Searcharxiv⌕ Search

arXiv subjects

Chao Li

Publications and source records attributed to Chao Li.

At least 559 records · Page 31Linked to original sources
arXiv2018

Model Trees for Identifying Exceptional Players in the NHL Draft

Drafting strong players is crucial for the team success. We describe a new data-driven interpretable approach for assessing draft prospects in the National Hockey League. Successful previous approaches have built a predictive model based on player features, or derived performance predictions from the observed performance of comparable players in a cohort. This paper develops model tree learning, which incorporates strengths of both model-based and cohort-based approaches. A model tree partitions the feature space according to the values of discrete features, or learned thresholds for continuous features. Each leaf node in the tree defines a group of players, easily described to hockey experts, with its own group regression model. Compared to a single model, the model tree forms an ensemble that increases predictive power. Compared to cohort-based approaches, the groups of comparables are discovered from the data, without requiring a similarity metric. The performance predictions of the model tree are competitive with the state-of-the-art methods, which validates our model empirically. We show in case studies that the model tree player ranking can be used to highlight strong and weak points of players.

cs.LG↗
arXiv2018

Combining Linear Non-Gaussian Acyclic Model with Logistic Regression Model for Estimating Causal Structure from Mixed Continuous and Discrete Data

Estimating causal models from observational data is a crucial task in data analysis. For continuous-valued data, Shimizu et al. have proposed a linear acyclic non-Gaussian model to understand the data generating process, and have shown that their model is identifiable when the number of data is sufficiently large. However, situations in which continuous and discrete variables coexist in the same problem are common in practice. Most existing causal discovery methods either ignore the discrete data and apply a continuous-valued algorithm or discretize all the continuous data and then apply a discrete Bayesian network approach. These methods possibly loss important information when we ignore discrete data or introduce the approximation error due to discretization. In this paper, we define a novel hybrid causal model which consists of both continuous and discrete variables. The model assumes: (1) the value of a continuous variable is a linear function of its parent variables plus a non-Gaussian noise, and (2) each discrete variable is a logistic variable whose distribution parameters depend on the values of its parent variables. In addition, we derive the BIC scoring function for model selection. The new discovery algorithm can learn causal structures from mixed continuous and discrete data without discretization. We empirically demonstrate the power of our method through thorough simulations.

cs.LG↗
arXiv2017

Congruences between Heegner points and quadratic twists of elliptic curves

We establish a congruence formula between $p$-adic logarithms of Heegner points for two elliptic curves with the same mod $p$ Galois representation. As a first application, we use the congruence formula when $p=2$ to explicitly construct many quadratic twists of analytic rank zero (resp. one) for a wide class of elliptic curves $E$. We show that the number of twists of $E$ up to twisting discriminant $X$ of analytic rank zero (resp. one) is $\gg X/\log^{5/6}X$, improving the current best general bound towards Goldfeld's conjecture due to Ono--Skinner (resp. Perelli--Pomykala). We also prove the 2-part of the Birch and Swinnerton-Dyer conjecture for many rank zero and rank one twists of $E$, which was only recently established for specific CM elliptic curves $E$.

math.NT↗
arXiv2017

Heegner points at Eisenstein primes and twists of elliptic curves

Given an elliptic curve $E$ over $\mathbb{Q}$, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (resp. 1). We show this conjecture holds whenever $E$ has a rational 3-isogeny. We also prove the analogous result for the sextic twists of $j$-invariant 0 curves (Mordell curves). To prove these results, we establish a general criterion for the non-triviality of the $p$-adic logarithm of Heegner points at an Eisenstein prime $p$, in terms of the relative $p$-class numbers of certain number fields and then apply this criterion to the special case $p=3$. As a by-product, we also prove the 3-part of the Birch and Swinnerton-Dyer conjecture for many elliptic curves of $j$-invariant 0.

math.NT↗
arXiv2017

Prime twists of elliptic curves

For certain elliptic curves $E/\mathbb{Q}$ with $E(\mathbb{Q})[2]=\mathbb{Z}/2 \mathbb{Z}$, we prove a criterion for prime twists of $E$ to have analytic rank 0 or 1, based on a mod 4 congruence of 2-adic logarithms of Heegner points. As an application, we prove new cases of Silverman's conjecture that there exists a positive proposition of prime twists of $E$ of rank zero (resp. positive rank).

math.NT↗
arXiv2017

Remarks on the arithmetic fundamental lemma

W. Zhang's arithmetic fundamental lemma (AFL) is a conjectural identity between the derivative of an orbital integral on a symmetric space with an arithmetic intersection number on a unitary Rapoport-Zink space. In the minuscule case, Rapoport-Terstiege-Zhang have verified the AFL conjecture via explicit evaluation of both sides of the identity. We present a simpler way for evaluating the arithmetic intersection number, thereby providing a new proof of the AFL conjecture in the minuscule case.

math.NT↗
arXiv2017

Cascade Region Proposal and Global Context for Deep Object Detection

Deep region-based object detector consists of a region proposal step and a deep object recognition step. In this paper, we make significant improvements on both of the two steps. For region proposal we propose a novel lightweight cascade structure which can effectively improve RPN proposal quality. For object recognition we re-implement global context modeling with a few modications and obtain a performance boost (4.2% mAP gain on the ILSVRC 2016 validation set). Besides, we apply the idea of pre-training extensively and show its importance in both steps. Together with common training and testing tricks, we improve Faster R-CNN baseline by a large margin. In particular, we obtain 87.9% mAP on the PASCAL VOC 2012 test set, 65.3% on the ILSVRC 2016 test set and 36.8% on the COCO test-std set.

cs.CV↗
arXiv2017

Index and topology of minimal hypersurfaces in R^n

In this paper, we consider immersed two-sided minimal hypersurfaces in $\mathbb{R}^n$ with finite total curvature. We prove that the sum of the Morse index and the nullity of the Jacobi operator is bounded from below by a linear function of the number of ends and the first Betti number of the hypersurface. When $n=4$, we are able to drop the nullity term by a careful study for the rigidity case. Our result is the first effective generalization of Li-Wang. Using our index estimates and ideas from the recent work of Chodosh-Ketover-Maximo, we prove compactness and finiteness results of minimal hypersurfaces in $\mathbb{R}^4$ with finite index.

math.DG↗
arXiv2017

Global regularity and fast small scale formation for Euler patch equation in a disk

It is well known that the Euler vortex patch in $\mathbb{R}^{2}$ will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solutions is less complete. We study here the Euler vortex patch in a disk. We prove global in time regularity by providing the upper bound of the growth of curvature of the patch boundary. For a special symmetric scenario, we construct an example of double exponential curvature growth, showing that such upper bound is qualitatively sharp.

math.AP↗
arXiv2017

Probing Growth-Induced Anisotropic Thermal Transport in CVD Diamond Membranes by Multi-frequency and Multi-spot-size Time-Domain Thermoreflectance

The maximum output power of GaN-based high-electron mobility transistors is limited by high channel temperature induced by localized self-heating which degrades device performance and reliability. With generated heat fluxes within these devices reaching magnitude close to ten times of that at the sun surface, chemical vapor deposition (CVD) diamond is an attractive candidate to aid in the extraction of this heat in order to keep the operating temperatures of these high power electronics as low as possible. Due to the observed inhomogeneous structure, CVD diamond membranes exhibit a 3D anisotropic thermal conductivity which may result in significantly different cooling performance from expected in a given application. In this work, time domain thermoreflectance (TDTR) is used to measure the thermal properties of an 11.8-μm CVD diamond membrane from its nucleation side. Starting with a spot size diameter larger than the thickness of the membrane, measurements are made at various modulation frequencies from 1.2 MHz to 11.6 MHz to tune the heat penetration depth, and subsequently the part of diamond sampled by TDTR. We divide the membrane into ten sublayers and assume isotropic thermal conductivity in each sublayer. From this, we observe a 2D gradient of the depth-dependent thermal conductivity for this membrane. By measuring the same region with a smaller spot size at multiple frequencies, the in-plane and cross-plane thermal conductivity are extracted respectively. Through this use of multiple spot sizes and modulation frequencies, the 3D anisotropic thermal conductivity of CVD diamond membrane is experimentally obtained by fitting the experimental data to a thermal model. This work provides insight toward an improved understanding of heat conduction inhomogeneity in CVD polycrystalline diamond membrane that is important for applications of thermal management of high power electronics.

cond-mat.mes-hall↗
arXiv2017

Deep Speaker: an End-to-End Neural Speaker Embedding System

We present Deep Speaker, a neural speaker embedding system that maps utterances to a hypersphere where speaker similarity is measured by cosine similarity. The embeddings generated by Deep Speaker can be used for many tasks, including speaker identification, verification, and clustering. We experiment with ResCNN and GRU architectures to extract the acoustic features, then mean pool to produce utterance-level speaker embeddings, and train using triplet loss based on cosine similarity. Experiments on three distinct datasets suggest that Deep Speaker outperforms a DNN-based i-vector baseline. For example, Deep Speaker reduces the verification equal error rate by 50% (relatively) and improves the identification accuracy by 60% (relatively) on a text-independent dataset. We also present results that suggest adapting from a model trained with Mandarin can improve accuracy for English speaker recognition.

cs.CL↗
arXiv2017

Skeleton-based Action Recognition with Convolutional Neural Networks

Current state-of-the-art approaches to skeleton-based action recognition are mostly based on recurrent neural networks (RNN). In this paper, we propose a novel convolutional neural networks (CNN) based framework for both action classification and detection. Raw skeleton coordinates as well as skeleton motion are fed directly into CNN for label prediction. A novel skeleton transformer module is designed to rearrange and select important skeleton joints automatically. With a simple 7-layer network, we obtain 89.3% accuracy on validation set of the NTU RGB+D dataset. For action detection in untrimmed videos, we develop a window proposal network to extract temporal segment proposals, which are further classified within the same network. On the recent PKU-MMD dataset, we achieve 93.7% mAP, surpassing the baseline by a large margin.

cs.CV↗
arXiv2017

Arithmetic intersection on GSpin Rapoport-Zink spaces

We prove an explicit formula for the arithmetic intersection number of diagonal cycles on GSpin Rapoport-Zink spaces in the minuscule case. This is a local problem arising from the arithmetic Gan-Gross-Prasad conjecture for orthogonal Shimura varieties. Our formula can be viewed as an orthogonal counterpart of the arithmetic-geometric side of the arithmetic fundamental lemma proved by Rapoport-Terstiege-Zhang in the minuscule case.

math.NT↗
arXiv2016

Optimizing Memory Efficiency for Deep Convolutional Neural Networks on GPUs

Leveraging large data sets, deep Convolutional Neural Networks (CNNs) achieve state-of-the-art recognition accuracy. Due to the substantial compute and memory operations, however, they require significant execution time. The massive parallel computing capability of GPUs make them as one of the ideal platforms to accelerate CNNs and a number of GPU-based CNN libraries have been developed. While existing works mainly focus on the computational efficiency of CNNs, the memory efficiency of CNNs have been largely overlooked. Yet CNNs have intricate data structures and their memory behavior can have significant impact on the performance. In this work, we study the memory efficiency of various CNN layers and reveal the performance implication from both data layouts and memory access patterns. Experiments show the universal effect of our proposed optimizations on both single layers and various networks, with up to 27.9x for a single layer and up to 5.6x on the whole networks.

cs.DC↗
arXiv2016

Measuring Economic Activities of China with Mobile Big Data

Emerging trends in smartphones, online maps, social media, and the resulting geo-located data, provide opportunities to collect traces of people's socio-economical activities in a much more granular and direct fashion, triggering a revolution in empirical research. These vast mobile data offer new perspectives and approaches for measurements of economic dynamics and are broadening the research fields of social science and economics. In this paper, we explore the potential of using mobile big data for measuring economic activities of China. Firstly, We build indices for gauging employment and consumer trends based on billions of geo-positioning data. Secondly, we advance the estimation of store offline foot traffic via location search data derived from Baidu Maps, which is then applied to predict revenues of Apple in China and detect box-office fraud accurately. Thirdly, we construct consumption indicators to track the trends of various industries in service sector, which are verified by several existing indicators. To the best of our knowledge, we are the first to measure the second largest economy by mining such unprecedentedly large scale and fine granular spatial-temporal data. Our research provides new approaches and insights on measuring economic activities.

cs.SI↗
arXiv2016

Silicon Photonics WDM Transceiver with SOA and Semiconductor Mode-Locked Laser

We demonstrate a complete Silicon Photonics WDM link relying on a single section semiconductor mode-locked laser and a single SOA to support up to 12 multiplexed channels with a bit error rate of 1e-12 at serial data rates of 14 Gbps without channel pre-emphasis, equalization or forward error correction. Individual channels reach error free operation at 25 Gbps and multi-channel operation at 25 Gbps is shown to be compatible with standard 7% overhead hard decision forward error correction. Silicon Photonics transmitter and receiver chips are hybridly integrated with driver and receiver electronics. A detailed link model is derived and verified. Particular emphasis is placed on accurate system level modeling of laser RIN, SOA amplified spontaneous emission noise and receiver noise. The impact of the electrical receiver bandwidth and non-Gaussian statistics on level dependent amplified spontaneous emission noise are investigated in detail. The channel count scalability as limited by SOA saturation is further analyzed taking cross gain modulation and four wave mixing into account. While semiconductor mode-locked lasers have been identified as a potential light source for low cost Datacom WDM transceivers for some time, this is, to the best of our knowledge, the first comprehensive investigation of the overall link budget in a Silicon Photonics implementation showing this technology to be a credible contender for low latency datacenter interconnects.

physics.optics↗