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Li Xu

Publications and source records attributed to Li Xu.

At least 91 records · Page 5Linked to original sources
arXiv2021

Modelling Universal Order Book Dynamics in Bitcoin Market

Understanding the emergence of universal features such as the stylized facts in markets is a long-standing challenge that has drawn much attention from economists and physicists. Most existing models, such as stochastic volatility models, focus mainly on price changes, neglecting the complex trading dynamics. Recently, there are increasing studies on order books, thanks to the availability of large-scale trading datasets, aiming to understand the underlying mechanisms governing the market dynamics. In this paper, we collect order-book datasets of Bitcoin platforms across three countries over millions of users and billions of daily turnovers. We find a 1+1D field theory, govern by a set of KPZ-like stochastic equations, predicts precisely the order book dynamics observed in empirical data. Despite the microscopic difference of markets, we argue the proposed effective field theory captures the correct universality class of market dynamics. We also show that the model agrees with the existing stochastic volatility models at the long-wavelength limit.

q-fin.TR↗
arXiv2021

Sequential Design of Computer Experiments with Quantitative and Qualitative Factors in Applications to HPC Performance Optimization

Computer experiments with both qualitative and quantitative factors are widely used in many applications. Motivated by the emerging need of optimal configuration in the high-performance computing (HPC) system, this work proposes a sequential design, denoted as adaptive composite exploitation and exploration (CEE), for optimization of computer experiments with qualitative and quantitative factors. The proposed adaptive CEE method combines the predictive mean and standard deviation based on the additive Gaussian process to achieve a meaningful balance between exploitation and exploration for optimization. Moreover, the adaptiveness of the proposed sequential procedure allows the selection of next design point from the adaptive design region. Theoretical justification of the adaptive design region is provided. The performance of the proposed method is evaluated by several numerical examples in simulations. The case study of HPC performance optimization further elaborates the merits of the proposed method.

cs.DC↗
arXiv2020

Prediction of High-Performance Computing Input/Output Variability and Its Application to Optimization for System Configurations

Performance variability is an important measure for a reliable high performance computing (HPC) system. Performance variability is affected by complicated interactions between numerous factors, such as CPU frequency, the number of input/output (IO) threads, and the IO scheduler. In this paper, we focus on HPC IO variability. The prediction of HPC variability is a challenging problem in the engineering of HPC systems and there is little statistical work on this problem to date. Although there are many methods available in the computer experiment literature, the applicability of existing methods to HPC performance variability needs investigation, especially, when the objective is to predict performance variability both in interpolation and extrapolation settings. A data analytic framework is developed to model data collected from large-scale experiments. Various promising methods are used to build predictive models for the variability of HPC systems. We evaluate the performance of the methods by measuring prediction accuracy at previously unseen system configurations. We also discuss a methodology for optimizing system configurations that uses the estimated variability map. The findings from method comparisons and developed tool sets in this paper yield new insights into existing statistical methods and can be beneficial for the practice of HPC variability management. This paper has supplementary materials online.

cs.DC↗
arXiv2020

Long time existence for a two-dimensional strongly dispersive Boussinesq system

We prove a long time existence result for the solutions of a two-dimensional Boussinesq system modeling the propagation of long, weakly nonlinear water waves. This system is exceptional in the sense that it is the only linearly well-posed system in the (abcd) family of Boussinesq systems whose eigenvalues of the linearized system have nontrivial zeroes. This new difficulty is solved by the use of "good unknowns " and of normal form techniques.

math.AP↗
arXiv2020

Construction of isodual codes from polycirculant matrices

Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can only occur over $ \F_2$ in the double circulant case. Building on an explicit infinite sequence of irreducible trinomials over $\F_2,$ we show that binary double polycirculant codes are asymptotically good.

cs.CR↗
arXiv2019

Long time existence for the Boussinesq -- Full Dispersion systems

We establish the long time existence of solutions for the "Boussinesq-Full Dispersion" systems modeling the propagation of internal waves in a two-layer system. For the two-dimensional Hamiltonian case we prove the global existence of small solutions of the corresponding systems.

math.AP↗
arXiv2019

Long time existence for a strongly dispersive Boussinesq system

This paper is concerned with the one-dimensional version of a specific member of the (abcd) family of Boussinesq systems having the higher possible dispersion. We will establish two different long time existence results for the solutions of the Cauchy problem. The proofs involve normal form transformations suitably modified away from the zero set of the phases.

math.AP↗
arXiv2019

Learning to Benchmark: Determining Best Achievable Misclassification Error from Training Data

We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previous work on learning bounds on Bayes misclassification rate since it learns the {\it exact} Bayes error rate instead of a bound on error rate. We propose a benchmark learner based on an ensemble of $ε$-ball estimators and Chebyshev approximation. Under a smoothness assumption on the class densities we show that our estimator achieves an optimal (parametric) mean squared error (MSE) rate of $O(N^{-1})$, where $N$ is the number of samples. Experiments on both simulated and real datasets establish that our proposed benchmark learning algorithm produces estimates of the Bayes error that are more accurate than previous approaches for learning bounds on Bayes error probability.

stat.ML↗
arXiv2019

Effective Domain Knowledge Transfer with Soft Fine-tuning

Convolutional neural networks require numerous data for training. Considering the difficulties in data collection and labeling in some specific tasks, existing approaches generally use models pre-trained on a large source domain (e.g. ImageNet), and then fine-tune them on these tasks. However, the datasets from source domain are simply discarded in the fine-tuning process. We argue that the source datasets could be better utilized and benefit fine-tuning. This paper firstly introduces the concept of general discrimination to describe ability of a network to distinguish untrained patterns, and then experimentally demonstrates that general discrimination could potentially enhance the total discrimination ability on target domain. Furthermore, we propose a novel and light-weighted method, namely soft fine-tuning. Unlike traditional fine-tuning which directly replaces optimization objective by a loss function on the target domain, soft fine-tuning effectively keeps general discrimination by holding the previous loss and removes it softly. By doing so, soft fine-tuning improves the robustness of the network to data bias, and meanwhile accelerates the convergence. We evaluate our approach on several visual recognition tasks. Extensive experimental results support that soft fine-tuning provides consistent improvement on all evaluated tasks, and outperforms the state-of-the-art significantly. Codes will be made available to the public.

cs.CV↗
arXiv2019

Dilated FCN: Listening Longer to Hear Better

Deep neural network solutions have emerged as a new and powerful paradigm for speech enhancement (SE). The capabilities to capture long context and extract multi-scale patterns are crucial to design effective SE networks. Such capabilities, however, are often in conflict with the goal of maintaining compact networks to ensure good system generalization. In this paper, we explore dilation operations and apply them to fully convolutional networks (FCNs) to address this issue. Dilations equip the networks with greatly expanded receptive fields, without increasing the number of parameters. Different strategies to fuse multi-scale dilations, as well as to install the dilation modules are explored in this work. Using Noisy VCTK and AzBio sentences datasets, we demonstrate that the proposed dilation models significantly improve over the baseline FCN and outperform the state-of-the-art SE solutions.

cs.SD↗
arXiv2019

On the number of resolvable Steiner triple systems of small 3-rank

In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order $v$, where $v=3^k$, and $3$-rank $v-k$. We develop an approach to generalize this bound and estimate the number of isomorphism classes of STS$(v)$ of rank $v-k-1$ for an arbitrary $v$ of form $3^kT$.

math.CO↗
arXiv2019

Regularity and projective dimension of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs

In this paper we provide some precise formulas for regularity of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs. For the projective dimension of such an edge ideal, we give its exact formula. Meanwhile, we also give the upper and lower bounds of projective dimension of higher power of such edge ideals. Some examples show that these formulas are related to direction selection.

math.AC↗
arXiv2019

Multi-Antenna Channel Interpolation via Tucker Decomposed Extreme Learning Machine

Channel interpolation is an essential technique for providing high-accuracy estimation of the channel state information (CSI) for wireless systems design where the frequency-space structural correlations of multi-antenna channel are typically hidden in matrix or tensor forms. In this letter, a modified extreme learning machine (ELM) that can process tensorial data, or ELM model with tensorial inputs (TELM), is proposed to handle the channel interpolation task. The TELM inherits many good properties from ELMs. Based on the TELM, the Tucker decomposed extreme learning machine (TDELM) is proposed for further improving the performance. Furthermore, we establish a theoretical argument to measure the interpolation capability of the proposed learning machines. Experimental results verify that our proposed learning machines can achieve comparable mean squared error (MSE) performance against the traditional ELMs but with 15% shorter running time, and outperform the other methods for a 20% margin measured in MSE for channel interpolation.

eess.SP↗
arXiv2019

Regularity of powers of edge ideals of vertex-weighted oriented unicyclic graphs

In this paper we provide some exact formulas for the regularity of powers of edge ideals of vertex-weighted oriented cycles and vertex-weighted unicyclic graphs. These formulas are functions of the weight of vertices and the number of edges. We also give some examples to show that these formulas are related to direction selection and the weight of vertices.

math.AC↗
arXiv2019

Projective dimension and regularity of powers of edge ideals of vertex-weighted rooted forests

In this paper we provide some exact formulas for projective dimension and the regularity of powers of edge ideals of vertex-weighted rooted forests. These formulas are functions of the weight of the vertices and the number of edges. We also give some examples to show that these formulas are related to direction selection and the assumptions about "rooted" forest such that $w(x)\geq 2$ if $d(x)\neq 1$ cannot be dropped.

math.AC↗
arXiv2018

Spatial Variable Selection and An Application to Virginia Lyme Disease Emergence

Lyme disease is an infectious disease that is caused by a bacterium called Borrelia burgdorferi sensu stricto. In the United States, Lyme disease is one of the most common infectious diseases. The major endemic areas of the disease are New England, Mid-Atlantic, East-North Central, South Atlantic, and West North-Central. Virginia is on the front-line of the disease's diffusion from the northeast to the south. One of the research objectives for the infectious disease community is to identify environmental and economic variables that are associated with the emergence of Lyme disease. In this paper, we use a spatial Poisson regression model to link the spatial disease counts and environmental and economic variables, and develop a spatial variable selection procedure to effectively identify important factors by using an adaptive elastic net penalty. The proposed methods can automatically select important covariates, while adjusting for possible spatial correlations of disease counts. The performance of the proposed method is studied and compared with existing methods via a comprehensive simulation study. We apply the developed variable selection methods to the Virginia Lyme disease data and identify important variables that are new to the literature. Supplementary materials for this paper are available online.

stat.AP↗
arXiv2018

Applications of the Fractional-Random-Weight Bootstrap

The bootstrap, based on resampling, has, for several decades, been a widely used method for computing confidence intervals for applications where no exact method is available and when sample sizes are not large enough to be able to rely on easy-to-compute large-sample approximate methods, such a Wald (normal-approximation) confidence intervals. Simulation based bootstrap intervals have been proven useful in that their actual coverage probabilities are close to the nominal confidence level in small samples. Small samples analytical approximations such as the Wald method, however, tend to have coverage probabilities that greatly exceed the nominal confidence level. There are, however, many applications where the resampling bootstrap method cannot be used. These include situations where the data are heavily censored, logistic regression when the success response is a rare event or where there is insufficient mixing of successes and failures across the explanatory variable(s), and designed experiments where the number of parameters is close to the number of observations. The thing that these three situations have in common is that there may be a substantial proportion of the resamples where is not possible to estimate all of the parameters in the model. This paper reviews the fractional-random-weight bootstrap method and demonstrates how it can be used to avoid these problems and construct confidence intervals. For the examples, it is seen that the fractional-random-weight bootstrap method is easy to use and has advantages over the resampling method in many challenging applications.

stat.AP↗