pwc-archive/papers-with-abstracts huggingface dataset:
Improved deep learning of chaotic dynamical systems with multistep penalty losses
Authors: Dibyajyoti Chakraborty, Seung Whan Chung, Ashesh Chattopadhyay, Romit Maulik
Date: 2024-10-08 00:00:00

Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a novel framework that addresses these challenges by leveraging the recently proposed multi-step penalty (MP) optimization technique. Our approach extends the applicability of MP optimization to a wide range of deep learning architectures, including Fourier Neural Operators and UNETs. By introducing penalized local discontinuities in the forecast trajectory, we effectively handle the non-convexity of loss landscapes commonly encountered in training neural networks for chaotic systems. We demonstrate the effectiveness of our method through its application to two challenging use-cases: the prediction of flow velocity evolution in two-dimensional turbulence and ocean dynamics using reanalysis data. Our results highlight the potential of this approach for accurate and stable long-term prediction of chaotic dynamics, paving the way for new advancements in data-driven modeling of complex natural phenomena.
A Kermack--McKendrick type epidemic model with double threshold phenomenon (and a possible application to Covid-19)
Authors: Joan Ponce, Horst R. Thieme
Date: 2024-09-25 00:00:00

The suggestion by K.L. Cooke (1967) that infected individuals become infective if they are exposed often enough for a natural disease resistance to be overcome is built into a Kermack-McKendrick type epidemic model with infectivity age. Both the case that the resistance may be the same for all hosts and the case that it is distributed among the host population are considered. In addition to the familiar threshold behavior of the final size of the epidemic with respect to a basic reproductive number, an Allee effect is generated with respect to the final cumulative force of infection exerted by the initial infectives. This offers a deterministic explanation of why geographic areas that appear to be epidemiologically similar have epidemic outbreaks of quite different severity.
A Novel Neural Filter to Improve Accuracy of Neural Network Models of Dynamic Systems
Authors: Parham Oveissi, Turibius Rozario, Ankit Goel
Date: 2024-09-20 00:00:00
Tasks: Prediction

The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where the prediction error diverges over time, thus degrading their accuracy. This paper presents a neural filter to enhance the accuracy of long-term state predictions of neural network-based models of dynamic systems. Motivated by the extended Kalman filter, the neural filter combines the neural network state predictions with the measurements from the physical system to improve the estimated state's accuracy. The neural filter's improvements in prediction accuracy are demonstrated through applications to four nonlinear dynamical systems. Numerical experiments show that the neural filter significantly improves prediction accuracy and bounds the state estimate covariance, outperforming the neural network predictions. Furthermore, it is also shown that the accuracy of a poorly trained neural network model can be improved to the same level as that of an adequately trained neural network model, potentially decreasing the training cost and required data to train a neural network.
Stability of sorting based embeddings
Authors: Radu Balan, Efstratios Tsoukanis, Matthias Wellershoff
Date: 2024-10-07 00:00:00

Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $\alpha : \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant map $\beta_\Phi : V \to \mathbb{R}^{M \times N}$ given by sorting the coorbits $(\langle v, g \phi_i \rangle_V)_{g \in G}$, where $(\phi_i)_{i=1}^N \in V$, satisfies a bi-Lipschitz condition if and only if it separates orbits. Additionally, we note that any invariant Lipschitz continuous map (into a Hilbert space) factors through the sorting based embedding, and that any invariant continuous map (into a locally convex space) factors through the sorting based embedding as well.
First order Martingale model risk and semi-static hedging
Authors: Nathan Sauldubois, Nizar Touzi
Date: 2024-10-09 00:00:00

We investigate model risk distributionally robust sensitivities for functionals on the Wasserstein space when the underlying model is constrained to the martingale class and/or is subject to constraints on the first marginal law. Our results extend the findings of Bartl, Drapeau, Obloj \& Wiesel \cite{bartl2021sensitivity} and Bartl \& Wiesel \cite{bartlsensitivityadapted} by introducing the minimization of the distributionally robust problem with respect to semi-static hedging strategies. We provide explicit characterizations of the model risk (first order) optimal semi-static hedging strategies. The distributional robustness is analyzed both in terms of the adapted Wasserstein metric and the more relevant standard Wasserstein metric.
Aiding Global Convergence in Federated Learning via Local Perturbation and Mutual Similarity Information
Authors: Emanuel Buttaci, Giuseppe Carlo Calafiore
Date: 2024-10-07 00:00:00
Tasks: Distributed Optimization, Federated Learning

Federated learning has emerged in the last decade as a distributed optimization paradigm due to the rapidly increasing number of portable devices able to support the heavy computational needs related to the training of machine learning models. Federated learning utilizes gradient-based optimization to minimize a loss objective shared across participating agents. To the best of our knowledge, the literature mostly lacks elegant solutions that naturally harness the reciprocal statistical similarity between clients to redesign the optimization procedure. To address this gap, by conceiving the federated network as a similarity graph, we propose a novel modified framework wherein each client locally performs a perturbed gradient step leveraging prior information about other statistically affine clients. We theoretically prove that our procedure, due to a suitably introduced adaptation in the update rule, achieves a quantifiable speedup concerning the exponential contraction factor in the strongly convex case compared with popular algorithms FedAvg and FedProx, here analyzed as baselines. Lastly, we legitimize our conclusions through experimental results on the CIFAR10 and FEMNIST datasets, where we show that our algorithm speeds convergence up to a margin of 30 global rounds compared with FedAvg while modestly improving generalization on unseen data in heterogeneous settings.
Individual vaccination as Nash equilibrium in a SIR model with application to the 2009-10 Influenza A(H1N1) epidemic in France
Authors: Laetitia Laguzet, Gabriel Turinici
Date: 2024-10-04 00:00:00

The vaccination against ongoing epidemics is seldom compulsory but remains one of the most classical means to fight epidemic propagation. However recent debates concerning the innocuity of vaccines and their risk with respect to the risk of the epidemic itself lead to severe vaccination campaign failures and new mass behaviors appeared driven by individual self-interest. Prompted by this context we analyze, in a Susceptible-Infected-Recovered (SIR) model, whether egocentric individuals can reach an equilibrium with the rest of the society. Using techniques from the "Mean Field Games" theory, we extend previous results and show that an equilibrium exists and characterizes completely the individual best vaccination strategy (with or without discounting). We also compare with a strategy based only on overall societal optimization and exhibit a situation with non-negative price of anarchy. Finally, we apply the theory to the 2009-2010 Influenza A (H1N1) vaccination campaign in France and hint that a group of individuals stopped vaccinating at levels that indicated a pessimistic perception of the risk of the vaccine.
Time-Consistent Portfolio Selection for Rank-Dependent Utilities in an Incomplete Market
Authors: Jiaqin Wei, Jianming Xia, Qian Zhao
Date: 2024-09-28 00:00:00

We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium strategies. In the case of time-invariant probability weighting function, we provide a comprehensive characterization of the deterministic strict equilibrium strategy. The unique non-zero equilibrium, if exists, can be determined by solving an autonomous ODE. In the case of time-variant probability weighting functions, we observe that there may be infinitely many non-zero deterministic strict equilibrium strategies, which are derived from the positive solutions to a nonlinear singular ODE. By specifying the maximal solution to the singular ODE, we are able to identify all the positive solutions. In addition, we address the issue of selecting an optimal strategy from the numerous equilibrium strategies available.
Systemic Risk Asymptotics in a Renewal Model with Multiple Business Lines and Heterogeneous Claims
Authors: Bingzhen Geng, Yang Liu, Hongfu Wan
Date: 2024-09-30 00:00:00

Systemic risk is receiving increasing attention in the insurance industry, as these risks can have severe impacts on the entire financial system. In this paper, we propose a multi-dimensional L/'{e}vy process-based renewal risk model with heterogeneous insurance claims, where every dimension indicates a business line of an insurer. We use the systemic expected shortfall (SES) and marginal expected shortfall (MES) defined with a Value-at-Risk (VaR) target level as the measurement of systemic risks. Assuming that all the claim sizes are pairwise asymptotically independent (PAI), we derive asymptotic formulas for the tail probabilities of discounted aggregate claims and total loss, which holds uniformly for all time horizons. We further obtain the asymptotics of the above systemic risk measures. The main technical issues involve the treatment of uniform convergence in the dynamic time setting. Finally, we conduct a Monte Carlo numerical study and verify that our asymptotics are accurate and convenient in computation.
Estimate of Koopman modes and eigenvalues with Kalman Filter
Authors: Ningxin Liu, Shuigen Liu, Xin T. Tong, Lijian Jiang
Date: 2024-09-24 00:00:00

Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the accuracy of DMD can be limited in extracting dynamical features due to sensor noise in measurements. We develop an adaptive method to constantly update dynamic modes and eigenvalues from noisy measurements arising from discrete systems. Our method is based on the Ensemble Kalman filter owing to its capability of handling time-varying systems and nonlinear observables. Our method can be extended to non-autonomous dynamical systems, accurately recovering short-time eigenvalue-eigenvector pairs and observables. Theoretical analysis shows that the estimation is accurate in long term data misfit. We demonstrate the method on both autonomous and non-autonomous dynamical systems to show its effectiveness.
Ages, sizes and (trees within) trees of taxa and of urns, from Yule to today
Authors: Amaury Lambert
Date: 2024-09-22 00:00:00

The paper written in 1925 by G. Udny Yule that we celebrate in this special issue introduces several novelties and results that we recall in detail. First, we discuss Yule (1925)'s main legacies over the past century, focusing on empirical frequency distributions with heavy tails and random tree models for phylogenies. We estimate the year when Yule's work was re-discovered by scientists interested in stochastic processes of population growth (1948) and the year from which it began to be cited (1951, Yule's death). We highlight overlooked aspects of Yule's work (e.g., the Yule process of Yule processes) and correct some common misattributions (e.g., the Yule tree). Second, we generalize Yule's results on the average frequency of genera of a given age and size (number of species). We show that his formula also applies to the age $A$ and size $S$ of any randomly chosen genus and that the pairs $(A_i, S_i)$ are equally distributed and independent across genera. This property extends to triples $(H_i, A_i, S_i)$, where $(H_i)$ are the coalescence times of the genus phylogeny, even when species diversification within genera follows any integer-valued process, including species extinctions. Studying $(A, S)$ in this broader context allows us to identify cases where $S$ has a power-law tail distribution, with new applications to urn schemes.
Heat modulated affine stochastic volatility models for forward curve dynamics
Authors: Sven Karbach
Date: 2024-09-19 00:00:00

We present a function-valued stochastic volatility model designed to capture the continuous-time evolution of forward curves in fixed-income or commodity markets. The dynamics of the (logarithmic) forward curves are defined by a Heath-Jarrow-Morton-Musiela stochastic partial differential equation modulated by an instantaneous volatility process that describes the second-order moment structure of forwards with different time-to-maturity. We propose to model the operator-valued instantaneous covariance by an affine process on the cone of positive trace-class operators with drift given by the Lyapunov operator of the Laplacian. The so defined infinite-rank stochastic volatility model is analytically tractable due to its affine structure and allows to model maturity specific risk and volatility clustering in forward markets. Furthermore, we introduce a numerically feasible spectral Galerkin approximation of the associated operator-valued generalized Riccati equations and study the robustness of the model with respect to finite-rank approximations by providing explicit error bounds on the approximation error.
Theoretical and Empirical Validation of Heston Model
Authors: Zheng Cao, Xinhao Lin
Date: 2024-09-19 00:00:00
Tasks: model

This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and analyzed to evaluate its effectiveness in pricing options. For practical application, we utilize Monte Carlo simulations alongside market data from the Crude Oil WTI market to test the model's accuracy. Machine learning based optimization methods are also applied for the estimation of the five Heston parameters. By calibrating the model with real-world data, we assess its robustness and relevance in current financial markets, aiming to bridge the gap between theoretical finance models and their practical implementations.
The Empirical Mean is Minimax Optimal for Local Glivenko-Cantelli
Authors: Doron Cohen, Aryeh Kontorovich, Roi Weiss
Date: 2024-10-02 00:00:00

We revisit the recently introduced Local Glivenko-Cantelli setting, which studies distribution-dependent uniform convergence rates of the Empirical Mean Estimator (EME). In this work, we investigate generalizations of this setting where arbitrary estimators are allowed rather than just the EME. Can a strictly larger class of measures be learned? Can better risk decay rates be obtained? We provide exhaustive answers to these questions, which are both negative, provided the learner is barred from exploiting some infinite-dimensional pathologies. On the other hand, allowing such exploits does lead to a strictly larger class of learnable measures.
Group lasso based selection for high-dimensional mediation analysis
Authors: Allan Jérolon, Flora Alarcon, Florence Pittion, Magali Richard, Olivier François, Etienne E. Birmelé, Vittorio Perduca
Date: 2024-09-30 00:00:00

Mediation analysis aims to identify and estimate the effect of an exposure on an outcome that is mediated through one or more intermediate variables. In the presence of multiple intermediate variables, two pertinent methodological questions arise: estimating mediated effects when mediators are correlated, and performing high-dimensional mediation analysis when the number of mediators exceeds the sample size. This paper presents a two-step procedure for high-dimensional mediation analysis. The first step selects a reduced number of candidate mediators using an ad-hoc lasso penalty. The second step applies a procedure we previously developed to estimate the mediated and direct effects, accounting for the correlation structure among the retained candidate mediators. We compare the performance of the proposed two-step procedure with state-of-the-art methods using simulated data. Additionally, we demonstrate its practical application by estimating the causal role of DNA methylation in the pathway between smoking and rheumatoid arthritis using real data.
Consistent Estimation of the High-Dimensional Efficient Frontier
Authors: Taras Bodnar, Nikolaus Hautsch, Yarema Okhrin, Nestor Parolya
Date: 2024-09-23 00:00:00

In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$ tend to infinity simultaneously and their ratio $p/n$ tends to a positive constant $c\in(0,1)$. We neither impose any distributional nor structural assumptions on the asset returns. For the developed theoretical framework, some regularity conditions, like the existence of the $4$th moments, are needed. It is shown that two out of three quantities of interest are biased and overestimated by their sample counterparts under the high-dimensional asymptotic regime. This becomes evident based on the asymptotic deterministic equivalents of the sample plug-in estimators. Using them we construct consistent estimators of the three characteristics of the efficient frontier. It it shown that the additive and/or the multiplicative biases of the sample estimates are solely functions of the concentration ratio $c$. Furthermore, the asymptotic normality of the considered estimators of the parameters of the efficient frontier is proved. Verifying the theoretical results based on an extensive simulation study we show that the proposed estimator for the efficient frontier is a valuable alternative to the sample estimator for high dimensional data. Finally, we present an empirical application, where we estimate the efficient frontier based on the stocks included in S\&P 500 index.
Mitigating Extremal Risks: A Network-Based Portfolio Strategy
Authors: Qian Hui, Tiandong Wang
Date: 2024-09-18 00:00:00

In financial markets marked by inherent volatility, extreme events can result in substantial investor losses. This paper proposes a portfolio strategy designed to mitigate extremal risks. By applying extreme value theory, we evaluate the extremal dependence between stocks and develop a network model reflecting these dependencies. We use a threshold-based approach to construct this complex network and analyze its structural properties. To improve risk diversification, we utilize the concept of the maximum independent set from graph theory to develop suitable portfolio strategies. Since finding the maximum independent set in a given graph is NP-hard, we further partition the network using either sector-based or community-based approaches. Additionally, we use value at risk and expected shortfall as specific risk measures and compare the performance of the proposed portfolios with that of the market portfolio.
Adapter-dependent Adapter Methylation Assay
Authors: Jia Zhang, Peng Qi, Li Xiao, Mengxi Yuan, Jun Chuan, Yaling Zeng, Li-mei Lin, Yue Gu, Yan Zhang, Duan-fang Liao, Kai Li
Date: 2024-10-05 00:00:00

Sensitive and reliable methylation assay is important for oncogentic studies and clinical applications. Here, a new methylation assay was developed by the use of adapter-dependent adapter in library preparation. This new assay avoids the use of bisulfite and provides a simple and highly sensitive scanning of methylation spectra of circulating free DNA and genomic DNA.
FlexSBDD: Structure-Based Drug Design with Flexible Protein Modeling
Authors: Zaixi Zhang, Mengdi Wang, Qi Liu
Date: 2024-09-29 00:00:00
Tasks: Data Augmentation, Drug Design, Drug Discovery

Structure-based drug design (SBDD), which aims to generate 3D ligand molecules binding to target proteins, is a fundamental task in drug discovery. Existing SBDD methods typically treat protein as rigid and neglect protein structural change when binding with ligand molecules, leading to a big gap with real-world scenarios and inferior generation qualities (e.g., many steric clashes). To bridge the gap, we propose FlexSBDD, a deep generative model capable of accurately modeling the flexible protein-ligand complex structure for ligand molecule generation. FlexSBDD adopts an efficient flow matching framework and leverages E(3)-equivariant network with scalar-vector dual representation to model dynamic structural changes. Moreover, novel data augmentation schemes based on structure relaxation/sidechain repacking are adopted to boost performance. Extensive experiments demonstrate that FlexSBDD achieves state-of-the-art performance in generating high-affinity molecules and effectively modeling the protein's conformation change to increase favorable protein-ligand interactions (e.g., Hydrogen bonds) and decrease steric clashes.
Generalized Protein Pocket Generation with Prior-Informed Flow Matching
Authors: Zaixi Zhang, Marinka Zitnik, Qi Liu
Date: 2024-09-29 00:00:00
Tasks: valid

Designing ligand-binding proteins, such as enzymes and biosensors, is essential in bioengineering and protein biology. One critical step in this process involves designing protein pockets, the protein interface binding with the ligand. Current approaches to pocket generation often suffer from time-intensive physical computations or template-based methods, as well as compromised generation quality due to the overlooking of domain knowledge. To tackle these challenges, we propose PocketFlow, a generative model that incorporates protein-ligand interaction priors based on flow matching. During training, PocketFlow learns to model key types of protein-ligand interactions, such as hydrogen bonds. In the sampling, PocketFlow leverages multi-granularity guidance (overall binding affinity and interaction geometry constraints) to facilitate generating high-affinity and valid pockets. Extensive experiments show that PocketFlow outperforms baselines on multiple benchmarks, e.g., achieving an average improvement of 1.29 in Vina Score and 0.05 in scRMSD. Moreover, modeling interactions make PocketFlow a generalized generative model across multiple ligand modalities, including small molecules, peptides, and RNA.