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Lan Wu

Publications and source records attributed to Lan Wu.

At least 37 records · Page 2Linked to original sources
arXiv2024

Exploring Probabilistic Distance Fields in Robotics

The success of intelligent robotic missions relies on integrating various research tasks, each demanding distinct representations. Designing task-specific representations for each task is costly and impractical. Unified representations suitable for multiple tasks remain unexplored. My outline introduces a series of research outcomes of GP-based probabilistic distance field (GPDF) representation that mathematically models the fundamental property of Euclidean distance field (EDF) along with gradients, surface normals and dense reconstruction. The progress to date and ongoing future works show that GPDF has the potential to offer a unified solution of representation for multiple tasks such as localisation, mapping, motion planning, obstacle avoidance, grasping, human-robot collaboration, and dense visualisation. I believe that GPDF serves as the cornerstone for robots to accomplish more complex and challenging tasks. By leveraging GPDF, robots can navigate through intricate environments, understand spatial relationships, and interact with objects and humans seamlessly.

cs.RO↗
arXiv2023

Accurate Gaussian-Process-based Distance Fields with applications to Echolocation and Mapping

This paper introduces a novel method to estimate distance fields from noisy point clouds using Gaussian Process (GP) regression. Distance fields, or distance functions, gained popularity for applications like point cloud registration, odometry, SLAM, path planning, shape reconstruction, etc. A distance field provides a continuous representation of the scene defined as the shortest distance from any query point and the closest surface. The key concept of the proposed method is the transformation of a GP-inferred latent scalar field into an accurate distance field by using a reverting function related to the kernel inverse. The latent field can be interpreted as a smooth occupancy map. This paper provides the theoretical derivation of the proposed method as well as a novel uncertainty proxy for the distance estimates. The improved performance compared with existing distance fields is demonstrated with simulated experiments. The level of accuracy of the proposed approach enables novel applications that rely on precise distance estimation: this work presents echolocation and mapping frameworks for ultrasonic-guided wave sensing in metallic structures. These methods leverage the proposed distance field with a physics-based measurement model accounting for the propagation of the ultrasonic waves in the material. Real-world experiments are conducted to demonstrate the soundness of these frameworks.

cs.RO↗
arXiv2023

Large-Scale Traffic Data Imputation with Spatiotemporal Semantic Understanding

Large-scale data missing is a challenging problem in Intelligent Transportation Systems (ITS). Many studies have been carried out to impute large-scale traffic data by considering their spatiotemporal correlations at a network level. In existing traffic data imputations, however, rich semantic information of a road network has been largely ignored when capturing network-wide spatiotemporal correlations. This study proposes a Graph Transformer for Traffic Data Imputation (GT-TDI) model to impute large-scale traffic data with spatiotemporal semantic understanding of a road network. Specifically, the proposed model introduces semantic descriptions consisting of network-wide spatial and temporal information of traffic data to help the GT-TDI model capture spatiotemporal correlations at a network level. The proposed model takes incomplete data, the social connectivity of sensors, and semantic descriptions as input to perform imputation tasks with the help of Graph Neural Networks (GNN) and Transformer. On the PeMS freeway dataset, extensive experiments are conducted to compare the proposed GT-TDI model with conventional methods, tensor factorization methods, and deep learning-based methods. The results show that the proposed GT-TDI outperforms existing methods in complex missing patterns and diverse missing rates. The code of the GT-TDI model will be available at https://github.com/KP-Zhang/GT-TDI.

cs.LG↗
arXiv2021

Constructing long-short stock portfolio with a new listwise learn-to-rank algorithm

Factor strategies have gained growing popularity in industry with the fast development of machine learning. Usually, multi-factors are fed to an algorithm for some cross-sectional return predictions, which are further used to construct a long-short portfolio. Instead of predicting the value of the stock return, emerging studies predict a ranked stock list using the mature learn-to-rank technology. In this study, we propose a new listwise learn-to-rank loss function which aims to emphasize both the top and the bottom of a rank list. Our loss function, motivated by the long-short strategy, is endogenously shift-invariant and can be viewed as a direct generalization of ListMLE. Under different transformation functions, our loss can lead to consistency with binary classification loss or permutation level 0-1 loss. A probabilistic explanation for our model is also given as a generalized Plackett-Luce model. Based on a dataset of 68 factors in China A-share market from 2006 to 2019, our empirical study has demonstrated the strength of our method which achieves an out-of-sample annual return of 38% with the Sharpe ratio being 2.

q-fin.PM↗
arXiv2021

The Success of AdaBoost and Its Application in Portfolio Management

We develop a novel approach to explain why AdaBoost is a successful classifier. By introducing a measure of the influence of the noise points (ION) in the training data for the binary classification problem, we prove that there is a strong connection between the ION and the test error. We further identify that the ION of AdaBoost decreases as the iteration number or the complexity of the base learners increases. We confirm that it is impossible to obtain a consistent classifier without deep trees as the base learners of AdaBoost in some complicated situations. We apply AdaBoost in portfolio management via empirical studies in the Chinese market, which corroborates our theoretical propositions.

stat.ML↗
arXiv2021

Faithful Euclidean Distance Field from Log-Gaussian Process Implicit Surfaces

In this letter, we introduce the Log-Gaussian Process Implicit Surface (Log-GPIS), a novel continuous and probabilistic mapping representation suitable for surface reconstruction and local navigation. Our key contribution is the realisation that the regularised Eikonal equation can be simply solved by applying the logarithmic transformation to a GPIS formulation to recover the accurate Euclidean distance field (EDF) and, at the same time, the implicit surface. To derive the proposed representation, Varadhan's formula is exploited to approximate the non-linear Eikonal partial differential equation (PDE) of the EDF by the logarithm of a linear PDE. We show that members of the Matern covariance family directly satisfy this linear PDE. The proposed approach does not require post-processing steps to recover the EDF. Moreover, unlike sampling-based methods, Log-GPIS does not use sample points inside and outside the surface as the derivative of the covariance allow direct estimation of the surface normals and distance gradients. We benchmarked the proposed method on simulated and real data against state-of-the-art mapping frameworks that also aim at recovering both the surface and a distance field. Our experiments show that Log-GPIS produces the most accurate results for the EDF and comparable results for surface reconstruction and its computation time still allows online operations.

cs.RO↗
arXiv2021

Active and Interactive Mapping with Dynamic Gaussian Process Implicit Surfaces for Mobile Manipulators

In this letter, we present an interactive probabilistic mapping framework for a mobile manipulator picking objects from a pile. The aim is to map the scene, actively decide where to go next and which object to pick, make changes to the scene by picking the chosen object, and then map these changes alongside. The proposed framework uses a novel dynamic Gaussian Process (GP) Implicit Surface method to incrementally build and update the scene map that reflects environment changes. Actively the framework provides the next-best-view, balancing the need for picking object reachability with map information gain (IG). To enforce a priority of visiting boundary segments over unknown regions, the IG formulation includes an uncertainty gradient-based frontier score by exploiting the GP kernel derivative. This leads to an efficient strategy that addresses the often conflicting requirement of unknown environment exploration and object picking exploitation given a limited execution horizon. We demonstrate the effectiveness of our framework with software simulation and real-life experiments.

cs.RO↗
arXiv2020

A factor-adjusted multiple testing of general alternatives

Factor-adjusted multiple testing is used for handling strong correlated tests. Since most of previous works control the false discovery rate under sparse alternatives, we develop a two-step method, namely the AdaFAT, for any true false proportion. In this paper, the proposed procedure is adjusted by latent factor loadings. Under the existence of explanatory variables, a uniform convergence rate of the estimated factor loadings is given. We also show that the power of AdaFAT goes to one along with the controlled false discovery rate. The performance of the proposed procedure is examined through simulations calibrated by China A-share market.

math.ST↗
arXiv2020

Centralizing-Unitizing Standardized High-Dimensional Directional Statistics and Its Applications in Finance

Cross-sectional "Information Coefficient" (IC) is a widely and deeply accepted measure in portfolio management. The paper gives an insight into IC in view of high-dimensional directional statistics: IC is a linear operator on the components of a centralizing-unitizing standardized random vector of next-period cross-sectional returns. Our primary research first clearly defines IC with the high-dimensional directional statistics, discussing its first two moments. We derive the closed-form expressions of the directional statistics' covariance matrix and IC's variance in a homoscedastic condition. Also, we solve the optimization of IC's maximum expectation and minimum variance. Simulation intuitively characterizes the standardized directional statistics and IC's p.d.f.. The empirical analysis of the Chinese stock market uncovers interesting facts about the standardized vectors of cross-sectional returns and helps obtain the time series of the measure in the real market. The paper discovers a potential application of directional statistics in finance, proves explicit results of the projected normal distribution, and reveals IC's nature.

stat.AP↗
arXiv2017

Occupation times of refracted Levy processes with jumps having rational Laplace transforms

We investigate a refracted Levy process driven by a jump diffusion process, whose jumps have rational Laplace transforms. For such a stochastic process, formulas for the Laplace transform of its occupation times are deduced. To derive the main results, some modifications on our previous approach have been made. In addition, we obtain a very interesting identity, which is conjectured to hold for a general refracted Levy process.

math.PR↗
arXiv2016

Equity Market Impact Modeling: an Empirical Analysis for Chinese Market

Market impact has become a subject of increasing concern among academics and industry experts. We put forward a price impact model which considers the heteroscedasticity of price in the time dimension and dependency between permanent impact and temporary impact. We discuss and derive the extremum of the expectation of permanent impact and realized impact by constructing several special trading trajectories. Given our use of a large trade and quote tick records of 17,213,238,343 compiled from the Chinese stock market, the model assessment ultimately suggest that our model is better than Almgren's model. Interestingly, the result of random effect analysis indicates the parameter $α$, which is the exponent of the impact function, is a constant with a value of around 0.7 across all stocks. Our model and empirical result would give academia some insight of mechanism of Chinese market, and can be applied to algorithm trading.

q-fin.TR↗
arXiv2016

Alternative approach to derive q-potential measures of refracted spectrally Lévy processes

For a refracted Lévy process driven by a spectrally negative Lévy process, we use a different approach to derive expressions for its q-potential measures without killing. Unlike previous methods whose derivations depend on scale functions which are defined only for spectrally negative Lévy processes, our approach is free of scale functions. This makes it possible to extend the result here to a quite general refracted Lévy process by applying the approach presented below.

math.PR↗
arXiv2016

A note on refracted Lévy processes without positive jumps

For a refracted spectrally negative Levy process, we find some new and fantastic formulas for its q-potential measures without killing. Unlike previous results, which are written in terms of the known q-scale functions, our formulas are free of the q-scale functions. This makes our results become extremely important since it is likely that our formulas also hold for a general refracted Levy process.

math.PR↗
arXiv2016

Occupation times of general Lévy processes

For an arbitrary Lévy process $X$ which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of $X$ and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of $X$. It is believed that our results are important not only for the study of stochastic processes, but also for financial applications.

math.PR↗
arXiv2016

The distribution of refracted Lévy processes with jumps having rational Laplace transforms

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its distribution. Our formulas are presented in an attractive form and the approach is novel. In particular, the idea in the application of an approximating procedure is remarkable. Besides, the results are used to price Variable Annuities with state-dependent fees.

math.PR↗
arXiv2015

Pricing variable annuities with multi-layer expense strategy

We study the problem of pricing variable annuities with a multi-layer expense strategy, under which the insurer charges fees from the policyholder's account only when the account value lies in some pre-specified disjoint intervals, where on each pre-specified interval, the fee rate is fixed and can be different from that on other interval. We model the asset that is the underlying fund of the variable annuity by a hyper-exponential jump diffusion process. Theoretically, for a jump diffusion process with hyper-exponential jumps and three-valued drift, we obtain expressions for the Laplace transforms of its distribution and its occupation times, i.e., the time that it spends below or above a pre-specified level. With these results, we derive closed-form formulas to determine the fair fee rate. Moreover, the total fees that will be collected by the insurer and the total time of deducting fees are also computed. In addition, some numerical examples are presented to illustrate our results.

math.PR↗
arXiv2015

Double-jump stochastic volatility model for VIX: evidence from VVIX

The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the existence of co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. With VVIX index as a proxy for the stochastic volatility, we use MCMC method to estimate the dynamics of VIX. Comparing nested models on VIX, we show the jump in VIX and the volatility factor is statistically significant. The jump intensity is also statedependent. We analyze the impact of jump factor on the VIX dynamics.

q-fin.CP↗