arXiv subjects

Hao Ni

Publications and source records attributed to Hao Ni.

At least 55 records · Page 3Linked to original sources

arXiv2021

Forex Trading Volatility Prediction using Neural Network Models

In this paper, we investigate the problem of predicting the future volatility of Forex currency pairs using the deep learning techniques. We show step-by-step how to construct the deep-learning network by the guidance of the empirical patterns of the intra-day volatility. The numerical results show that the multiscale Long Short-Term Memory (LSTM) model with the input of multi-currency pairs consistently achieves the state-of-the-art accuracy compared with both the conventional baselines, i.e. autoregressive and GARCH model, and the other deep learning models.

q-fin.ST↗

arXiv2021

Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition

This paper contributes to the challenge of skeleton-based human action recognition in videos. The key step is to develop a generic network architecture to extract discriminative features for the spatio-temporal skeleton data. In this paper, we propose a novel module, namely Logsig-RNN, which is the combination of the log-signature layer and recurrent type neural networks (RNNs). The former one comes from the mathematically principled technology of signatures and log-signatures as representations for streamed data, which can manage high sample rate streams, non-uniform sampling and time series of variable length. It serves as an enhancement of the recurrent layer, which can be conveniently plugged into neural networks. Besides we propose two path transformation layers to significantly reduce path dimension while retaining the essential information fed into the Logsig-RNN module. Finally, numerical results demonstrate that replacing the RNN module by the Logsig-RNN module in SOTA networks consistently improves the performance on both Chalearn gesture data and NTU RGB+D 120 action data in terms of accuracy and robustness. In particular, we achieve the state-of-the-art accuracy on Chalearn2013 gesture data by combining simple path transformation layers with the Logsig-RNN. Codes are available at https://github.com/steveliao93/GCN_LogsigRNN.

cs.CV↗

arXiv2021

Sig-Wasserstein GANs for Time Series Generation

Synthetic data is an emerging technology that can significantly accelerate the development and deployment of AI machine learning pipelines. In this work, we develop high-fidelity time-series generators, the SigWGAN, by combining continuous-time stochastic models with the newly proposed signature $W_1$ metric. The former are the Logsig-RNN models based on the stochastic differential equations, whereas the latter originates from the universal and principled mathematical features to characterize the measure induced by time series. SigWGAN allows turning computationally challenging GAN min-max problem into supervised learning while generating high fidelity samples. We validate the proposed model on both synthetic data generated by popular quantitative risk models and empirical financial data. Codes are available at https://github.com/SigCGANs/Sig-Wasserstein-GANs.git.

cs.LG↗

arXiv2021

Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN

Due to the curse of dimensionality, solving high dimensional parabolic partial differential equations (PDEs) has been a challenging problem for decades. Recently, a weak adversarial network (WAN) proposed in (Y.Zang et al., 2020) offered a flexible and computationally efficient approach to tackle this problem defined on arbitrary domains by leveraging the weak solution. WAN reformulates the PDE problem as a generative adversarial network, where the weak solution (primal network) and the test function (adversarial network) are parameterized by the multi-layer deep neural networks (DNNs). However, it is not yet clear whether DNNs are the most effective model for the parabolic PDE solutions as they do not take into account the fundamentally different roles played by time and spatial variables in the solution. To reinforce the difference, we design a novel so-called XNODE model for the primal network, which is built on the neural ODE (NODE) model with additional spatial dependency to incorporate the a priori information of the PDEs and serve as a universal and effective approximation to the solution. The proposed hybrid method (XNODE-WAN), by integrating the XNODE model within the WAN framework, leads to significant improvement in the performance and efficiency of training. Numerical results show that our method can reduce the training time to a fraction of that of the WAN model.

math.NA↗

arXiv2021

Expected signature of stopped Brownian motion on $d$-dimensional $C^{2, α}$-domains has finite radius of convergence everywhere: $2\leq d \leq 8$

A fundamental question in rough path theory is whether the expected signature of a geometric rough path completely determines the law of signature. One sufficient condition is that the expected signature has infinite radius of convergence, which is satisfied by various stochastic processes on a fixed time interval, including the Brownian motion. In contrast, for the Brownian motion stopped upon the first exit time from a bounded domain $Ω$, it is only known that the radius of convergence for the expected signature on sufficiently regular $Ω$ is strictly positive everywhere, and that the radius of convergence is finite at some point when $Ω$ is the $2$-dimensional unit disc ([1]). In this paper, we prove that on any bounded $C^{2,α}$-domain $Ω\subset \mathbb{R}^d$ with $2\leq d \leq 8$, the expected signature of the stopped Brownian motion has finite radius of convergence everywhere. A key ingredient of our proof is the introduction of a "domain-averaging hyperbolic development" (see Definition 4.1), which allows us to symmetrize the PDE system for the hyperbolic development of expected signature by averaging over rotated domains.

math.PR↗

arXiv2020

An efficient representation of chronological events in medical texts

In this work we addressed the problem of capturing sequential information contained in longitudinal electronic health records (EHRs). Clinical notes, which is a particular type of EHR data, are a rich source of information and practitioners often develop clever solutions how to maximise the sequential information contained in free-texts. We proposed a systematic methodology for learning from chronological events available in clinical notes. The proposed methodological {\it path signature} framework creates a non-parametric hierarchical representation of sequential events of any type and can be used as features for downstream statistical learning tasks. The methodology was developed and externally validated using the largest in the UK secondary care mental health EHR data on a specific task of predicting survival risk of patients diagnosed with Alzheimer's disease. The signature-based model was compared to a common survival random forest model. Our results showed a 15.4$\%$ increase of risk prediction AUC at the time point of 20 months after the first admission to a specialist memory clinic and the signature method outperformed the baseline mixed-effects model by 13.2 $\%$.

cs.CL↗

arXiv2020

Signature features with the visibility transformation

In this paper we put the visibility transformation on a clear theoretical footing and show that this transform is able to embed the effect of the absolute position of the data stream into signature features in a unified and efficient way. The generated feature set is particularly useful in pattern recognition tasks, for its simplifying role in allowing the signature feature set to accommodate nonlinear functions of absolute and relative values.

cs.LG↗

arXiv2020

The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence

The expected signature is an analogue of the Laplace transform for rough paths. Chevyrev and Lyons showed that, under certain moment conditions, the expected signature determines the laws of signatures. Lyons and Ni posed the question of whether the expected signature of Brownian motion up to the exit time of a domain satisfies Chevyrev and Lyons' moment condition. We provide the first example where the answer is negative.

math.PR↗

arXiv2020

Simultaneous Left Atrium Anatomy and Scar Segmentations via Deep Learning in Multiview Information with Attention

Three-dimensional late gadolinium enhanced (LGE) cardiac MR (CMR) of left atrial scar in patients with atrial fibrillation (AF) has recently emerged as a promising technique to stratify patients, to guide ablation therapy and to predict treatment success. This requires a segmentation of the high intensity scar tissue and also a segmentation of the left atrium (LA) anatomy, the latter usually being derived from a separate bright-blood acquisition. Performing both segmentations automatically from a single 3D LGE CMR acquisition would eliminate the need for an additional acquisition and avoid subsequent registration issues. In this paper, we propose a joint segmentation method based on multiview two-task (MVTT) recursive attention model working directly on 3D LGE CMR images to segment the LA (and proximal pulmonary veins) and to delineate the scar on the same dataset. Using our MVTT recursive attention model, both the LA anatomy and scar can be segmented accurately (mean Dice score of 93% for the LA anatomy and 87% for the scar segmentations) and efficiently (~0.27 seconds to simultaneously segment the LA anatomy and scars directly from the 3D LGE CMR dataset with 60-68 2D slices). Compared to conventional unsupervised learning and other state-of-the-art deep learning based methods, the proposed MVTT model achieved excellent results, leading to an automatic generation of a patient-specific anatomical model combined with scar segmentation for patients in AF.

eess.IV↗

arXiv2019

Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition

Landmark-based human action recognition in videos is a challenging task in computer vision. One key step is to design a generic approach that generates discriminative features for the spatial structure and temporal dynamics. To this end, we regard the evolving landmark data as a high-dimensional path and apply non-linear path signature techniques to provide an expressive, robust, non-linear, and interpretable representation for the sequential events. We do not extract signature features from the raw path, rather we propose path disintegrations and path transformations as preprocessing steps. Path disintegrations turn a high-dimensional path linearly into a collection of lower-dimensional paths; some of these paths are in pose space while others are defined over a multiscale collection of temporal intervals. Path transformations decorate the paths with additional coordinates in standard ways to allow the truncated signatures of transformed paths to expose additional features. For spatial representation, we apply the signature transform to vectorize the paths that arise out of pose disintegration, and for temporal representation, we apply it again to describe this evolving vectorization. Finally, all the features are collected together to constitute the input vector of a linear single-hidden-layer fully-connected network for classification. Experimental results on four datasets demonstrated that the proposed feature set with only a linear shallow network and Dropconnect is effective and achieves comparable state-of-the-art results to the advanced deep networks, and meanwhile, is capable of interpretation.

cs.CV↗

arXiv2019

Learning stochastic differential equations using RNN with log signature features

This paper contributes to the challenge of learning a function on streamed multimodal data through evaluation. The core of the result of our paper is the combination of two quite different approaches to this problem. One comes from the mathematically principled technology of signatures and log-signatures as representations for streamed data, while the other draws on the techniques of recurrent neural networks (RNN). The ability of the former to manage high sample rate streams and the latter to manage large scale nonlinear interactions allows hybrid algorithms that are easy to code, quicker to train, and of lower complexity for a given accuracy. We illustrate the approach by approximating the unknown functional as a controlled differential equation. Linear functionals on solutions of controlled differential equations are the natural universal class of functions on data streams. Following this approach, we propose a hybrid Logsig-RNN algorithm that learns functionals on streamed data. By testing on various datasets, i.e. synthetic data, NTU RGB+D 120 skeletal action data, and Chalearn2013 gesture data, our algorithm achieves the outstanding accuracy with superior efficiency and robustness.

cs.LG↗

arXiv2019

$ε$-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations

Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_ε^H $ such that $$\sup_{t\in [0,1]}|B^H(t)-\hat B_ε^H(t)| \le ε$$ with probability one for any user specified error parameter $ε>0$. When $H>1/2$, we further enhance our error guarantee to the $α$-Hölder norm for any $α\in (1/2,H)$. This enables us to extend our algorithm to the simulation of fBM driven stochastic differential equations $Y=\{Y(t):t \in[0,1]\}$. Under mild regularity conditions on the drift and diffusion coefficients of $Y$, we construct a probability space supporting both $Y$ and a fully simulatable process $\hat Y_ε$ such that $$\sup_{t\in [0,1]}|Y(t)-\hat Y_ε^H(t)| \le ε$$ with probability one. Our algorithms enjoy the tolerance-enforcement feature, i.e., the error bounds can be updated sequentially. Thus, the algorithms can be readily combined with other simulation techniques like multilevel Monte Carlo to estimate expectation of functionals of fBMs efficiently.

math.PR↗

arXiv2018

Multiview Two-Task Recursive Attention Model for Left Atrium and Atrial Scars Segmentation

Late Gadolinium Enhanced Cardiac MRI (LGE-CMRI) for detecting atrial scars in atrial fibrillation (AF) patients has recently emerged as a promising technique to stratify patients, guide ablation therapy and predict treatment success. Visualisation and quantification of scar tissues require a segmentation of both the left atrium (LA) and the high intensity scar regions from LGE-CMRI images. These two segmentation tasks are challenging due to the cancelling of healthy tissue signal, low signal-to-noise ratio and often limited image quality in these patients. Most approaches require manual supervision and/or a second bright-blood MRI acquisition for anatomical segmentation. Segmenting both the LA anatomy and the scar tissues automatically from a single LGE-CMRI acquisition is highly in demand. In this study, we proposed a novel fully automated multiview two-task (MVTT) recursive attention model working directly on LGE-CMRI images that combines a sequential learning and a dilated residual learning to segment the LA (including attached pulmonary veins) and delineate the atrial scars simultaneously via an innovative attention model. Compared to other state-of-the-art methods, the proposed MVTT achieves compelling improvement, enabling to generate a patient-specific anatomical and atrial scar assessment model.

cs.CV↗

arXiv2017

Learning Spatial-Semantic Context with Fully Convolutional Recurrent Network for Online Handwritten Chinese Text Recognition

Online handwritten Chinese text recognition (OHCTR) is a challenging problem as it involves a large-scale character set, ambiguous segmentation, and variable-length input sequences. In this paper, we exploit the outstanding capability of path signature to translate online pen-tip trajectories into informative signature feature maps using a sliding window-based method, successfully capturing the analytic and geometric properties of pen strokes with strong local invariance and robustness. A multi-spatial-context fully convolutional recurrent network (MCFCRN) is proposed to exploit the multiple spatial contexts from the signature feature maps and generate a prediction sequence while completely avoiding the difficult segmentation problem. Furthermore, an implicit language model is developed to make predictions based on semantic context within a predicting feature sequence, providing a new perspective for incorporating lexicon constraints and prior knowledge about a certain language in the recognition procedure. Experiments on two standard benchmarks, Dataset-CASIA and Dataset-ICDAR, yielded outstanding results, with correct rates of 97.10% and 97.15%, respectively, which are significantly better than the best result reported thus far in the literature.

cs.CV↗

arXiv2016

Signature inversion for monotone paths

The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the signature. We show that these weights on lattice paths satisfy the large deviations principle. In particular, this implies that the probability of picking up a "wrong" path is exponentially small in N. The argument relies on a probabilistic interpretation of the signature for monotone paths.

math.PR↗

arXiv2016

Cascading Bandits for Large-Scale Recommendation Problems

Most recommender systems recommend a list of items. The user examines the list, from the first item to the last, and often chooses the first attractive item and does not examine the rest. This type of user behavior can be modeled by the cascade model. In this work, we study cascading bandits, an online learning variant of the cascade model where the goal is to recommend $K$ most attractive items from a large set of $L$ candidate items. We propose two algorithms for solving this problem, which are based on the idea of linear generalization. The key idea in our solutions is that we learn a predictor of the attraction probabilities of items from their features, as opposing to learning the attraction probability of each item independently as in the existing work. This results in practical learning algorithms whose regret does not depend on the number of items $L$. We bound the regret of one algorithm and comprehensively evaluate the other on a range of recommendation problems. The algorithm performs well and outperforms all baselines.

cs.LG↗

arXiv2016

Learning from the past, predicting the statistics for the future, learning an evolving system

We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a stream. A certain graded feature set of a stream, known in the rough path literature as the signature, has a universality that allows formally, linear regression to be used to characterise the functional relationship between independent explanatory variables and the conditional distribution of the dependent response. This approach, via linear regression on the signature of the stream, is almost totally general, and yet it still allows explicit computation. The grading allows truncation of the feature set and so leads to an efficient local description for streams (rough paths). In the statistical context this method offers potentially significant, even transformational dimension reduction. By way of illustration, our approach is applied to stationary time series including the familiar AR model and ARCH model. In the numerical examples we examined, our predictions achieve similar accuracy to the Gaussian Process (GP) approach with much lower computational cost especially when the sample size is large.

q-fin.ST↗

arXiv2015

Expected signature of Brownian motion up to the first exit time from a bounded domain

The signature of a path provides a top down description of the path in terms of its effects as a control [Differential Equations Driven by Rough Paths (2007) Springer]. The signature transforms a path into a group-like element in the tensor algebra and is an essential object in rough path theory. The expected signature of a stochastic process plays a similar role to that played by the characteristic function of a random variable. In [Chevyrev (2013)], it is proved that under certain boundedness conditions, the expected value of a random signature already determines the law of this random signature. It becomes of great interest to be able to compute examples of expected signatures and obtain the upper bounds for the decay rates of expected signatures. For instance, the computation for Brownian motion on $[0,1]$ leads to the ``cubature on Wiener space'' methodology [Lyons and Victoir, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004) 169-198]. In this paper we fix a bounded domain $Γ$ in a Euclidean space $E$ and study the expected signature of a Brownian path starting at $z\inΓ$ and stopped at the first exit time from $Γ$. We denote this tensor series valued function by $Φ_Γ(z)$ and focus on the case $E=\mathbb{R}^d$. We show that $Φ_Γ(z)$ satisfies an elliptic PDE system and a boundary condition. The equations determining $Φ_Γ$ can be recursively solved; by an iterative application of Sobolev estimates we are able, under certain smoothness and boundedness condition of the domain $Γ$, to prove geometric bounds for the terms in $Φ_Γ(z)$. However, there is still a gap and we have not shown that $Φ_Γ(z)$ determines the law of the signature of this stopped Brownian motion even if $Γ$ is a unit ball.

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