n$ is the sample size of the data and $N$ is a measure of the Monte Carlo averaging. We also consider the trade-off between accuracy and computational cost.

stat.CO↗

arXiv2021

Back-n White Neutron Source at CSNS and its Applications

Back-streaming neutrons from the spallation target of the China Spallation Neutron Source (CSNS) that emit through the incoming proton channel were exploited to build a white neutron beam facility (the so-called Back-n white neutron source), which was completed in March 2018. The Back-n neutron beam is very intense, at approximately 2*10^7 n/cm^2/s at 55 m from the target, and has a nominal proton beam with a power of 100 kW in the CSNS-I phase and a kinetic energy of 1.6 GeV and a thick tungsten target in multiple slices with modest moderation from the cooling water through the slices. In addition, the excellent energy spectrum spanning from 0.5 eV to 200 MeV, and a good time resolution related to the time-of-flight measurements make it a typical white neutron source for nuclear data measurements; its overall performance is among that of the best white neutron sources in the world. Equipped with advanced spectrometers, detectors, and application utilities, the Back-n facility can serve wide applications, with a focus on neutron-induced cross-section measurements. This article presents an overview of the neutron beam characteristics, the experimental setups, and the ongoing applications at Back-n.

physics.acc-ph↗

arXiv2020

Intelligent Hotel ROS-based Service Robot

With the advances of artificial intelligence (AI) technology, many studies and work have been carried out on how robots could replace human labor. In this paper, we present a ROS based intelligence hotel robot, which simplifies the check-in process. We use pioneer 3dx robot and considered different environment settings. The robot combined with Hokuyo Lidar and Kinect Xbox camera, can plan the routes accurately and reach rooms in different floors. In addition, we added an intelligent voice system which provides an assistant for the customers.

cs.RO↗

arXiv2020

Coresets for Clustering in Excluded-minor Graphs and Beyond

Coresets are modern data-reduction tools that are widely used in data analysis to improve efficiency in terms of running time, space and communication complexity. Our main result is a fast algorithm to construct a small coreset for k-Median in (the shortest-path metric of) an excluded-minor graph. Specifically, we give the first coreset of size that depends only on $k$, $ε$ and the excluded-minor size, and our running time is quasi-linear (in the size of the input graph). The main innovation in our new algorithm is that is iterative; it first reduces the $n$ input points to roughly $O(\log n)$ reweighted points, then to $O(\log\log n)$, and so forth until the size is independent of $n$. Each step in this iterative size reduction is based on the importance sampling framework of Feldman and Langberg (STOC 2011), with a crucial adaptation that reduces the number of \emph{distinct points}, by employing a terminal embedding (where low distortion is guaranteed only for the distance from every terminal to all other points). Our terminal embedding is technically involved and relies on shortest-path separators, a standard tool in planar and excluded-minor graphs. Furthermore, our new algorithm is applicable also in Euclidean metrics, by simply using a recent terminal embedding result of Narayanan and Nelson, (STOC 2019), which extends the Johnson-Lindenstrauss Lemma. We thus obtain an efficient coreset construction in high-dimensional Euclidean spaces, thereby matching and simplifying state-of-the-art results (Sohler and Woodruff, FOCS 2018; Huang and Vishnoi, STOC 2020). In addition, we also employ terminal embedding with additive distortion to obtain small coresets in graphs with bounded highway dimension, and use applications of our coresets to obtain improved approximation schemes, e.g., an improved PTAS for planar k-Median via a new centroid set.

cs.DS↗

arXiv2020

Measurement of the neutron beam profile of the Back-n white neutron facility at CSNS with a Micromegas detector

The Back-n white neutron beam line, which uses back-streaming white neutrons from the spallation target of the China Spallation Neutron Source, is used for nuclear data measurements. A Micromegas-based neutron detector with two variants was specially developed to measure the beam spot distribution for this beam line. In this article, the design, fabrication, and characterization of the detector are described. The results of the detector performance tests are presented, which include the relative electron transparency, the gain and the gain uniformity, and the neutron beam profile reconstruction capability. The result of the first measurement of the Back-n neutron beam spot distribution is also presented.

physics.ins-det↗

arXiv2019

KMT coupling for random walk bridges

In this paper we prove an analogue of the Komlós-Major-Tusnády (KMT) embedding theorem for random walk bridges. The random bridges we consider are constructed through random walks with i.i.d jumps that are conditioned on the locations of their endpoints. We prove that such bridges can be strongly coupled to Brownian bridges of appropriate variance when the jumps are either continuous or integer valued under some mild technical assumptions on the jump distributions. Our arguments follow a similar dyadic scheme to KMT's original proof, but they require more refined estimates and stronger assumptions necessitated by the endpoint conditioning. In particular, our result does not follow from the KMT embedding theorem, which we illustrate via a counterexample.

math.PR↗

arXiv2019

Measurements of differential and angle-integrated cross sections for the $^{10}$B($n, α$)$^{7}$Li reaction in the neutron energy range from 1.0 eV to 2.5 MeV

Differential and angle-integrated cross sections for the $^{10}$B($n, α$)$^{7}$Li, $^{10}$B($n, α$$_{0}$)$^{7}$Li and $^{10}$B($n, α$$_{1}$)$^{7}$Li$^{*}$ reactions have been measured at CSNS Back-n white neutron source. Two enriched (90%) $^{10}$B samples 5.0 cm in diameter and ~85.0 $μ$g/cm$^{2}$ in thickness each with an aluminum backing were prepared, and back-to-back mounted at the sample holder. The charged particles were detected using the silicon-detector array of the Light-charged Particle Detector Array (LPDA) system. The neutron energy E$_{n}$ was determined by TOF (time-of-flight) method, and the valid $α$ events were extracted from the E$_{n}$-Amplitude two-dimensional spectrum. With 15 silicon detectors, the differential cross sections of $α$-particles were measured from 19.2° to 160.8°. Fitted with the Legendre polynomial series, the ($n, α$) cross sections were obtained through integration. The absolute cross sections were normalized using the standard cross sections of the $^{10}$B($n, α$)$^{7}$Li reaction in the 0.3 - 0.5 MeV neutron energy region. The measurement neutron energy range for the $^{10}$B($n, α$)$^{7}$Li reaction is 1.0 eV $\le$ En < 2.5 MeV (67 energy points), and for the $^{10}$B($n, α$$_{0}$)$^{7}$Li and $^{10}$B($n, α$$_{1}$)$^{7}$Li$^{*}$ reactions is 1.0 eV $\le$ En < 1.0 MeV (59 energy points). The present results have been analyzed by the resonance reaction mechanism and the level structure of the $^{11}$B compound system, and compared with existing measurements and evaluations.

nucl-ex↗

arXiv2019

A Quest for Structure: Jointly Learning the Graph Structure and Semi-Supervised Classification

Semi-supervised learning (SSL) is effectively used for numerous classification problems, thanks to its ability to make use of abundant unlabeled data. The main assumption of various SSL algorithms is that the nearby points on the data manifold are likely to share a label. Graph-based SSL constructs a graph from point-cloud data as an approximation to the underlying manifold, followed by label inference. It is no surprise that the quality of the constructed graph in capturing the essential structure of the data is critical to the accuracy of the subsequent inference step [6]. How should one construct a graph from the input point-cloud data for graph-based SSL? In this work we introduce a new, parallel graph learning framework (called PG-learn) for the graph construction step of SSL. Our solution has two main ingredients: (1) a gradient-based optimization of the edge weights (more specifically, different kernel bandwidths in each dimension) based on a validation loss function, and (2) a parallel hyperparameter search algorithm with an adaptive resource allocation scheme. In essence, (1) allows us to search around a (random) initial hyperparameter configuration for a better one with lower validation loss. Since the search space of hyperparameters is huge for high-dimensional problems, (2) empowers our gradient-based search to go through as many different initial configurations as possible, where runs for relatively unpromising starting configurations are terminated early to allocate the time for others. As such, PG-learn is a carefully-designed hybrid of random and adaptive search. Through experiments on multi-class classification problems, we show that PG-learn significantly outperforms a variety of existing graph construction schemes in accuracy (per fixed time budget for hyperparameter tuning), and scales more effectively to high dimensional problems.

cs.LG↗

arXiv2019

Coresets for Gaussian Mixture Models of Any Shape

An $\varepsilon$-coreset for a given set $D$ of $n$ points, is usually a small weighted set, such that querying the coreset \emph{provably} yields a $(1+\varepsilon)$-factor approximation to the original (full) dataset, for a given family of queries. Using existing techniques, coresets can be maintained for streaming, dynamic (insertion/deletions), and distributed data in parallel, e.g. on a network, GPU or cloud. We suggest the first coresets that approximate the negative log-likelihood for $k$-Gaussians Mixture Models (GMM) of arbitrary shapes (ratio between eigenvalues of their covariance matrices). For example, for any input set $D$ whose coordinates are integers in $[-n^{100},n^{100}]$ and any fixed $k,d\geq 1$, the coreset size is $(\log n)^{O(1)}/\varepsilon^2$, and can be computed in time near-linear in $n$, with high probability. The optimal GMM may then be approximated quickly by learning the small coreset. Previous results [NIPS'11, JMLR'18] suggested such small coresets for the case of semi-speherical unit Gaussians, i.e., where their corresponding eigenvalues are constants between $\frac{1}{2π}$ to $2π$. Our main technique is a reduction between coresets for $k$-GMMs and projective clustering problems. We implemented our algorithms, and provide open code, and experimental results. Since our coresets are generic, with no special dependency on GMMs, we hope that they will be useful for many other functions.

cs.LG↗

arXiv2019

Coresets for Ordered Weighted Clustering

We design coresets for Ordered k-Median, a generalization of classical clustering problems such as k-Median and k-Center, that offers a more flexible data analysis, like easily combining multiple objectives (e.g., to increase fairness or for Pareto optimization). Its objective function is defined via the Ordered Weighted Averaging (OWA) paradigm of Yager (1988), where data points are weighted according to a predefined weight vector, but in order of their contribution to the objective (distance from the centers). A powerful data-reduction technique, called a coreset, is to summarize a point set $X$ in $\mathbb{R}^d$ into a small (weighted) point set $X'$, such that for every set of $k$ potential centers, the objective value of the coreset $X'$ approximates that of $X$ within factor $1\pm ε$. When there are multiple objectives (weights), the above standard coreset might have limited usefulness, whereas in a \emph{simultaneous} coreset, which was introduced recently by Bachem and Lucic and Lattanzi (2018), the above approximation holds for all weights (in addition to all centers). Our main result is a construction of a simultaneous coreset of size $O_{ε, d}(k^2 \log^2 |X|)$ for Ordered k-Median. To validate the efficacy of our coreset construction we ran experiments on a real geographical data set. We find that our algorithm produces a small coreset, which translates to a massive speedup of clustering computations, while maintaining high accuracy for a range of weights.

cs.DS↗

arXiv2018

$\varepsilon$-Coresets for Clustering (with Outliers) in Doubling Metrics

We study the problem of constructing $\varepsilon$-coresets for the $(k, z)$-clustering problem in a doubling metric $M(X, d)$. An $\varepsilon$-coreset is a weighted subset $S\subseteq X$ with weight function $w : S \rightarrow \mathbb{R}_{\geq 0}$, such that for any $k$-subset $C \in [X]^k$, it holds that $\sum_{x \in S}{w(x) \cdot d^z(x, C)} \in (1 \pm \varepsilon) \cdot \sum_{x \in X}{d^z(x, C)}$. We present an efficient algorithm that constructs an $\varepsilon$-coreset for the $(k, z)$-clustering problem in $M(X, d)$, where the size of the coreset only depends on the parameters $k, z, \varepsilon$ and the doubling dimension $\mathsf{ddim}(M)$. To the best of our knowledge, this is the first efficient $\varepsilon$-coreset construction of size independent of $|X|$ for general clustering problems in doubling metrics. To this end, we establish the first relation between the doubling dimension of $M(X, d)$ and the shattering dimension (or VC-dimension) of the range space induced by the distance $d$. Such a relation was not known before, since one can easily construct instances in which neither one can be bounded by (some function of) the other. Surprisingly, we show that if we allow a small $(1\pmε)$-distortion of the distance function $d$, and consider the notion of $τ$-error probabilistic shattering dimension, we can prove an upper bound of $O( \mathsf{ddim}(M)\cdot \log(1/\varepsilon) +\log\log{\frac{1}τ} )$ for the probabilistic shattering dimension for even weighted doubling metrics. We believe this new relation is of independent interest and may find other applications. We also study the robust coresets and centroid sets in doubling metrics. Our robust coreset construction leads to new results in clustering and property testing, and the centroid sets can be used to accelerate the local search algorithms for clustering problems.

cs.DS↗