pwc-archive/papers-with-abstracts huggingface dataset:
Greedy Selection under Independent Increments: A Toy Model Analysis
Authors: Huitao Yang
Date: 2025-06-22 00:00:00

We study an iterative selection problem over N i.i.d. discrete-time stochastic processes with independent increments. At each stage, a fixed number of processes are retained based on their observed values. Under this simple model, we prove that the optimal strategy for selecting the final maximum-value process is to apply greedy selection at each stage. While the result relies on strong independence assumptions, it offers a clean justification for greedy heuristics in multi-stage elimination settings and may serve as a toy example for understanding related algorithms in high-dimensional applications.
On Design of Representative Distributionally Robust Formulations for Evaluation of Tail Risk Measures
Authors: Anand Deo
Date: 2025-06-19 00:00:00

Conditional Value-at-Risk (CVaR) is a risk measure widely used to quantify the impact of extreme losses. Owing to the lack of representative samples CVaR is sensitive to the tails of the underlying distribution. In order to combat this sensitivity, Distributionally Robust Optimization (DRO), which evaluates the worst-case CVaR measure over a set of plausible data distributions is often deployed. Unfortunately, an improper choice of the DRO formulation can lead to a severe underestimation of tail risk. This paper aims at leveraging extreme value theory to arrive at a DRO formulation which leads to representative worst-case CVaR evaluations in that the above pitfall is avoided while simultaneously, the worst case evaluation is not a gross over-estimate of the true CVaR. We demonstrate theoretically that even when there is paucity of samples in the tail of the distribution, our formulation is readily implementable from data, only requiring calibration of a single scalar parameter. We showcase that our formulation can be easily extended to provide robustness to tail risk in multivariate applications as well as in the evaluation of other commonly used risk measures. Numerical illustrations on synthetic and real-world data showcase the practical utility of our approach.
Sampling conditioned diffusions via Pathspace Projected Monte Carlo
Authors: Tobias Grafke
Date: 2025-06-17 00:00:00

We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace Metropolis-adjusted manifold sampling scheme, which samples stochastic paths on the submanifold of realizations that adhere to the conditioning constraint. We demonstrate the effectiveness of the algorithm by sampling a dynamical condensation phase transition, conditioning a random walk on a fixed Levy stochastic area, conditioning a stochastic nonlinear wave equation on high amplitude waves, and sampling a stochastic partial differential equation model of turbulent pipe flow conditioned on relaminarization events.
Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $\mathbb{so}(d)$
Authors: Amit Daniely
Date: 2025-06-14 00:00:00

We show that adversarial examples exist for various random convolutional networks, and furthermore, that this is a relatively simple consequence of the isoperimetric inequality on the special orthogonal group $\mathbb{so}(d)$. This extends and simplifies a recent line of work which shows similar results for random fully connected networks.
Credit risk for large portfolios of green and brown loans: extending the ASRF model
Authors: Alessandro Ramponi, Sergio Scarlatti
Date: 2025-06-14 00:00:00

We propose a credit risk model for portfolios composed of green and brown loans, extending the ASRF framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, CDO pricing, and empirical analysis of green loan portfolios.
Multi-dimensional queue-reactive model and signal-driven models: a unified framework
Authors: Emmanouil Sfendourakis
Date: 2025-06-13 00:00:00

We present a Markovian market model driven by a hidden Brownian efficient price. In particular, we extend the queue-reactive model, making its dynamics dependent on the efficient price. Our study focuses on two sub-models: a signal-driven price model where the mid-price jump rates depend on the efficient price and an observable signal, and the usual queue-reactive model dependent on the efficient price via the intensities of the order arrivals. This way, we are able to correlate the evolution of limit order books of different stocks. We prove the stability of the observed mid-price around the efficient price under natural assumptions. Precisely, we show that at the macroscopic scale, prices behave as diffusions. We also develop a maximum likelihood estimation procedure for the model, and test it numerically. Our model is them used to backest trading strategies in a liquidation context.
Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments
Authors: Yaroslav Kivva, Sina Akbari, Saber Salehkaleybar, Negar Kiyavash
Date: 2025-06-13 00:00:00

We investigate the estimation of the causal effect of a treatment variable on an outcome in the presence of a latent confounder. We first show that the causal effect is identifiable under certain conditions when data is available from multiple environments, provided that the target causal effect remains invariant across these environments. Secondly, we propose a moment-based algorithm for estimating the causal effect as long as only a single parameter of the data-generating mechanism varies across environments -- whether it be the exogenous noise distribution or the causal relationship between two variables. Conversely, we prove that identifiability is lost if both exogenous noise distributions of both the latent and treatment variables vary across environments. Finally, we propose a procedure to identify which parameter of the data-generating mechanism has varied across the environments and evaluate the performance of our proposed methods through experiments on synthetic data.
Robust Alignment via Partial Gromov-Wasserstein Distances
Authors: Xiaoyun Gong, Sloan Nietert, Ziv Goldfeld
Date: 2025-06-26 00:00:00

The Gromov-Wasserstein (GW) problem provides a powerful framework for aligning heterogeneous datasets by matching their internal structures in a way that minimizes distortion. However, GW alignment is sensitive to data contamination by outliers, which can greatly distort the resulting matching scheme. To address this issue, we study robust GW alignment, where upon observing contaminated versions of the clean data distributions, our goal is to accurately estimate the GW alignment cost between the original (uncontaminated) measures. We propose an estimator based on the partial GW distance, which trims out a fraction of the mass from each distribution before optimally aligning the rest. The estimator is shown to be minimax optimal in the population setting and is near-optimal in the finite-sample regime, where the optimality gap originates only from the suboptimality of the plug-in estimator in the empirical estimation setting (i.e., without contamination). Towards the analysis, we derive new structural results pertaining to the approximate pseudo-metric structure of the partial GW distance. Overall, our results endow the partial GW distance with an operational meaning by posing it as a robust surrogate of the classical distance when the observed data may be contaminated.
Wild refitting for black box prediction
Authors: Martin J. Wainwright
Date: 2025-06-26 00:00:00
Tasks: Image Restoration, Prediction

We describe and analyze a computionally efficient refitting procedure for computing high-probability upper bounds on the instance-wise mean-squared prediction error of penalized nonparametric estimates based on least-squares minimization. Requiring only a single dataset and black box access to the prediction method, it consists of three steps: computing suitable residuals, symmetrizing and scaling them with a pre-factor $\rho$, and using them to define and solve a modified prediction problem recentered at the current estimate. We refer to it as wild refitting, since it uses Rademacher residual symmetrization as in a wild bootstrap variant. Under relatively mild conditions allowing for noise heterogeneity, we establish a high probability guarantee on its performance, showing that the wild refit with a suitably chosen wild noise scale $\rho$ gives an upper bound on prediction error. This theoretical analysis provides guidance into the design of such procedures, including how the residuals should be formed, the amount of noise rescaling in the wild sub-problem needed for upper bounds, and the local stability properties of the block-box procedure. We illustrate the applicability of this procedure to various problems, including non-rigid structure-from-motion recovery with structured matrix penalties; plug-and-play image restoration with deep neural network priors; and randomized sketching with kernel methods.
Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution
Authors: Lukas Sablica, Kurt Hornik
Date: 2025-06-26 00:00:00

We propose a novel variational autoencoder (VAE) architecture that employs a spherical Cauchy (spCauchy) latent distribution. Unlike traditional Gaussian latent spaces or the widely used von Mises-Fisher (vMF) distribution, spCauchy provides a more natural hyperspherical representation of latent variables, better capturing directional data while maintaining flexibility. Its heavy-tailed nature prevents over-regularization, ensuring efficient latent space utilization while offering a more expressive representation. Additionally, spCauchy circumvents the numerical instabilities inherent to vMF, which arise from computing normalization constants involving Bessel functions. Instead, it enables a fully differentiable and efficient reparameterization trick via M\"obius transformations, allowing for stable and scalable training. The KL divergence can be computed through a rapidly converging power series, eliminating concerns of underflow or overflow associated with evaluation of ratios of hypergeometric functions. These properties make spCauchy a compelling alternative for VAEs, offering both theoretical advantages and practical efficiency in high-dimensional generative modeling.
An introduction to Causal Modelling
Authors: Gauranga Kumar Baishya
Date: 2025-06-19 00:00:00
Tasks: Blocking, counterfactual, Counterfactual Reasoning

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments and potential outcomes. We discuss causal effect measures-including average treatment effects on the treated and on the untreated-and choices of effect scales for binary outcomes. We derive identification in randomized experiments under exchangeability and consistency, and extend to stratification and blocking designs. We present inverse probability weighting with propensity score estimation and robust inference via sandwich estimators. Finally, we introduce causal graphs, d-separation, the backdoor criterion, single-world intervention graphs, and structural equation models, showing how graphical and potential-outcome approaches complement each other. Emphasis is placed on clear notation, intuitive explanations, and practical examples for applied researchers.
Lower Bounds on the Size of Markov Equivalence Classes
Authors: Erik Jahn, Frederick Eberhardt, Leonard J. Schulman
Date: 2025-06-26 00:00:00
Tasks: Causal Discovery

Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.
The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series
Authors: Pola Bereta, Ioannis Diamantis
Date: 2025-06-24 00:00:00
Tasks: Clustering, Marketing, Time Series, Topological Data Analysis

Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time-series data present challenges for effective clustering. This study evaluates three unsupervised clustering approaches, Symbolic Aggregate approXimation (SAX), enhanced SAX (eSAX), and Topological Data Analysis (TDA), applied to 20 Google Trends keywords representing major consumer categories. Our results show that while SAX and eSAX offer fast and interpretable clustering for stable time series, they struggle with volatility and complexity, often producing ambiguous ``catch-all'' clusters. TDA, by contrast, captures global structural features through persistent homology and achieves more balanced and meaningful groupings. We conclude with practical guidance for using symbolic and topological methods in consumer analytics and suggest that hybrid approaches combining both perspectives hold strong potential for future applications.
Cross-regularization: Adaptive Model Complexity through Validation Gradients
Authors: Carlos Stein Brito
Date: 2025-06-24 00:00:00
Tasks: Data Augmentation

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The method splits parameter optimization - training data guides feature learning while validation data shapes complexity controls - converging provably to cross-validation optima. When implemented through noise injection in neural networks, this approach reveals striking patterns: unexpectedly high noise tolerance and architecture-specific regularization that emerges organically during training. Beyond complexity control, the framework integrates seamlessly with data augmentation, uncertainty calibration and growing datasets while maintaining single-run efficiency through a simple gradient-based approach.
When Can We Reuse a Calibration Set for Multiple Conformal Predictions?
Authors: A. A. Balinsky, A. D. Balinsky
Date: 2025-06-24 00:00:00
Tasks: Conformal Prediction, Prediction, Uncertainty Quantification

Reliable uncertainty quantification is crucial for the trustworthiness of machine learning applications. Inductive Conformal Prediction (ICP) offers a distribution-free framework for generating prediction sets or intervals with user-specified confidence. However, standard ICP guarantees are marginal and typically require a fresh calibration set for each new prediction to maintain their validity. This paper addresses this practical limitation by demonstrating how e-conformal prediction, in conjunction with Hoeffding's inequality, can enable the repeated use of a single calibration set with a high probability of preserving the desired coverage. Through a case study on the CIFAR-10 dataset, we train a deep neural network and utilise a calibration set to estimate a Hoeffding correction. This correction allows us to apply a modified Markov's inequality, leading to the construction of prediction sets with quantifiable confidence. Our results illustrate the feasibility of maintaining provable performance in conformal prediction while enhancing its practicality by reducing the need for repeated calibration. The code for this work is publicly available.
Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives
Authors: Sivaraman Balakrishnan, Tudor Manole, Larry Wasserman
Date: 2025-06-23 00:00:00

In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified cost. In this paper we review recent advances in estimating and developing limit theorems for the OT map, using samples from the underlying distributions. We also review parallel lines of work that establish similar results for special cases and variants of the basic OT setup. We conclude with a discussion of key directions for future research with the goal of providing practitioners with reliable inferential tools.
A Random Matrix Analysis of In-context Memorization for Nonlinear Attention
Authors: Zhenyu Liao, Jiaqing Liu, Tianqi Hou, Difan Zou, Zenan Ling
Date: 2025-06-23 00:00:00
Tasks: Memorization

Attention mechanisms have revolutionized machine learning (ML) by enabling efficient modeling of global dependencies across inputs. Their inherently parallelizable structures allow for efficient scaling with the exponentially increasing size of both pretrained data and model parameters. Yet, despite their central role as the computational backbone of modern large language models (LLMs), the theoretical understanding of Attentions, especially in the nonlinear setting, remains limited. In this paper, we provide a precise characterization of the \emph{in-context memorization error} of \emph{nonlinear Attention}, in the high-dimensional proportional regime where the number of input tokens $n$ and their embedding dimension $p$ are both large and comparable. Leveraging recent advances in the theory of large kernel random matrices, we show that nonlinear Attention typically incurs higher memorization error than linear ridge regression on random inputs. However, this gap vanishes, and can even be reversed, when the input exhibits statistical structure, particularly when the Attention weights align with the input signal direction. Our results reveal how nonlinearity and input structure interact with each other to govern the memorization performance of nonlinear Attention. The theoretical insights are supported by numerical experiments.
Distributed Poisson multi-Bernoulli filtering via generalised covariance intersection
Authors: Ángel F. García-Fernández, Giorgio Battistelli
Date: 2025-06-23 00:00:00
Tasks: Future prediction

This paper presents the distributed Poisson multi-Bernoulli (PMB) filter based on the generalised covariance intersection (GCI) fusion rule for distributed multi-object filtering. Since the exact GCI fusion of two PMB densities is intractable, we derive a principled approximation. Specifically, we approximate the power of a PMB density as an unnormalised PMB density, which corresponds to an upper bound of the PMB density. Then, the GCI fusion rule corresponds to the normalised product of two unnormalised PMB densities. We show that the result is a Poisson multi-Bernoulli mixture (PMBM), which can be expressed in closed form. Future prediction and update steps in each filter preserve the PMBM form, which can be projected back to a PMB density before the next fusion step. Experimental results show the benefits of this approach compared to other distributed multi-object filters.
Identifiable Convex-Concave Regression via Sub-gradient Regularised Least Squares
Authors: William Chung
Date: 2025-06-22 00:00:00
Tasks: Benchmarking, regression

We propose a novel nonparametric regression method that models complex input-output relationships as the sum of convex and concave components. The method-Identifiable Convex-Concave Nonparametric Least Squares (ICCNLS)-decomposes the target function into additive shape-constrained components, each represented via sub-gradient-constrained affine functions. To address the affine ambiguity inherent in convex-concave decompositions, we introduce global statistical orthogonality constraints, ensuring that residuals are uncorrelated with both intercept and input variables. This enforces decomposition identifiability and improves interpretability. We further incorporate L1, L2 and elastic net regularisation on sub-gradients to enhance generalisation and promote structural sparsity. The proposed method is evaluated on synthetic and real-world datasets, including healthcare pricing data, and demonstrates improved predictive accuracy and model simplicity compared to conventional CNLS and difference-of-convex (DC) regression approaches. Our results show that statistical identifiability, when paired with convex-concave structure and sub-gradient regularisation, yields interpretable models suited for forecasting, benchmarking, and policy evaluation.
Multi-Armed Bandits With Machine Learning-Generated Surrogate Rewards
Authors: Wenlong Ji, Yihan Pan, Ruihao Zhu, Lihua Lei
Date: 2025-06-20 00:00:00
Tasks: Decision Making Under Uncertainty, Multi-Armed Bandits, Sequential Decision Making

Multi-armed bandit (MAB) is a widely adopted framework for sequential decision-making under uncertainty. Traditional bandit algorithms rely solely on online data, which tends to be scarce as it must be gathered during the online phase when the arms are actively pulled. However, in many practical settings, rich auxiliary data, such as covariates of past users, is available prior to deploying any arms. We introduce a new setting for MAB where pre-trained machine learning (ML) models are applied to convert side information and historical data into \emph{surrogate rewards}. A prominent feature of this setting is that the surrogate rewards may exhibit substantial bias, as true reward data is typically unavailable in the offline phase, forcing ML predictions to heavily rely on extrapolation. To address the issue, we propose the Machine Learning-Assisted Upper Confidence Bound (MLA-UCB) algorithm, which can be applied to any reward prediction model and any form of auxiliary data. When the predicted and true rewards are jointly Gaussian, it provably improves the cumulative regret, provided that the correlation is non-zero -- even in cases where the mean surrogate reward completely misaligns with the true mean rewards. Notably, our method requires no prior knowledge of the covariance matrix between true and surrogate rewards. We compare MLA-UCB with the standard UCB on a range of numerical studies and show a sizable efficiency gain even when the size of the offline data and the correlation between predicted and true rewards are moderate.