pwc-archive/papers-with-abstracts huggingface dataset:
Spiking Neural Models for Decision-Making Tasks with Learning
Authors: Sophie Jaffard, Giulia Mezzadri, Patricia Reynaud-Bouret, Etienne Tanré
Date: 2025-06-10 00:00:00
Tasks: Decision Making

In cognition, response times and choices in decision-making tasks are commonly modeled using Drift Diffusion Models (DDMs), which describe the accumulation of evidence for a decision as a stochastic process, specifically a Brownian motion, with the drift rate reflecting the strength of the evidence. In the same vein, the Poisson counter model describes the accumulation of evidence as discrete events whose counts over time are modeled as Poisson processes, and has a spiking neurons interpretation as these processes are used to model neuronal activities. However, these models lack a learning mechanism and are limited to tasks where participants have prior knowledge of the categories. To bridge the gap between cognitive and biological models, we propose a biologically plausible Spiking Neural Network (SNN) model for decision-making that incorporates a learning mechanism and whose neurons activities are modeled by a multivariate Hawkes process. First, we show a coupling result between the DDM and the Poisson counter model, establishing that these two models provide similar categorizations and reaction times and that the DDM can be approximated by spiking Poisson neurons. To go further, we show that a particular DDM with correlated noise can be derived from a Hawkes network of spiking neurons governed by a local learning rule. In addition, we designed an online categorization task to evaluate the model predictions. This work provides a significant step toward integrating biologically relevant neural mechanisms into cognitive models, fostering a deeper understanding of the relationship between neural activity and behavior.
Smile asymptotic for Bachelier Implied Volatility
Authors: Roberto Baviera, Michele Domenico Massaria
Date: 2025-06-09 00:00:00

We investigate the asymptotic behaviour of the Implied Volatility in the Bachelier setting, extending the framework introduced by Benaim and Friz for the Black-Scholes setting. Exploiting the theory of regular variation, we derive explicit expressions for the Bachelier Implied Volatility in the wings of the smile, linking these to the tail behaviour of the underlying's returns' distribution. Furthermore, we establish a direct connection between the analyticity strip of the returns' characteristic function and the asymptotic formula for the Implied Volatility smile at extreme moneyness.
Accelerating Constrained Sampling: A Large Deviations Approach
Authors: Yingli Wang, Changwei Tu, Xiaoyu Wang, Lingjiong Zhu
Date: 2025-06-09 00:00:00

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC) based on the discretization of reflected Langevin dynamics (RLD) and more generally skew-reflected non-reversible Langevin Monte Carlo (SRNLMC) based on the discretization of skew-reflected non-reversible Langevin dynamics (SRNLD) have been proposed and studied in the literature. This work focuses on the long-time behavior of SRNLD, where a skew-symmetric matrix is added to RLD. Although the non-asymptotic convergence analysis for SRNLD (and SRNLMC) and the acceleration compared to RLD (and PMLC) have been studied in the literature, it is not clear how one should design the skew-symmetric matrix in the dynamics to achieve good performance in practice. We establish a large deviation principle (LDP) for the empirical measure of SRNLD when the skew-symmetric matrix is chosen such that its product with the inward unit normal vector field on the boundary is zero. By explicitly characterizing the rate functions, we show that SRNLD can accelerate the convergence to the target distribution compared to RLD with this choice of the skew-symmetric matrix. Numerical experiments for SRNLMC based on the proposed skew-symmetric matrix show superior performance which validate the theoretical findings from the large deviations theory.
Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds
Authors: Rishikesh Srinivasan, Dheeraj Nagaraj
Date: 2025-06-09 00:00:00

We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its convergence in the 2-Wasserstein distance ($W_2$), achieving a cubic speedup in dependence on the target accuracy ($\epsilon$) over the Euler-Maruyama discretization, surpassing existing bounds for randomized midpoint methods. Notably, in the case of underdamped Langevin dynamics, we demonstrate the complexity of $W_2$ convergence is much smaller than the complexity lower bounds for convergence in $L^2$ strong error established in the literature.
Enabling Probabilistic Learning on Manifolds through Double Diffusion Maps
Authors: Dimitris G Giovanis, Nikolaos Evangelou, Ioannis G Kevrekidis, Roger G Ghanem
Date: 2025-06-02 00:00:00
Tasks: Density Estimation

We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a limited (yet representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to uncover the intrinsic low-dimensional manifold structure, and (c) a reduced-order Ito Stochastic Differential Equation (ISDE) to sample from the learned distribution. A key challenge arises, however, when the number of available data points N is small and the dimensionality of the diffusion-map basis approaches N, resulting in overfitting and loss of generalization. To overcome this limitation, we propose an enabling extension that implements a synthesis of Double Diffusion Maps -- a technique capable of capturing multiscale geometric features of the data -- with Geometric Harmonics (GH), a nonparametric reconstruction method that allows smooth nonlinear interpolation in high-dimensional ambient spaces. This approach enables us to solve a full-order ISDE directly in the latent space, preserving the full dynamical complexity of the system, while leveraging its reduced geometric representation. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.
Variational Inference for Latent Variable Models in High Dimensions
Authors: Chenyang Zhong, Sumit Mukherjee, Bodhisattva Sen
Date: 2025-06-02 00:00:00
Tasks: Bayesian Inference, Variational Inference

Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifying the statistical accuracy of mean-field variational inference (MFVI) for posterior approximation in Bayesian latent variable models with categorical local latent variables. Utilizing our general framework, we capture the exact asymptotic regime where MFVI `works' for the celebrated latent Dirichlet allocation (LDA) model. Focusing on the mixed membership stochastic blockmodel (MMSB), we show that the vanilla fully factorized MFVI, often used in the literature, is suboptimal. We propose a partially grouped VI algorithm for this model and show that it works, and derive its exact asymptotic performance. We further illustrate that our bounds are tight for both the above models.
Path Signatures for Feature Extraction. An Introduction to the Mathematics Underpinning an Efficient Machine Learning Technique
Authors: Stephan Sturm
Date: 2025-06-02 00:00:00

We provide an introduction to the topic of path signatures as means of feature extraction for machine learning from data streams. The article stresses the mathematical theory underlying the signature methodology, highlighting the conceptual character without plunging into the technical details of rigorous proofs. These notes are based on an introductory presentation given to students of the Research Experience for Undergraduates in Industrial Mathematics and Statistics at Worcester Polytechnic Institute in June 2024.
Estimating Unobservable States in Stochastic Epidemic Models with Partial Information
Authors: Florent Ouabo Kamkumo, Ibrahim Mbouandi Njiasse, Ralf Wunderlich
Date: 2025-06-01 00:00:00

This article investigates stochastic epidemic models with partial information and addresses the estimation of current values of not directly observable states. The latter is also called nowcasting and related to the so-called "dark figure" problem, which concerns, for example, the estimation of unknown numbers of asymptomatic and undetected infections. The study is based on Ouabo Kamkumo et al. (2025), which provides detailed information about stochastic multi-compartment epidemic models with partial information and various examples. Starting point is a description of the state dynamics by a system of nonlinear stochastic recursions resulting from a time-discretization of a diffusion approximation of the underlying counting processes. The state vector is decomposed into an observable and an unobservable component. The latter is estimated from the observations using the extended Kalman filter approach in order to take into account the nonlinearity of the state dynamics. Numerical simulations for a Covid-19 model with partial information are presented to verify the performance and accuracy of the estimation method.
Towards an Explainable Comparison and Alignment of Feature Embeddings
Authors: Mohammad Jalali, Bahar Dibaei Nia, Farzan Farnia
Date: 2025-06-06 00:00:00

While several feature embedding models have been developed in the literature, comparisons of these embeddings have largely focused on their numerical performance in classification-related downstream applications. However, an interpretable comparison of different embeddings requires identifying and analyzing mismatches between sample groups clustered within the embedding spaces. In this work, we propose the \emph{Spectral Pairwise Embedding Comparison (SPEC)} framework to compare embeddings and identify their differences in clustering a reference dataset. Our approach examines the kernel matrices derived from two embeddings and leverages the eigendecomposition of the difference kernel matrix to detect sample clusters that are captured differently by the two embeddings. We present a scalable implementation of this kernel-based approach, with computational complexity that grows linearly with the sample size. Furthermore, we introduce an optimization problem using this framework to align two embeddings, ensuring that clusters identified in one embedding are also captured in the other model. We provide numerical results demonstrating the SPEC's application to compare and align embeddings on large-scale datasets such as ImageNet and MS-COCO. The code is available at [https://github.com/mjalali/embedding-comparison](github.com/mjalali/embedding-comparison).
Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
Authors: Vahan Arsenyan, Elen Vardanyan, Arnak Dalalyan
Date: 2025-06-11 00:00:00
Tasks: Denoising

Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guarantees in Wasserstein-2 distance that exhibit two key features: (i) they characterize and quantify the robustness of DDPMs to noisy score estimates, and (ii) they achieve faster convergence rates than previously known results. Furthermore, we observe that the obtained rates match those known in the Gaussian case, implying their optimality.
Strongly Consistent Community Detection in Popularity Adjusted Block Models
Authors: Quan Yuan, Binghui Liu, Danning Li, Lingzhou Xue
Date: 2025-06-08 00:00:00
Tasks: Clustering, Community Detection

The Popularity Adjusted Block Model (PABM) provides a flexible framework for community detection in network data by allowing heterogeneous node popularity across communities. However, this flexibility increases model complexity and raises key unresolved challenges, particularly in effectively adapting spectral clustering techniques and efficiently achieving strong consistency in label recovery. To address these challenges, we first propose the Thresholded Cosine Spectral Clustering (TCSC) algorithm and establish its weak consistency under the PABM. We then introduce the one-step Refined TCSC algorithm and prove that it achieves strong consistency under the PABM, correctly recovering all community labels with high probability. We further show that the two-step Refined TCSC accelerates clustering error convergence, especially with small sample sizes. Additionally, we propose a data-driven approach for selecting the number of communities, which outperforms existing methods under the PABM. The effectiveness and robustness of our methods are validated through extensive simulations and real-world applications.
On the Benefits of Accelerated Optimization in Robust and Private Estimation
Authors: Laurentiu Andrei Marchis, Po-Ling Loh
Date: 2025-06-03 00:00:00

We study the advantages of accelerated gradient methods, specifically based on the Frank-Wolfe method and projected gradient descent, for privacy and heavy-tailed robustness. Our approaches are as follows: For the Frank-Wolfe method, our technique is based on a tailored learning rate and a uniform lower bound on the gradient of the $\ell_2$-norm over the constraint set. For accelerating projected gradient descent, we use the popular variant based on Nesterov's momentum, and we optimize our objective over $\mathbb{R}^p$. These accelerations reduce iteration complexity, translating into stronger statistical guarantees for empirical and population risk minimization. Our analysis covers three settings: non-random data, random model-free data, and parametric models (linear regression and generalized linear models). Methodologically, we approach both privacy and robustness based on noisy gradients. We ensure differential privacy via the Gaussian mechanism and advanced composition, and we achieve heavy-tailed robustness using a geometric median-of-means estimator, which also sharpens the dependency on the dimension of the covariates. Finally, we compare our rates to existing bounds and identify scenarios where our methods attain optimal convergence.
Sample complexity of Schrödinger potential estimation
Authors: Nikita Puchkin, Iurii Pustovalov, Yuri Sapronov, Denis Suchkov, Alexey Naumov, Denis Belomestny
Date: 2025-06-03 00:00:00

We address the problem of Schr\"odinger potential estimation, which plays a crucial role in modern generative modelling approaches based on Schr\"odinger bridges and stochastic optimal control for SDEs. Given a simple prior diffusion process, these methods search for a path between two given distributions $\rho_0$ and $\rho_T^*$ requiring minimal efforts. The optimal drift in this case can be expressed through a Schr\"odinger potential. In the present paper, we study generalization ability of an empirical Kullback-Leibler (KL) risk minimizer over a class of admissible log-potentials aimed at fitting the marginal distribution at time $T$. Under reasonable assumptions on the target distribution $\rho_T^*$ and the prior process, we derive a non-asymptotic high-probability upper bound on the KL-divergence between $\rho_T^*$ and the terminal density corresponding to the estimated log-potential. In particular, we show that the excess KL-risk may decrease as fast as $O(\log^2 n / n)$ when the sample size $n$ tends to infinity even if both $\rho_0$ and $\rho_T^*$ have unbounded supports.
Assumption-free stability for ranking problems
Authors: Ruiting Liang, Jake A. Soloff, Rina Foygel Barber, Rebecca Willett
Date: 2025-06-02 00:00:00
Tasks: Informativeness

In this work, we consider ranking problems among a finite set of candidates: for instance, selecting the top-$k$ items among a larger list of candidates or obtaining the full ranking of all items in the set. These problems are often unstable, in the sense that estimating a ranking from noisy data can exhibit high sensitivity to small perturbations. Concretely, if we use data to provide a score for each item (say, by aggregating preference data over a sample of users), then for two items with similar scores, small fluctuations in the data can alter the relative ranking of those items. Many existing theoretical results for ranking problems assume a separation condition to avoid this challenge, but real-world data often contains items whose scores are approximately tied, limiting the applicability of existing theory. To address this gap, we develop a new algorithmic stability framework for ranking problems, and propose two novel ranking operators for achieving stable ranking: the \emph{inflated top-$k$} for the top-$k$ selection problem and the \emph{inflated full ranking} for ranking the full list. To enable stability, each method allows for expressing some uncertainty in the output. For both of these two problems, our proposed methods provide guaranteed stability, with no assumptions on data distributions and no dependence on the total number of candidates to be ranked. Experiments on real-world data confirm that the proposed methods offer stability without compromising the informativeness of the output.
Active Learning via Regression Beyond Realizability
Authors: Atul Ganju, Shashaank Aiyer, Ved Sriraman, Karthik Sridharan
Date: 2025-05-31 00:00:00
Tasks: Active Learning, regression

We present a new active learning framework for multiclass classification based on surrogate risk minimization that operates beyond the standard realizability assumption. Existing surrogate-based active learning algorithms crucially rely on realizability$\unicode{x2014}$the assumption that the optimal surrogate predictor lies within the model class$\unicode{x2014}$limiting their applicability in practical, misspecified settings. In this work we show that under conditions significantly weaker than realizability, as long as the class of models considered is convex, one can still obtain a label and sample complexity comparable to prior work. Despite achieving similar rates, the algorithmic approaches from prior works can be shown to fail in non-realizable settings where our assumption is satisfied. Our epoch-based active learning algorithm departs from prior methods by fitting a model from the full class to the queried data in each epoch and returning an improper classifier obtained by aggregating these models.
Riemannian Principal Component Analysis
Authors: Oldemar Rodríguez
Date: 2025-05-30 00:00:00
Tasks: Dimensionality Reduction

This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge addressed is the lack of vector space operations on such manifolds. Fletcher et al., in their work {\em Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape}, proposed Principal Geodesic Analysis (PGA) as a geometric approach to analyze data on Riemannian manifolds, particularly effective for structured datasets like medical images, where the manifold's intrinsic structure is apparent. However, PGA's applicability is limited when dealing with general datasets that lack an implicit local distance notion. In this work, we introduce a generalized framework, termed {\em Riemannian Principal Component Analysis (R-PCA)}, to extend PGA for any data endowed with a local distance structure. Specifically, we adapt the PCA methodology to Riemannian manifolds by equipping data tables with local metrics, enabling the incorporation of manifold geometry. This framework provides a unified approach for dimensionality reduction and statistical analysis directly on manifolds, opening new possibilities for datasets with region-specific or part-specific distance notions, ensuring respect for their intrinsic geometric properties.
Immunological mechanisms and immunoregulatory strategies in intervertebral disc degeneration
Authors: Xianyi Yan, Xi Wang, Ying Che, Peng Feng, Ting Zhang
Date: 2025-06-11 00:00:00

Intervertebral discs are avascular and maintain immune privilege. However, during intervertebral disc degeneration (IDD), this barrier is disrupted, leading to extensive immune cell infiltration and localized inflammation. In degenerated discs, macrophages, T lymphocytes, neutrophils, and granulocytic myeloid-derived suppressor cells (G-MDSCs) are key players, exhibiting functional heterogeneity. Dysregulated activation of inflammatory pathways, including nuclear factor kappa-B (NF-kappaB), interleukin-17 (IL-17), and nucleotide-binding oligomerization domain-like receptor protein 3 (NLRP3) inflammasome activation, drives local pro-inflammatory responses, leading to cell apoptosis and extracellular matrix (ECM) degradation. Innovative immunotherapies, including exosome-based treatments, CRISPR/Cas9-mediated gene editing, and chemokine-loaded hydrogel systems, have shown promise in reshaping the immunological niche of intervertebral discs. These strategies can modulate dysregulated immune responses and create a supportive environment for tissue regeneration. However, current studies have not fully elucidated the mechanisms of inflammatory memory and the immunometabolic axis, and they face challenges in balancing tissue regeneration with immune homeostasis. Future studies should employ interdisciplinary approaches such as single-cell and spatial transcriptomics to map a comprehensive immune atlas of IDD, elucidate intercellular crosstalk and signaling networks, and develop integrated therapies combining targeted immunomodulation with regenerative engineering, thereby facilitating the clinical translation of effective IDD treatments.