pwc-archive/papers-with-abstracts huggingface dataset:
The GFB Tree and Tree Imbalance Indices
Authors: Sean Cleary, Mareike Fischer, Katherine St. John
Date: 2025-02-18 00:00:00

Tree balance plays an important role in various research areas in phylogenetics and computer science. Typically, it is measured with the help of a balance index or imbalance index. There are more than 25 such indices available, recently surveyed in a book by Fischer et al. They are used to rank rooted binary trees on a scale from the most balanced to the stringiest. We show that a wide range of subtree-sized based measures satisfying concavity and monotonicity conditions are minimized by the complete or greedy-from-the-bottom (GFB) tree and maximized by the caterpillar tree, yielding an infinitely large family of distinct new imbalance indices. Answering an open question from the literature, we show that one such established measure, the $\widehat{s}$-shape statistic, has the GFB tree as its unique minimizer. We also provide an alternative characterization of GFB trees, showing that they are equivalent to complete trees, which arise in different contexts. We give asymptotic bounds on the expected $\widehat{s}$-shape statistic under the uniform and Yule-Harding distributions of trees, and answer questions for the related $Q$-shape statistic as well.
Learning the symmetric group: large from small
Authors: Max Petschack, Alexandr Garbali, Jan de Gier
Date: 2025-02-18 00:00:00

Machine learning explorations can make significant inroads into solving difficult problems in pure mathematics. One advantage of this approach is that mathematical datasets do not suffer from noise, but a challenge is the amount of data required to train these models and that this data can be computationally expensive to generate. Key challenges further comprise difficulty in a posteriori interpretation of statistical models and the implementation of deep and abstract mathematical problems. We propose a method for scalable tasks, by which models trained on simpler versions of a task can then generalize to the full task. Specifically, we demonstrate that a transformer neural-network trained on predicting permutations from words formed by general transpositions in the symmetric group $S_{10}$ can generalize to the symmetric group $S_{25}$ with near 100\% accuracy. We also show that $S_{10}$ generalizes to $S_{16}$ with similar performance if we only use adjacent transpositions. We employ identity augmentation as a key tool to manage variable word lengths, and partitioned windows for training on adjacent transpositions. Finally we compare variations of the method used and discuss potential challenges with extending the method to other tasks.
Learning Is a Kan Extension
Authors: Matthew Pugh, Jo Grundy, Corina Cirstea, Nick Harris
Date: 2025-02-19 00:00:00

Previous work has demonstrated that efficient algorithms exist for computing Kan extensions and that some Kan extensions have interesting similarities to various machine learning algorithms. This paper closes the gap by proving that all error minimisation algorithms may be presented as a Kan extension. This result provides a foundation for future work to investigate the optimisation of machine learning algorithms through their presentation as Kan extensions. A corollary of this representation of error-minimising algorithms is a presentation of error from the perspective of lossy and lossless transformations of data.
Towards Variational Flow Matching on General Geometries
Authors: Olga Zaghen, Floor Eijkelboom, Alison Pouplin, Erik J. Bekkers
Date: 2025-02-18 00:00:00

We introduce Riemannian Gaussian Variational Flow Matching (RG-VFM), an extension of Variational Flow Matching (VFM) that leverages Riemannian Gaussian distributions for generative modeling on structured manifolds. We derive a variational objective for probability flows on manifolds with closed-form geodesics, making RG-VFM comparable - though fundamentally different to Riemannian Flow Matching (RFM) in this geometric setting. Experiments on a checkerboard dataset wrapped on the sphere demonstrate that RG-VFM captures geometric structure more effectively than Euclidean VFM and baseline methods, establishing it as a robust framework for manifold-aware generative modeling.
On the Learnability of Knot Invariants: Representation, Predictability, and Neural Similarity
Authors: Audrey Lindsay, Fabian Ruehle
Date: 2025-02-17 00:00:00

We analyze different aspects of neural network predictions of knot invariants. First, we investigate the impact of different knot representations on the prediction of invariants and find that braid representations work in general the best. Second, we study which knot invariants are easy to learn, with invariants derived from hyperbolic geometry and knot diagrams being very easy to learn, while invariants derived from topological or homological data are harder. Predicting the Arf invariant could not be learned for any representation. Third, we propose a cosine similarity score based on gradient saliency vectors, and a joint misclassification score to uncover similarities in neural networks trained to predict related topological invariants.
Navigating Demand Uncertainty in Container Shipping: Deep Reinforcement Learning for Enabling Adaptive and Feasible Master Stowage Planning
Authors: Jaike van Twiller, Yossiri Adulyasak, Erick Delage, Djordje Grbic, Rune Møller Jensen
Date: 2025-02-18 00:00:00
Tasks: Combinatorial Optimization, Deep Reinforcement Learning, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL), Stochastic Optimization

Reinforcement learning (RL) has shown promise in solving various combinatorial optimization problems. However, conventional RL faces challenges when dealing with real-world constraints, especially when action space feasibility is explicit and dependent on the corresponding state or trajectory. In this work, we focus on using RL in container shipping, often considered the cornerstone of global trade, by dealing with the critical challenge of master stowage planning. The main objective is to maximize cargo revenue and minimize operational costs while navigating demand uncertainty and various complex operational constraints, namely vessel capacity and stability, which must be dynamically updated along the vessel's voyage. To address this problem, we implement a deep reinforcement learning framework with feasibility projection to solve the master stowage planning problem (MPP) under demand uncertainty. The experimental results show that our architecture efficiently finds adaptive, feasible solutions for this multi-stage stochastic optimization problem, outperforming traditional mixed-integer programming and RL with feasibility regularization. Our AI-driven decision-support policy enables adaptive and feasible planning under uncertainty, optimizing operational efficiency and capacity utilization while contributing to sustainable and resilient global supply chains.
Constrained Online Convex Optimization with Polyak Feasibility Steps
Authors: Spencer Hutchinson, Mahnoosh Alizadeh
Date: 2025-02-18 00:00:00

In this work, we study online convex optimization with a fixed constraint function $g : \mathbb{R}^d \rightarrow \mathbb{R}$. Prior work on this problem has shown $O(\sqrt{T})$ regret and cumulative constraint satisfaction $\sum_{t=1}^{T} g(x_t) \leq 0$, while only accessing the constraint value and subgradient at the played actions $g(x_t), \partial g(x_t)$. Using the same constraint information, we show a stronger guarantee of anytime constraint satisfaction $g(x_t) \leq 0 \ \forall t \in [T]$, and matching $O(\sqrt{T})$ regret guarantees. These contributions are thanks to our approach of using Polyak feasibility steps to ensure constraint satisfaction, without sacrificing regret. Specifically, after each step of online gradient descent, our algorithm applies a subgradient descent step on the constraint function where the step-size is chosen according to the celebrated Polyak step-size. We further validate this approach with numerical experiments.
Fragility-aware Classification for Understanding Risk and Improving Generalization
Authors: Chen Yang, Zheng Cui, Daniel Zhuoyu Long, Jin Qi, Ruohan Zhan
Date: 2025-02-18 00:00:00
Tasks: Autonomous Driving, Medical Diagnosis, Recommendation Systems

Classification models play a critical role in data-driven decision-making applications such as medical diagnosis, user profiling, recommendation systems, and default detection. Traditional performance metrics, such as accuracy, focus on overall error rates but fail to account for the confidence of incorrect predictions, thereby overlooking the risk of confident misjudgments. This risk is particularly significant in cost-sensitive and safety-critical domains like medical diagnosis and autonomous driving, where overconfident false predictions may cause severe consequences. To address this issue, we introduce the Fragility Index (FI), a novel metric that evaluates classification performance from a risk-averse perspective by explicitly capturing the tail risk of confident misjudgments. To enhance generalizability, we define FI within the robust satisficing (RS) framework, incorporating data uncertainty. We further develop a model training approach that optimizes FI while maintaining tractability for common loss functions. Specifically, we derive exact reformulations for cross-entropy loss, hinge-type loss, and Lipschitz loss, and extend the approach to deep learning models. Through synthetic experiments and real-world medical diagnosis tasks, we demonstrate that FI effectively identifies misjudgment risk and FI-based training improves model robustness and generalizability. Finally, we extend our framework to deep neural network training, further validating its effectiveness in enhancing deep learning models.
A Novel Unified Parametric Assumption for Nonconvex Optimization
Authors: Artem Riabinin, Ahmed Khaled, Peter Richtárik
Date: 2025-02-17 00:00:00
Tasks: Stochastic Optimization

Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables efficient optimization, it is of limited applicability to many practical problems. To bridge this gap and better understand the practical success of optimization algorithms in nonconvex settings, we introduce a novel unified parametric assumption. Our assumption is general enough to encompass a broad class of nonconvex functions while also being specific enough to enable the derivation of a unified convergence theorem for gradient-based methods. Notably, by tuning the parameters of our assumption, we demonstrate its versatility in recovering several existing function classes as special cases and in identifying functions amenable to efficient optimization. We derive our convergence theorem for both deterministic and stochastic optimization, and conduct experiments to verify that our assumption can hold practically over optimization trajectories.
Integrated Scheduling Model for Arrivals and Departures in Metroplex Terminal Area
Authors: Tonghe li, Jixin Liu, Hao Jiang, Weili Zeng, Lei Yang
Date: 2025-02-15 00:00:00
Tasks: Scheduling

In light of the rapid expansion of civil aviation, addressing the delays and congestion phenomena in the vicinity of metroplex caused by the imbalance between air traffic flow and capacity is crucial. This paper first proposes a bi-level optimization model for the collaborative flight sequencing of arrival and departure flights in the metroplex with multiple airports, considering both the runway systems and TMA (Terminal Control Area) entry/exit fixes. Besides, the model is adaptive to various traffic scenarios. The genetic algorithm is employed to solve the proposed model. The Shanghai TMA, located in China, is used as a case study, and it includes two airports, Shanghai Hongqiao International Airport and Shanghai Pudong International Airport. The results demonstrate that the model can reduce arrival delay by 51.52%, departure delay by 18.05%, and the runway occupation time of departure flights by 23.83%. Furthermore, the model utilized in this study significantly enhances flight scheduling efficiency, providing a more efficient solution than the traditional FCFS (First Come, First Served) approach. Additionally, the algorithm employed offers further improvements over the NSGA II algorithm.
When defaults cannot be hedged: an actuarial approach to xVA calculations via local risk-minimization
Authors: Francesca Biagini, Alessandro Gnoatto, Katharina Oberpriller
Date: 2025-02-18 00:00:00

We consider the pricing and hedging of counterparty credit risk and funding when there is no possibility to hedge the jump to default of either the bank or the counterparty. This represents the situation which is most often encountered in practice, due to the absence of quoted corporate bonds or CDS contracts written on the counterparty and the difficulty for the bank to buy/sell protection on her own default. We apply local risk-minimization to find the optimal strategy and compute it via a BSDE.
Arbitrage-free catastrophe reinsurance valuation for compound dynamic contagion claims
Authors: Jiwook Jang, Patrick J. Laub, Tak Kuen Siu, Hongbiao Zhao
Date: 2025-02-18 00:00:00

In this paper, we consider catastrophe stop-loss reinsurance valuation for a reinsurance company with dynamic contagion claims. To deal with conventional and emerging catastrophic events, we propose the use of a compound dynamic contagion process for the catastrophic component of the liability. Under the premise that there is an absence of arbitrage opportunity in the market, we obtain arbitrage-free premiums for these contacts. To this end, the Esscher transform is adopted to specify an equivalent martingale probability measure. We show that reinsurers have various ways of levying the security loading on the net premiums to quantify the catastrophic liability in light of the growing challenges posed by emerging risks arising from climate change, cyberattacks, and pandemics. We numerically compare arbitrage-free catastrophe stop-loss reinsurance premiums via the Monte Carlo simulation method. Sensitivity analyzes are performed by changing the Esscher parameters and the retention level.
Analysis of a household-scale model for the invasion of Wolbachia into a resident mosquito population
Authors: Abby Barlow, Sarah Penington, Ben Adams
Date: 2025-02-18 00:00:00

In areas infested with Aedes aegypti mosquitoes it may be possible to control dengue, and some other vector-borne diseases, by introducing Wolbachia-infected mosquitoes into the wildtype population. Thus far, empirical and theoretical studies of Wolbachia release have tended to focus on the dynamics at the community scale. However, Ae. aegypti mosquitoes typically dwell in and around the same houses as the people they bite and it can be insightful to explore what happens at the household scale where small population sizes lead to inherently stochastic dynamics. Here we use a continuous-time Markov framework to develop a stochastic household model for small populations of wildtype and Wolbachia-infected mosquitoes. We investigate the transient and long term dynamics of the system, in particular examining the impact of stochasticity on the Wolbachia invasion threshold and bistability between the wildtype-only and Wolbachia-only steady states previously observed in deterministic models. We focus on the influence of key parameters which determine the fitness cost of Wolbachia infection and the probability of Wolbachia vertical transmission. Using Markov and matrix population theory, we derive salient characteristics of the system including the probability of successful Wolbachia invasion, the expected time until invasion and the probability that a Wolbachia-infected population reverts to a wildtype population. These attributes can inform strategies for the release of Wolbachia-infected mosquitoes. In addition, we find that releasing the minimum number of Wolbachia-infected mosquitoes required to displace a resident wildtype population according to the deterministic model, only results in that outcome about 20% of the time in the stochastic model; a significantly larger release is required to reach a steady state composed entirely of Wolbachia-infected mosquitoes 90% of the time.
Bayesian inference from time series of allele frequency data using exact simulation techniques
Authors: Jaromir Sant, Paul A. Jenkins, Jere Koskela, Dario Spano
Date: 2025-02-17 00:00:00
Tasks: Bayesian Inference, Time Series

A central statistical problem in population genetics is to infer evolutionary and biological parameters such as the strength of natural selection and allele age from DNA samples extracted from a contemporary population. That all samples come only from the present-day has long been known to limit statistical inference; there is potentially more information available if one also has access to ancient DNA so that inference is based on a time-series of historical changes in allele frequencies. We introduce a Markov Chain Monte Carlo (MCMC) method for Bayesian inference from allele frequency time-series data based on an underlying Wright--Fisher diffusion model of evolution, through which one can infer the parameters of essentially any selection model including those with frequency-dependent effects. The chief novelty is that we show this method to be exact in the sense that it is possible to augment the state space explored by MCMC with the unobserved diffusion trajectory, even though the transition function of this diffusion is intractable. Through careful design of a proposal distribution, we describe an efficient method in which updates to the trajectory and accept/reject decisions are calculated without error. We illustrate the method on data capturing changes in coat colour over the past 20,000 years, and find evidence to support previous findings that the mutant alleles ASIP and MC1R responsible for changes in coat color have experienced very strong, possibly overdominant, selection and further provide estimates for the ages of these genes.
Tight Generalization Bounds for Large-Margin Halfspaces
Authors: Kasper Green Larsen, Natascha Schalburg
Date: 2025-02-19 00:00:00
Tasks: Generalization Bounds

We prove the first generalization bound for large-margin halfspaces that is asymptotically tight in the tradeoff between the margin, the fraction of training points with the given margin, the failure probability and the number of training points.
Generalization error bound for denoising score matching under relaxed manifold assumption
Authors: Konstantin Yakovlev, Nikita Puchkin
Date: 2025-02-19 00:00:00
Tasks: Denoising, valid

We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away from the manifold. At the same time, we are still able to leverage a nice distribution structure. We derive non-asymptotic bounds on the approximation and generalization errors of the denoising score matching estimate. The rates of convergence are determined by the intrinsic dimension. Furthermore, our bounds remain valid even if we allow the ambient dimension grow polynomially with the sample size.
An Efficient Permutation-Based Kernel Two-Sample Test
Authors: Antoine Chatalic, Marco Letizia, Nicolas Schreuder, Lorenzo Rosasco
Date: 2025-02-19 00:00:00

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing, maximum mean discrepancy (MMD) has gained popularity as a test statistic due to its flexibility and strong theoretical foundations. However, its use in large-scale scenarios is plagued by high computational costs. In this work, we use a Nystr\"om approximation of the MMD to design a computationally efficient and practical testing algorithm while preserving statistical guarantees. Our main result is a finite-sample bound on the power of the proposed test for distributions that are sufficiently separated with respect to the MMD. The derived separation rate matches the known minimax optimal rate in this setting. We support our findings with a series of numerical experiments, emphasizing realistic scientific data.
Flow-based generative models as iterative algorithms in probability space
Authors: Yao Xie, Xiuyuan Cheng
Date: 2025-02-19 00:00:00
Tasks: Anomaly Detection, Density Estimation, Image Generation, Language Modeling, Language Modelling

Generative AI (GenAI) has revolutionized data-driven modeling by enabling the synthesis of high-dimensional data across various applications, including image generation, language modeling, biomedical signal processing, and anomaly detection. Flow-based generative models provide a powerful framework for capturing complex probability distributions, offering exact likelihood estimation, efficient sampling, and deterministic transformations between distributions. These models leverage invertible mappings governed by Ordinary Differential Equations (ODEs), enabling precise density estimation and likelihood evaluation. This tutorial presents an intuitive mathematical framework for flow-based generative models, formulating them as neural network-based representations of continuous probability densities. We explore key theoretical principles, including the Wasserstein metric, gradient flows, and density evolution governed by ODEs, to establish convergence guarantees and bridge empirical advancements with theoretical insights. By providing a rigorous yet accessible treatment, we aim to equip researchers and practitioners with the necessary tools to effectively apply flow-based generative models in signal processing and machine learning.
Asymptotic Optimism of Random-Design Linear and Kernel Regression Models
Authors: Hengrui Luo, Yunzhang Zhu
Date: 2025-02-18 00:00:00
Tasks: regression

We derived the closed-form asymptotic optimism of linear regression models under random designs, and generalizes it to kernel ridge regression. Using scaled asymptotic optimism as a generic predictive model complexity measure, we studied the fundamental different behaviors of linear regression model, tangent kernel (NTK) regression model and three-layer fully connected neural networks (NN). Our contribution is two-fold: we provided theoretical ground for using scaled optimism as a model predictive complexity measure; and we show empirically that NN with ReLUs behaves differently from kernel models under this measure. With resampling techniques, we can also compute the optimism for regression models with real data.
A Simplified and Numerically Stable Approach to the BG/NBD Churn Prediction model
Authors: Dylan Zammit, Christopher Zerafa
Date: 2025-02-18 00:00:00

This study extends the BG/NBD churn probability model, addressing its limitations in industries where customer behaviour is often influenced by seasonal events and possibly high purchase counts. We propose a modified definition of churn, considering a customer to have churned if they make no purchases within M days. Our contribution is twofold: First, we simplify the general equation for the specific case of zero purchases within M days. Second, we derive an alternative expression using numerical techniques to mitigate numerical overflow or underflow issues. This approach provides a more practical and robust method for predicting customer churn in industries with irregular purchase patterns.