arXiv subjects

Richard Y. Chen

Publications and source records attributed to Richard Y. Chen.

13 recordsLinked to original sources

arXiv2024

"Sound and Fury": Nonlinear Functionals of Volatility Matrix in the Presence of Jump and Noise

This paper resolves a pivotal open problem on nonparametric inference for nonlinear functionals of volatility matrix. Multiple prominent statistical tasks can be formulated as functionals of volatility matrix, yet a unified statistical theory of general nonlinear functionals based on noisy data remains challenging and elusive. Nonetheless, this paper shows it can be achieved by combining the strengths of pre-averaging, jump truncation and nonlinearity bias correction. In light of general nonlinearity, bias correction beyond linear approximation becomes necessary. Resultant estimators are nonparametric and robust over a wide spectrum of stochastic models. Moreover, the estimators can be rate-optimal and stable central limit theorems are obtained. The proposed framework lends itself conveniently to uncertainty quantification and permits fully feasible inference. With strong theoretical guarantees, this paper provides an inferential foundation for a wealth of statistical methods for noisy high-frequency data, such as realized principal component analysis, continuous-time linear regression, realized Laplace transform, generalized method of integrated moments and specification tests, hence extends current application scopes to noisy data which is more prevalent in practice.

stat.ME↗

arXiv2019

Inference for Volatility Functionals of Multivariate Itô Semimartingales Observed with Jump and Noise

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate Itô semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correction. Estimators based on this framework achieve the optimal convergence rate. A class of stable central limit theorems are attained with estimable asymptotic covariance matrices. This paper form a basis for infill asymptotic results of, for example, the realized Laplace transform, the realized principal component analysis, the continuous-time linear regression, and the generalized method of integrated moments, hence helps to extend the application scopes to more frequently sampled noisy data.

math.ST↗

arXiv2019

The Fourier Transform Method for Volatility Functional Inference by Asynchronous Observations

We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time alignment nor data imputation. Under conditions, this spectral approach is consistent and we provide limit distributions using irregular and asynchronous observations. When observations are synchronous, the Fourier transform method for volatility functionals attains both the optimal convergence rate and the efficient bound in the sense of Le Cam and Hájek. Another finding is asynchronicity or missing data as a form of noise produces "interference" in the spectrum estimation and impacts on the convergence rate of volatility functional estimators. This new methodology extends previous applications of volatility functionals, including principal component analysis, generalized method of moments, continuous-time linear regression models et cetera, to high-frequency datasets of which asynchronicity is a prevailing feature.

math.ST↗

arXiv2018

Model-Free Approaches to Discern Non-Stationary Microstructure Noise and Time-Varying Liquidity in High-Frequency Data

In this paper, we provide non-parametric statistical tools to test stationarity of microstructure noise in general hidden Ito semimartingales, and discuss how to measure liquidity risk using high frequency financial data. In particular, we investigate the impact of non-stationary microstructure noise on some volatility estimators, and design three complementary tests by exploiting edge effects, information aggregation of local estimates and high-frequency asymptotic approximation. The asymptotic distributions of these tests are available under both stationary and non-stationary assumptions, thereby enable us to conservatively control type-I errors and meanwhile ensure the proposed tests enjoy the asymptotically optimal statistical power. Besides it also enables us to empirically measure aggregate liquidity risks by these test statistics. As byproducts, functional dependence and endogenous microstructure noise are briefly discussed. Simulation with a realistic configuration corroborates our theoretical results, and our empirical study indicates the prevalence of non-stationary microstructure noise in New York Stock Exchange.

q-fin.ST↗

arXiv2018

Learning with Opponent-Learning Awareness

Multi-agent settings are quickly gathering importance in machine learning. This includes a plethora of recent work on deep multi-agent reinforcement learning, but also can be extended to hierarchical RL, generative adversarial networks and decentralised optimisation. In all these settings the presence of multiple learning agents renders the training problem non-stationary and often leads to unstable training or undesired final results. We present Learning with Opponent-Learning Awareness (LOLA), a method in which each agent shapes the anticipated learning of the other agents in the environment. The LOLA learning rule includes a term that accounts for the impact of one agent's policy on the anticipated parameter update of the other agents. Results show that the encounter of two LOLA agents leads to the emergence of tit-for-tat and therefore cooperation in the iterated prisoners' dilemma, while independent learning does not. In this domain, LOLA also receives higher payouts compared to a naive learner, and is robust against exploitation by higher order gradient-based methods. Applied to repeated matching pennies, LOLA agents converge to the Nash equilibrium. In a round robin tournament we show that LOLA agents successfully shape the learning of a range of multi-agent learning algorithms from literature, resulting in the highest average returns on the IPD. We also show that the LOLA update rule can be efficiently calculated using an extension of the policy gradient estimator, making the method suitable for model-free RL. The method thus scales to large parameter and input spaces and nonlinear function approximators. We apply LOLA to a grid world task with an embedded social dilemma using recurrent policies and opponent modelling. By explicitly considering the learning of the other agent, LOLA agents learn to cooperate out of self-interest. The code is at github.com/alshedivat/lola.

cs.AI↗

arXiv2018

Evolved Policy Gradients

We propose a metalearning approach for learning gradient-based reinforcement learning (RL) algorithms. The idea is to evolve a differentiable loss function, such that an agent, which optimizes its policy to minimize this loss, will achieve high rewards. The loss is parametrized via temporal convolutions over the agent's experience. Because this loss is highly flexible in its ability to take into account the agent's history, it enables fast task learning. Empirical results show that our evolved policy gradient algorithm (EPG) achieves faster learning on several randomized environments compared to an off-the-shelf policy gradient method. We also demonstrate that EPG's learned loss can generalize to out-of-distribution test time tasks, and exhibits qualitatively different behavior from other popular metalearning algorithms.

cs.LG↗

arXiv2018

Parameter Space Noise for Exploration

Deep reinforcement learning (RL) methods generally engage in exploratory behavior through noise injection in the action space. An alternative is to add noise directly to the agent's parameters, which can lead to more consistent exploration and a richer set of behaviors. Methods such as evolutionary strategies use parameter perturbations, but discard all temporal structure in the process and require significantly more samples. Combining parameter noise with traditional RL methods allows to combine the best of both worlds. We demonstrate that both off- and on-policy methods benefit from this approach through experimental comparison of DQN, DDPG, and TRPO on high-dimensional discrete action environments as well as continuous control tasks. Our results show that RL with parameter noise learns more efficiently than traditional RL with action space noise and evolutionary strategies individually.

cs.LG↗

arXiv2017

UCB Exploration via Q-Ensembles

We show how an ensemble of $Q^*$-functions can be leveraged for more effective exploration in deep reinforcement learning. We build on well established algorithms from the bandit setting, and adapt them to the $Q$-learning setting. We propose an exploration strategy based on upper-confidence bounds (UCB). Our experiments show significant gains on the Atari benchmark.

cs.LG↗

arXiv2017

Convolutional neural networks that teach microscopes how to image

Deep learning algorithms offer a powerful means to automatically analyze the content of medical images. However, many biological samples of interest are primarily transparent to visible light and contain features that are difficult to resolve with a standard optical microscope. Here, we use a convolutional neural network (CNN) not only to classify images, but also to optimize the physical layout of the imaging device itself. We increase the classification accuracy of a microscope's recorded images by merging an optical model of image formation into the pipeline of a CNN. The resulting network simultaneously determines an ideal illumination arrangement to highlight important sample features during image acquisition, along with a set of convolutional weights to classify the detected images post-capture. We demonstrate our joint optimization technique with an experimental microscope configuration that automatically identifies malaria-infected cells with 5-10% higher accuracy than standard and alternative microscope lighting designs.

cs.CV↗

arXiv2014

Solving ptychography with a convex relaxation

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the current standard algorithm for ptychographic reconstruction.

physics.optics↗

arXiv2014

Matrix concentration inequalities via the method of exchangeable pairs

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein's method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoeffding, Bernstein, Khintchine and Rosenthal. The same technique delivers bounds for sums of dependent random matrices and more general matrix-valued functions of dependent random variables.

math.PR↗

arXiv2013

Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices

Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities.

cs.IT↗

arXiv2012

The Masked Sample Covariance Estimator: An Analysis via Matrix Concentration Inequalities

Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is nearly sparse and to focus on estimating only the significant entries. To analyze this approach, Levina and Vershynin (2011) introduce a formalism called masked covariance estimation, where each entry of the sample covariance estimator is reweighted to reflect an a priori assessment of its importance. This paper provides a short analysis of the masked sample covariance estimator by means of a matrix concentration inequality. The main result applies to general distributions with at least four moments. Specialized to the case of a Gaussian distribution, the theory offers qualitative improvements over earlier work. For example, the new results show that n = O(B log^2 p) samples suffice to estimate a banded covariance matrix with bandwidth B up to a relative spectral-norm error, in contrast to the sample complexity n = O(B log^5 p) obtained by Levina and Vershynin.

math.PR↗