arXiv subjects

Lin Xiao

Publications and source records attributed to Lin Xiao.

At least 91 records · Page 5Linked to original sources

arXiv2018

Emission-line diagnostics of nearby HII regions including interacting binary populations

We present numerical models of the nebular emission from H II regions around young stellar populations over a range of compositions and ages. The synthetic stellar pop- ulations include both single stars and interacting binary stars. We compare these models to the observed emission lines of 254 HII regions of 13 nearby spiral galax- ies and 21 dwarf galaxies drawn from archival data. The models are created using the combination of the Binary Population and Spectral Synthesis (bpass) code with the photoionization code cloudy to study the differences caused by the inclusion of interacting binary stars in the stellar population. We obtain agreement with the observed emission line ratios from the nearby star-forming regions and discuss the effect of binary star evolution pathways on the nebular ionization of H II regions. We find that at population ages above 10 Myr, single-star models rapidly decrease in flux and ionization strength, while binary-star model still produce strong flux and high O III/H\b{eta} ratios. Our models can reproduce the metallicity of H II regions from spiral galaxies but we find higher metallicities than previously estimated for the H II regions from dwarf galaxies. Comparing the equivalent width of H\b{eta} emission between mod- els and observations, we find that accounting for ionizing photon leakage can affect age estimates for HII regions. When it is included, the typical age derived for HII regions is 5Myr from single-star models, and up to 10Myr with binary-star models. This is due to the existence of binary-star evolution pathways which produce more hot WR and helium stars at older ages. For future reference, we calculate new BPASS binary maximal starburst lines as a function of metallicity, and for the total model population, and present these in Appendix A.

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arXiv2018

Learning SMaLL Predictors

We present a new machine learning technique for training small resource-constrained predictors. Our algorithm, the Sparse Multiprototype Linear Learner (SMaLL), is inspired by the classic machine learning problem of learning $k$-DNF Boolean formulae. We present a formal derivation of our algorithm and demonstrate the benefits of our approach with a detailed empirical study.

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arXiv2017

DSCOVR: Randomized Primal-Dual Block Coordinate Algorithms for Asynchronous Distributed Optimization

Machine learning with big data often involves large optimization models. For distributed optimization over a cluster of machines, frequent communication and synchronization of all model parameters (optimization variables) can be very costly. A promising solution is to use parameter servers to store different subsets of the model parameters, and update them asynchronously at different machines using local datasets. In this paper, we focus on distributed optimization of large linear models with convex loss functions, and propose a family of randomized primal-dual block coordinate algorithms that are especially suitable for asynchronous distributed implementation with parameter servers. In particular, we work with the saddle-point formulation of such problems which allows simultaneous data and model partitioning, and exploit its structure by doubly stochastic coordinate optimization with variance reduction (DSCOVR). Compared with other first-order distributed algorithms, we show that DSCOVR may require less amount of overall computation and communication, and less or no synchronization. We discuss the implementation details of the DSCOVR algorithms, and present numerical experiments on an industrial distributed computing system.

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arXiv2017

Spatially resolved MaNGA observations of the host galaxy of superluminous supernova 2017egm

Superluminous supernovae (SLSNe) are found predominantly in dwarf galaxies, indicating that their progenitors have a low metallicity. However, the most nearby SLSN to date, SN 2017egm, occurred in the spiral galaxy NGC 3191, which has a relatively high stellar mass and correspondingly high metallicity. In this paper, we present detailed analysis of the nearby environment of SN 2017egm using MaNGA IFU data, which provides spectral data on kiloparsec scales. From the velocity map we find no evidence that SN 2017egm occurred within some intervening satellite galaxy, and at the SN position most metallicity diagnostics yield a solar and above solar metallicity (12 + log (O/H) = 8.8-9.1). Additionally we measure a small H-alpha equivalent width (EW) at the SN position of just 34 Angs, which is one of the lowest EWs measured at any SLSN or Gamma-Ray Burst position, and indicative of the progenitor star being comparatively old. We also compare the observed properties of NGC 3191 with other SLSN host galaxies. The solar-metallicity environment at the position of SN 2017egm presents a challenge to our theoretical understanding, and our spatially resolved spectral analysis provides further constraints on the progenitors of SLSNe.

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arXiv2017

Stochastic Variance Reduction Methods for Policy Evaluation

Policy evaluation is a crucial step in many reinforcement-learning procedures, which estimates a value function that predicts states' long-term value under a given policy. In this paper, we focus on policy evaluation with linear function approximation over a fixed dataset. We first transform the empirical policy evaluation problem into a (quadratic) convex-concave saddle point problem, and then present a primal-dual batch gradient method, as well as two stochastic variance reduction methods for solving the problem. These algorithms scale linearly in both sample size and feature dimension. Moreover, they achieve linear convergence even when the saddle-point problem has only strong concavity in the dual variables but no strong convexity in the primal variables. Numerical experiments on benchmark problems demonstrate the effectiveness of our methods.

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arXiv2017

Emission-line Diagnostics of Nearby HII Regions Including Supernova Hosts

We present a new model of the optical nebular emission from HII regions by combin- ing the results of the Binary Population and Spectral Synthesis (bpass) code with the photoion- ization code cloudy (Ferland et al. 1998). We explore a variety of emission-line diagnostics of these star-forming HII regions and examine the effects of metallicity and interacting binary evo- lution on the nebula emission-line production. We compare the line emission properties of HII regions with model stellar populations, and provide new constraints on their stellar populations and supernova progenitors. We find that models including massive binary stars can successfully match all the observational constraints and provide reasonable age and mass estimation of the HII regions and supernova progenitors.

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arXiv2017

Variational Gram Functions: Convex Analysis and Optimization

We propose a new class of convex penalty functions, called \emph{variational Gram functions} (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as regularizers in convex optimization problems arising from hierarchical classification, multitask learning, and estimating vectors with disjoint supports, among other applications. We study convexity for VGFs, and give efficient characterizations for their convex conjugates, subdifferentials, and proximal operators. We discuss efficient optimization algorithms for regularized loss minimization problems where the loss admits a common, yet simple, variational representation and the regularizer is a VGF. These algorithms enjoy a simple kernel trick, an efficient line search, as well as computational advantages over first order methods based on the subdifferential or proximal maps. We also establish a general representer theorem for such learning problems. Lastly, numerical experiments on a hierarchical classification problem are presented to demonstrate the effectiveness of VGFs and the associated optimization algorithms.

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arXiv2017

Exploiting Strong Convexity from Data with Primal-Dual First-Order Algorithms

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in order to obtain fast linear convergence, and the required dual proximal mapping may not admit closed-form or efficient solution. In this paper, we develop both batch and randomized primal-dual algorithms that can exploit strong convexity from data adaptively and are capable of achieving linear convergence even without regularization. We also present dual-free variants of the adaptive primal-dual algorithms that do not require computing the dual proximal mapping, which are especially suitable for logistic regression.

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arXiv2016

Direct Urca processes involving singlet proton superfluidity in neutron star cooling

A detailed description of the baryon direct Urca processes A: $n\rightarrow p+e+\barν_{e}$, B: $Λ\rightarrow p+e+\barν_{e}$, C: $Ξ^{-}\rightarrowΛ+e+\barν_{e}$ related to the neutron star cooling is given in the relativistic mean field approximation.The contributions of the reactions B and C on the neutrino luminosity are calculated by means of the relativistic expressions of the neutrino energy losses.Our results show that the total neutrino luminosities of the reactions A, B, C within the mass range 1.603-2.067$M_{\odot}$ (1.515-1.840$M_{\odot}$ for TM1 model) for GM1 model are larger than the corresponding values for neutron stars in npe$μ$ matter. Although the hyperon direct Urca processes B and C reduce the neutrino emissivity of the reaction A, it illustrates the reactions B and C still make the total neutrino luminosity enhancement in the above mentioned areas.Furthermore, when we only consider the $^{1}S_{0}$ proton superfluidity in neutron star cooling, we find that although the neutrino emissivity of the reactions A and B is suppressed with the appearance of $^{1}S_{0}$ proton superfluidity, the total contribution of the reactions A, B, C can still quicken a massive neutron star cooling.These results could be used to help prove appearing hyperons in PSR J1614-2230 and J0348+0432 from neutron star cooling perspective.

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arXiv2015

End-to-end Learning of LDA by Mirror-Descent Back Propagation over a Deep Architecture

We develop a fully discriminative learning approach for supervised Latent Dirichlet Allocation (LDA) model using Back Propagation (i.e., BP-sLDA), which maximizes the posterior probability of the prediction variable given the input document. Different from traditional variational learning or Gibbs sampling approaches, the proposed learning method applies (i) the mirror descent algorithm for maximum a posterior inference and (ii) back propagation over a deep architecture together with stochastic gradient/mirror descent for model parameter estimation, leading to scalable and end-to-end discriminative learning of the model. As a byproduct, we also apply this technique to develop a new learning method for the traditional unsupervised LDA model (i.e., BP-LDA). Experimental results on three real-world regression and classification tasks show that the proposed methods significantly outperform the previous supervised topic models, neural networks, and is on par with deep neural networks.

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arXiv2015

Stochastic Primal-Dual Coordinate Method for Regularized Empirical Risk Minimization

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a stochastic primal-dual coordinate (SPDC) method, which alternates between maximizing over a randomly chosen dual variable and minimizing over the primal variable. An extrapolation step on the primal variable is performed to obtain accelerated convergence rate. We also develop a mini-batch version of the SPDC method which facilitates parallel computing, and an extension with weighted sampling probabilities on the dual variables, which has a better complexity than uniform sampling on unnormalized data. Both theoretically and empirically, we show that the SPDC method has comparable or better performance than several state-of-the-art optimization methods.

math.OC↗

arXiv2015

Core-Collapse Supernova Rate Synthesis Within 11 Mpc

The 11 Mpc H-alpha and Ultraviolet Galaxy (11HUGS) Survey traces the star formation activity of nearby galaxies. In addition within this volume the detection completeness of core-collapse supernovae (CCSNe) is high therefore by comparing these observed stellar births and deaths we can make a sensitive test of our understanding of how stars live and die. In this paper, we use the results of the Binary Population and Spectral Synthesis (BPASS) code to simulate the 11HUGS galaxies H-alpha and far-ultraviolet (FUV) star formation rate indicators (SFRIs) and simultaneously match the core-collapse supernova (CCSN) rate. We find that stellar population including interacting binary stars makes little difference to the total CCSN rate but increases the H-alpha and FUV fluxes for a constant number of stars being formed. In addition they significantly increase the predicted rate of type Ibc supernovae (SNe) relative to type II SNe to the level observed in the 11HUGS galaxies. We also find that instead of assuming a constant star formation history (SFH) for the galaxies our best fitting models have a star formation rate (SFR) that peaked more than 3 Myrs ago.

astro-ph.GA↗

arXiv2015

A Randomized Nonmonotone Block Proximal Gradient Method for a Class of Structured Nonlinear Programming

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves typically several associated proximal subproblems that usually have a closed-form solution, until a certain progress on objective value is achieved. In contrast to the usual randomized block coordinate descent method [23,20], our method has a nonmonotone flavor and uses variable stepsizes that can partially utilize the local curvature information of the smooth component of objective function. We show that any accumulation point of the solution sequence of the method is a stationary point of the problem {\it almost surely} and the method is capable of finding an approximate stationary point with high probability. We also establish a sublinear rate of convergence for the method in terms of the minimal expected squared norm of certain proximal gradients over the iterations. When the problem under consideration is convex, we show that the expected objective values generated by RNBPG converge to the optimal value of the problem. Under some assumptions, we further establish a sublinear and linear rate of convergence on the expected objective values generated by a monotone version of RNBPG. Finally, we conduct some preliminary experiments to test the performance of RNBPG on the $\ell_1$-regularized least-squares problem and a dual SVM problem in machine learning. The computational results demonstrate that our method substantially outperforms the randomized block coordinate {\it descent} method with fixed or variable stepsizes.

math.OC↗

arXiv2015

Communication-Efficient Distributed Optimization of Self-Concordant Empirical Loss

We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to minimize the overall empirical loss, which is the average of the local empirical losses. The algorithm is based on an inexact damped Newton method, where the inexact Newton steps are computed by a distributed preconditioned conjugate gradient method. We analyze its iteration complexity and communication efficiency for minimizing self-concordant empirical loss functions, and discuss the results for distributed ridge regression, logistic regression and binary classification with a smoothed hinge loss. In a standard setting for supervised learning, the required number of communication rounds of the algorithm does not increase with the sample size, and only grows slowly with the number of machines.

math.OC↗

arXiv2014

An Accelerated Proximal Coordinate Gradient Method and its Application to Regularized Empirical Risk Minimization

We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an accelerated randomized proximal coordinate gradient (APCG) method for minimizing such convex composite functions. For strongly convex functions, our method achieves faster linear convergence rates than existing randomized proximal coordinate gradient methods. Without strong convexity, our method enjoys accelerated sublinear convergence rates. We show how to apply the APCG method to solve the regularized empirical risk minimization (ERM) problem, and devise efficient implementations that avoid full-dimensional vector operations. For ill-conditioned ERM problems, our method obtains improved convergence rates than the state-of-the-art stochastic dual coordinate ascent (SDCA) method.

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arXiv2014

A Proximal Stochastic Gradient Method with Progressive Variance Reduction

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole objective function is strongly convex. Such problems often arise in machine learning, known as regularized empirical risk minimization. We propose and analyze a new proximal stochastic gradient method, which uses a multi-stage scheme to progressively reduce the variance of the stochastic gradient. While each iteration of this algorithm has similar cost as the classical stochastic gradient method (or incremental gradient method), we show that the expected objective value converges to the optimum at a geometric rate. The overall complexity of this method is much lower than both the proximal full gradient method and the standard proximal stochastic gradient method.

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arXiv2013

Online Classification Using a Voted RDA Method

We propose a voted dual averaging method for online classification problems with explicit regularization. This method employs the update rule of the regularized dual averaging (RDA) method, but only on the subsequence of training examples where a classification error is made. We derive a bound on the number of mistakes made by this method on the training set, as well as its generalization error rate. We also introduce the concept of relative strength of regularization, and show how it affects the mistake bound and generalization performance. We experimented with the method using $\ell_1$ regularization on a large-scale natural language processing task, and obtained state-of-the-art classification performance with fairly sparse models.

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arXiv2013

On the Complexity Analysis of Randomized Block-Coordinate Descent Methods

In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [8,11] for minimizing the sum of a smooth convex function and a block-separable convex function. In particular, we extend Nesterov's technique developed in [8] for analyzing the RBCD method for minimizing a smooth convex function over a block-separable closed convex set to the aforementioned more general problem and obtain a sharper expected-value type of convergence rate than the one implied in [11]. Also, we obtain a better high-probability type of iteration complexity, which improves upon the one in [11] by at least the amount $O(n/ε)$, where $ε$ is the target solution accuracy and $n$ is the number of problem blocks. In addition, for unconstrained smooth convex minimization, we develop a new technique called {\it randomized estimate sequence} to analyze the accelerated RBCD method proposed by Nesterov [11] and establish a sharper expected-value type of convergence rate than the one given in [11].

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