arXiv subjects

Donggyu Kim

Publications and source records attributed to Donggyu Kim.

At least 55 records · Page 3Linked to original sources

arXiv2023

Preparation of Entangled Many-Body States with Machine Learning

Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state, have been prepared, but fundamental difficulties in systems with many qubits remain, including the Lieb-Robinson bounds for the number of quantum operations. Here, we provide one algorithm with an implementation of a deep learning process and achieve to prepare the target ground states with many qubits. Our strategy is to train a machine-learning model and predict parameters with many qubits by utilizing a pattern of quantum states from the corresponding quantum states with small numbers of qubits. For example, we demonstrate that our algorithm with the Quantum Approximate Optimization Ansatz can effectively generate the ground state for a 1D XY model with 64 spins. We also demonstrate that the reduced density operator of two qubits can be utilized to capture the pattern of quantum many-body states such as correlation lengths even for quantum critical states.

quant-ph↗

arXiv2022

Large Volatility Matrix Analysis Using Global and National Factor Models

Several large volatility matrix inference procedures have been developed, based on the latent factor model. They often assumed that there are a few of common factors, which can account for volatility dynamics. However, several studies have demonstrated the presence of local factors. In particular, when analyzing the global stock market, we often observe that nation-specific factors explain their own country's volatility dynamics. To account for this, we propose the Double Principal Orthogonal complEment Thresholding (Double-POET) method, based on multi-level factor models, and also establish its asymptotic properties. Furthermore, we demonstrate the drawback of using the regular principal orthogonal component thresholding (POET) when the local factor structure exists. We also describe the blessing of dimensionality using Double-POET for local covariance matrix estimation. Finally, we investigate the performance of the Double-POET estimator in an out-of-sample portfolio allocation study using international stocks from 20 financial markets.

econ.EM↗

arXiv2022

Benchmark Dataset for Precipitation Forecasting by Post-Processing the Numerical Weather Prediction

Precipitation forecasting is an important scientific challenge that has wide-reaching impacts on society. Historically, this challenge has been tackled using numerical weather prediction (NWP) models, grounded on physics-based simulations. Recently, many works have proposed an alternative approach, using end-to-end deep learning (DL) models to replace physics-based NWP models. While these DL methods show improved performance and computational efficiency, they exhibit limitations in long-term forecasting and lack the explainability. In this work, we present a hybrid NWP-DL workflow to fill the gap between standalone NWP and DL approaches. Under this workflow, the outputs of NWP models are fed into a deep neural network, which post-processes the data to yield a refined precipitation forecast. The deep model is trained with supervision, using Automatic Weather Station (AWS) observations as ground-truth labels. This can achieve the best of both worlds, and can even benefit from future improvements in NWP technology. To facilitate study in this direction, we present a novel dataset focused on the Korean Peninsula, termed KoMet (Korea Meteorological Dataset), comprised of NWP outputs and AWS observations. For the NWP model, the Global Data Assimilation and Prediction Systems-Korea Integrated Model (GDAPS-KIM) is utilized. We provide analysis on a comprehensive set of baseline methods aimed at addressing the challenges of KoMet, including the sparsity of AWS observations and class imbalance. To lower the barrier to entry and encourage further study, we also provide an extensive open-source Python package for data processing and model development. Our benchmark data and code are available at https://github.com/osilab-kaist/KoMet-Benchmark-Dataset.

cs.LG↗

arXiv2022

Bounds for the Twin-width of Graphs

Bonnet, Kim, Thomassé, and Watrigant (2020) introduced the twin-width of a graph. We show that the twin-width of an $n$-vertex graph is less than $(n+\sqrt{n\ln n}+\sqrt{n}+2\ln n)/2$, and the twin-width of an $m$-edge graph for a positive $m$ is less than $\sqrt{3m}+ m^{1/4} \sqrt{\ln m} / (4\cdot 3^{1/4}) + 3m^{1/4} / 2$. Conference graphs of order $n$ (when such graphs exist) have twin-width at least $(n-1)/2$, and we show that Paley graphs achieve this lower bound. We also show that the twin-width of the Erdős-Rényi random graph $G(n,p)$ with $1/n\leq p=p(n)\leq 1/2$ is larger than $2p(1-p)n - (2\sqrt{2}+\varepsilon)\sqrt{p(1-p)n\ln n}$ asymptotically almost surely for any positive $\varepsilon$. Lastly, we calculate the twin-width of random graphs $G(n,p)$ with $p\leq c/n$ for a constant $c<1$, determining the thresholds at which the twin-width jumps from $0$ to $1$ and from $1$ to $2$.

math.CO↗

arXiv2022

Overnight GARCH-Itô Volatility Models

Various parametric volatility models for financial data have been developed to incorporate high-frequency realized volatilities and better capture market dynamics. However, because high-frequency trading data are not available during the close-to-open period, the volatility models often ignore volatility information over the close-to-open period and thus may suffer from loss of important information relevant to market dynamics. In this paper, to account for whole-day market dynamics, we propose an overnight volatility model based on Itô diffusions to accommodate two different instantaneous volatility processes for the open-to-close and close-to-open periods. We develop a weighted least squares method to estimate model parameters for two different periods and investigate its asymptotic properties. We conduct a simulation study to check the finite sample performance of the proposed model and method. Finally, we apply the proposed approaches to real trading data.

q-fin.ST↗

arXiv2022

Volatility Models for Stylized Facts of High-Frequency Financial Data

This paper introduces novel volatility diffusion models to account for the stylized facts of high-frequency financial data such as volatility clustering, intra-day U-shape, and leverage effect. For example, the daily integrated volatility of the proposed volatility process has a realized GARCH structure with an asymmetric effect on log-returns. To further explain the heavy-tailedness of the financial data, we assume that the log-returns have a finite $2b$-th moment for $b \in (1,2]$. Then, we propose a Huber regression estimator which has an optimal convergence rate of $n^{(1-b)/b}$. We also discuss how to adjust bias coming from Huber loss and show its asymptotic properties.

stat.ME↗

arXiv2022

Dynamic Realized Beta Models Using Robust Realized Integrated Beta Estimator

This paper introduces a unified parametric modeling approach for time-varying market betas that can accommodate continuous-time diffusion and discrete-time series models based on a continuous-time series regression model to better capture the dynamic evolution of market betas. We call this the dynamic realized beta (DR Beta). We first develop a non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noises, which is robust to the stylized features, such as the time-varying beta and the dependence structure of microstructure noises, and construct the estimator's asymptotic properties. Then, with the robust realized integrated beta estimator, we propose a quasi-likelihood procedure for estimating the model parameters based on the combined high-frequency data and low frequency dynamic structure. We also establish asymptotic theorems for the proposed estimator and conduct a simulation study to check the performance of finite samples of the estimator. The empirical study with the S&P 500 index and the top 50 large trading volume stocks from the S&P 500 illustrates that the proposed DR Beta model effectively accounts for dynamics in the market beta of individual stocks and better predicts future market betas.

stat.ME↗

arXiv2022

Next Generation Models for Portfolio Risk Management: An Approach Using Financial Big Data

This paper proposes a dynamic process of portfolio risk measurement to address potential information loss. The proposed model takes advantage of financial big data to incorporate out-of-target-portfolio information that may be missed when one considers the Value at Risk (VaR) measures only from certain assets of the portfolio. We investigate how the curse of dimensionality can be overcome in the use of financial big data and discuss where and when benefits occur from a large number of assets. In this regard, the proposed approach is the first to suggest the use of financial big data to improve the accuracy of risk analysis. We compare the proposed model with benchmark approaches and empirically show that the use of financial big data improves small portfolio risk analysis. Our findings are useful for portfolio managers and financial regulators, who may seek for an innovation to improve the accuracy of portfolio risk estimation.

q-fin.RM↗

arXiv2021

Eigenvalues and parity factors in graphs

Let $G$ be a graph and let $g, f$ be nonnegative integer-valued functions defined on $V(G)$ such that $g(v) \le f(v)$ and $g(v) \equiv f(v) \pmod{2}$ for all $v \in V(G)$. A $(g,f)$-parity factor of $G$ is a spanning subgraph $H$ such that for each vertex $v \in V(G)$, $g(v) \le d_H(v) \le f(v)$ and $f(v)\equiv d_H(v) \pmod{2}$. We prove sharp upper bounds for certain eigenvalues in an $h$-edge-connected graph $G$ with given minimum degree to guarantee the existence of a $(g,f)$-parity factor; we provide graphs showing that the bounds are optimal. This result extends the recent one of the second author (2022), extending the one of Gu (2014), Lu (2010), Bollb{á}s, Saito, and Wormald (1985), and Gallai (1950).

math.CO↗

arXiv2021

Effect of the U.S.--China Trade War on Stock Markets: A Financial Contagion Perspective

In this paper, we investigate the effect of the U.S.--China trade war on stock markets from a financial contagion perspective, based on high-frequency financial data. Specifically, to account for risk contagion between the U.S. and China stock markets, we develop a novel jump-diffusion process. For example, we consider three channels for volatility contagion--such as integrated volatility, positive jump variation, and negative jump variation--and each stock market is able to affect the other stock market as an overnight risk factor. We develop a quasi-maximum likelihood estimator for model parameters and establish its asymptotic properties. Furthermore, to identify contagion channels and test the existence of a structural break, we propose hypothesis test procedures. From the empirical study, we find evidence of financial contagion from the U.S. to China and evidence that the risk contagion channel has changed from integrated volatility to negative jump variation.

q-fin.ST↗

arXiv2021

Exponential GARCH-Ito Volatility Models

This paper introduces a novel Ito diffusion process to model high-frequency financial data, which can accommodate low-frequency volatility dynamics by embedding the discrete-time non-linear exponential GARCH structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Ito models, the instantaneous volatility process has a non-linear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Ito (ERGI) model. Given the auto-regressive structure of the log-integrated volatility, we propose a quasi-likelihood estimation procedure for parameter estimation and establish its asymptotic properties. We conduct a simulation study to check the finite sample performance of the proposed model and an empirical study with 50 assets among the S\&P 500 compositions. The numerical studies show the advantages of the new proposed model.

econ.EM↗

arXiv2021

$Γ$-graphic delta-matroids and their applications

For an abelian group $Γ$, a $Γ$-labelled graph is a graph whose vertices are labelled by elements of $Γ$. We prove that a certain collection of edge sets of a $Γ$-labelled graph forms a delta-matroid, which we call a $Γ$-graphic delta-matroid, and provide a polynomial-time algorithm to solve the separation problem, which allows us to apply the symmetric greedy algorithm of Bouchet to find a maximum weight feasible set in such a delta-matroid. We present two algorithmic applications on graphs; Maximum Weight Packing of Trees of Order Not Divisible by $k$ and Maximum Weight $S$-Tree Packing. We also discuss various properties of $Γ$-graphic delta-matroids.

math.CO↗

arXiv2021

Conditional Quantile Analysis for Realized GARCH Models

This paper introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized GARCH model and employ conditional standard deviation, realized volatility, realized quantile, and absolute overnight return as innovations in the proposed dynamic quantile models. We devise a two-step estimation procedure to estimate the conditional quantile parameters. The first step applies a quasi-maximum likelihood estimation procedure, with the realized volatility as a proxy for the volatility proxy, to estimate the conditional standard deviation parameters. The second step utilizes a quantile regression estimation procedure with the estimated conditional standard deviation in the first step. Asymptotic theory is established for the proposed estimation methods, and a simulation study is conducted to check their finite-sample performance. Finally, we apply the proposed methodology to calculate the value at risk (VaR) of 20 individual assets and compare its performance with existing competitors.

stat.ME↗

arXiv2021

Advancing Hybrid Quantum-Classical Algorithms via Mean-Operators

Entanglement in quantum many-body systems is the key concept for future technology and science, opening up a possibility to explore uncharted realms in an enormously large Hilbert space. The hybrid quantum-classical algorithms have been suggested to control quantum entanglement of many-body systems, and yet their applicability is intrinsically limited by the numbers of qubits and quantum operations. Here we propose a theory which overcomes the limitations by combining advantages of the hybrid algorithms and the standard mean-field-theory in condensed matter physics, named as mean-operator-theory. We demonstrate that the number of quantum operations to prepare an entangled target many-body state such as symmetry-protected-topological states is significantly reduced by introducing a mean-operator. We also show that a class of mean-operators is expressed as time-evolution operators and our theory is directly applicable to quantum simulations with $^{87}$Rb neutral atoms or trapped $^{40}$Ca$^+$ ions.

cond-mat.str-el↗

arXiv2021

Single-Crystalline Metallic Films Induced by van der Waals Epitaxy on Black Phosphorus

The properties of metal-semiconductor junctions are often unpredictable because of non-ideal interfacial structures, such as interfacial defects or chemical reactions introduced at junctions. Black phosphorus (BP), an elemental two-dimensional (2D) semiconducting crystal, possesses the puckered atomic structure with high chemical reactivity, and the establishment of a realistic atomic-scale picture of BP's interface toward metallic contact has remained elusive. Here we examine the interfacial structures and properties of physically-deposited metals of various kinds on BP. We find that Au, Ag, and Bi form single-crystalline films with (110) orientation through guided van der Waals epitaxy. Transmission electron microscopy and X-ray photoelectron spectroscopy confirm that atomically sharp van der Waals metal-BP interfaces forms with exceptional rotational alignment. Under a weak metal-BP interaction regime, the BP's puckered structure play an essential role in the adatom assembly process and can lead to the formation of a single crystal, which is supported by our theoretical analysis and calculations. The experimental survey also demonstrates that the BP-metal junctions can exhibit various types of interfacial structures depending on metals, such as the formation of polycrystalline microstructure or metal phosphides. This study provides a guideline for obtaining a realistic view on metal-2D semiconductor interfacial structures, especially for atomically puckered 2D crystals.

cond-mat.mtrl-sci↗

arXiv2021

Self-supervised Text-to-SQL Learning with Header Alignment Training

Since we can leverage a large amount of unlabeled data without any human supervision to train a model and transfer the knowledge to target tasks, self-supervised learning is a de-facto component for the recent success of deep learning in various fields. However, in many cases, there is a discrepancy between a self-supervised learning objective and a task-specific objective. In order to tackle such discrepancy in Text-to-SQL task, we propose a novel self-supervised learning framework. We utilize the task-specific properties of Text-to-SQL task and the underlying structures of table contents to train the models to learn useful knowledge of the \textit{header-column} alignment task from unlabeled table data. We are able to transfer the knowledge to the supervised Text-to-SQL training with annotated samples, so that the model can leverage the knowledge to better perform the \textit{header-span} alignment task to predict SQL statements. Experimental results show that our self-supervised learning framework significantly improves the performance of the existing strong BERT based models without using large external corpora. In particular, our method is effective for training the model with scarce labeled data. The source code of this work is available in GitHub.

cs.CL↗

arXiv2021

State Heterogeneity Analysis of Financial Volatility Using High-Frequency Financial Data

Recently, to account for low-frequency market dynamics, several volatility models, employing high-frequency financial data, have been developed. However, in financial markets, we often observe that financial volatility processes depend on economic states, so they have a state heterogeneous structure. In this paper, to study state heterogeneous market dynamics based on high-frequency data, we introduce a novel volatility model based on a continuous Ito diffusion process whose intraday instantaneous volatility process evolves depending on the exogenous state variable, as well as its integrated volatility. We call it the state heterogeneous GARCH-Ito (SG-Ito) model. We suggest a quasi-likelihood estimation procedure with the realized volatility proxy and establish its asymptotic behaviors. Moreover, to test the low-frequency state heterogeneity, we develop a Wald test-type hypothesis testing procedure. The results of empirical studies suggest the existence of leverage, investor attention, market illiquidity, stock market comovement, and post-holiday effect in S&P 500 index volatility.

stat.AP↗

arXiv2020

How and When the Cassie-Baxter Droplet Starts to Slide on the Textured Surfaces

The Cassie-Baxter state droplet has many local energy minima on the textured surface, while the amount of the energy barrier between them can be affected by the gravity. When the droplet cannot find any local energy minimum point on the surface, the droplet starts to slide. Based on the Laplace pressure equation, the shape of a two-dimensional Cassie-Baxter droplet on a textured surface is predicted. Then the stability of the droplet is examined by considering the interference between the liquid and the surface microstructure as well as analyzing the free energy change upon the de-pinning. Afterward, the theoretical analysis is validated against the line-tension based front tracking method simulation (LTM), that seamlessly captures the attachment and detachment between the liquid and the substrate. We answer to the open debates on the sliding research field: (i) Whether the sliding initiates with the front end slip or the rear end slip, and (ii) whether the advancing and receding contact angles measured on the horizontal surface are comparable with the front and rear contact angle of the droplet at the onset of sliding. Additionally, a new droplet translation mechanism promoted by cycle of condensation and evaporation is suggested.

cond-mat.soft↗