pwc-archive/papers-with-abstracts huggingface dataset:
Revenue Optimization with Price-Sensitive and Interdependent Demand
Authors: Julien Laasri, Marc Revol
Date: 2025-05-22 00:00:00
Tasks: Management

As Kalyan T. Talluri and Garrett J. Van Ryzin describe in their work [3], Revenue Management aims to maximize an organization's revenue by considering three types of decision categories: structural, pricing, and quantity. In this document, our primary focus will be on decisions related to pricing and quantity for the sale of airline tickets on a direct flight over a certain number of time periods. More specifically, we will only focus on the optimization aspect of this problem. We will assume the demand data to be given, since Air France estimates it beforehand using real data. Similarly, we assume all price options to be predetermined by Air France's algorithms and verified by their analysts. Our objective will be to maximize the revenue of a direct flight by choosing the prices for each product from the predefined set of options. -- Comme d\'ecrit par Kalyan T. Talluri et Garrett J. Van Ryzin dans leur ouvrage [3], le Revenue Management consiste en la maximisation du revenu d'un organisme \`a partir de trois types de cat\'egories de d\'ecision : structurelles, prix et quantit\'e. Dans ce document, nous nous int\'eresserons principalement aux d\'ecisions de type prix et quantit\'e pour la vente de billets d'avion sur un vol direct au cours d'un certain nombre de pas de temps. Plus pr\'ecis\'ement, nous nous situerons dans la partie optimisation du probl\`eme. Nous prendrons ainsi les donn\'ees de demande comme acquises, car elles sont estim\'ees au pr\'ealable par Air France \`a partir des donn\'ees r\'eelles. De m\^eme, pour chaque produit que l'on cherchera \`a vendre, on nous impose en amont les prix possibles que l'on a droit d'utiliser et qui se basent sur des algorithmes d'Air France dont les r\'esultats sont v\'erifi\'es par des analystes. Notre but sera alors de maximiser le revenu d'un vol direct en choisissant les prix de chaque produit parmi ceux impos\'es.
Meta-reinforcement learning with minimum attention
Authors: Pilhwa Lee, Shashank Gupta
Date: 2025-05-22 00:00:00
Tasks: Meta-Learning, Meta Reinforcement Learning, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

Minimum attention applies the least action principle in the changes of control concerning state and time, first proposed by Brockett. The involved regularization is highly relevant in emulating biological control, such as motor learning. We apply minimum attention in reinforcement learning (RL) as part of the rewards and investigate its connection to meta-learning and stabilization. Specifically, model-based meta-learning with minimum attention is explored in high-dimensional nonlinear dynamics. Ensemble-based model learning and gradient-based meta-policy learning are alternately performed. Empirically, we show that the minimum attention does show outperforming competence in comparison to the state-of-the-art algorithms in model-free and model-based RL, i.e., fast adaptation in few shots and variance reduction from the perturbations of the model and environment. Furthermore, the minimum attention demonstrates the improvement in energy efficiency.
Arrival Control in Quasi-Reversible Queueing Systems: Optimization and Reinforcement Learning
Authors: Céline Comte, Pascal Moyal
Date: 2025-05-22 00:00:00

In this paper, we introduce a versatile scheme for optimizing the arrival rates of quasi-reversible queueing systems. We first propose an alternative definition of quasi-reversibility that encompasses reversibility and highlights the importance of the definition of customer classes. In a second time, we introduce balanced arrival control policies, which generalize the notion of balanced arrival rates introduced in the context of Whittle networks, to the much broader class of quasi-reversible queueing systems. We prove that supplementing a quasi-reversible queueing system with a balanced arrival-control policy preserves the quasi-reversibility, and we specify the form of the stationary measures. We revisit two canonical examples of quasi-reversible queueing systems, Whittle networks and order-independent queues. Lastly, we focus on the problem of admission control and leverage our results in the frameworks of optimization and reinforcement learning.
Dimension-adapted Momentum Outscales SGD
Authors: Damien Ferbach, Katie Everett, Gauthier Gidel, Elliot Paquette, Courtney Paquette
Date: 2025-05-22 00:00:00

We investigate scaling laws for stochastic momentum algorithms with small batch on the power law random features model, parameterized by data complexity, target complexity, and model size. When trained with a stochastic momentum algorithm, our analysis reveals four distinct loss curve shapes determined by varying data-target complexities. While traditional stochastic gradient descent with momentum (SGD-M) yields identical scaling law exponents to SGD, dimension-adapted Nesterov acceleration (DANA) improves these exponents by scaling momentum hyperparameters based on model size and data complexity. This outscaling phenomenon, which also improves compute-optimal scaling behavior, is achieved by DANA across a broad range of data and target complexities, while traditional methods fall short. Extensive experiments on high-dimensional synthetic quadratics validate our theoretical predictions and large-scale text experiments with LSTMs show DANA's improved loss exponents over SGD hold in a practical setting.
Critical Points of Random Neural Networks
Authors: Simmaco Di Lillo
Date: 2025-05-22 00:00:00

This work investigates the expected number of critical points of random neural networks with different activation functions as the depth increases in the infinite-width limit. Under suitable regularity conditions, we derive precise asymptotic formulas for the expected number of critical points of fixed index and those exceeding a given threshold. Our analysis reveals three distinct regimes depending on the value of the first derivative of the covariance evaluated at 1: the expected number of critical points may converge, grow polynomially, or grow exponentially with depth. The theoretical predictions are supported by numerical experiments. Moreover, we provide numerical evidence suggesting that, when the regularity condition is not satisfied (e.g. for neural networks with ReLU as activation function), the number of critical points increases as the map resolution increases, indicating a potential divergence in the number of critical points.
Sharp concentration of uniform generalization errors in binary linear classification
Authors: Shogo Nakakita
Date: 2025-05-22 00:00:00

We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincar\'{e} and log-Sobolev inequalities for the joint distribution of the output labels and the label-weighted input vectors, which we apply to derive concentration bounds. The derived concentration bounds are sharp up to moderate multiplicative constants by those under well-balanced labels. In asymptotic analysis, we also show that almost sure convergence of uniform generalization errors to their expectation occurs in very broad settings, such as proportionally high-dimensional regimes. Using this convergence, we establish uniform laws of large numbers under dimension-free conditions.
Generalized Power Priors for Improved Bayesian Inference with Historical Data
Authors: Masanari Kimura, Howard Bondell
Date: 2025-05-22 00:00:00
Tasks: Bayesian Inference

The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and adaptability. A key property of the power prior is that the resulting posterior minimizes a linear combination of KL divergences between two pseudo-posterior distributions: one ignoring historical data and the other fully incorporating it. We extend this framework by identifying the posterior distribution as the minimizer of a linear combination of Amari's $\alpha$-divergence, a generalization of KL divergence. We show that this generalization can lead to improved performance by allowing for the data to adapt to appropriate choices of the $\alpha$ parameter. Theoretical properties of this generalized power posterior are established, including behavior as a generalized geodesic on the Riemannian manifold of probability distributions, offering novel insights into its geometric interpretation.
Directional Convergence, Benign Overfitting of Gradient Descent in leaky ReLU two-layer Neural Networks
Authors: Ichiro Hashimoto
Date: 2025-05-22 00:00:00

In this paper, we prove directional convergence of network parameters of fixed width leaky ReLU two-layer neural networks optimized by gradient descent with exponential loss, which was previously only known for gradient flow. By a careful analysis of the convergent direction, we establish sufficient conditions of benign overfitting and discover a new phase transition in the test error bound. All of these results hold beyond the nearly orthogonal data setting which was studied in prior works. As an application, we demonstrate that benign overfitting occurs with high probability in sub-Gaussian mixture models.
Selective profiling of non-canonical nucleic acid structures via size-discriminative supramolecular probes
Authors: Runyu Shi, Dan Huang, Yanxi Wang, Qiuju Zhou, Zhenzhen Zhao, Binwu Ying, Qianfan Yang, Feng Li
Date: 2025-05-21 00:00:00

Nucleic acids can form diverse non-canonical structures, such as G-quadruplexes (G4s) and i-motifs (iMs), which are critical in biological processes and disease pathways. This study presents an innovative probe design strategy based on groove size differences, leading to the development of BT-Cy-1, a supramolecular cyanine probe optimized by fine-tuning dimer "thickness". BT-Cy-1 demonstrated high sensitivity in detecting structural transitions and variations in G4s and iMs, even in complex environments with excess dsDNA. Applied to clinical blood samples, it revealed significant differences in RNA G4 and iM levels between liver cancer patients and healthy individuals, marking the first report of altered iM levels in clinical samples. This work highlights a novel approach for precise nucleic acid structural profiling, offering insights into their biological significance and potential in disease diagnostics.
Learning Genomic Structure from $k$-mers
Authors: Filip Thor, Carl Nettelblad
Date: 2025-05-22 00:00:00
Tasks: Contrastive Learning

Sequencing a genome to determine an individual's DNA produces an enormous number of short nucleotide subsequences known as reads, which must be reassembled to reconstruct the full genome. We present a method for analyzing this type of data using contrastive learning, in which an encoder model is trained to produce embeddings that cluster together sequences from the same genomic region. The sequential nature of genomic regions is preserved in the form of trajectories through this embedding space. Trained solely to reflect the structure of the genome, the resulting model provides a general representation of $k$-mer sequences, suitable for a range of downstream tasks involving read data. We apply our framework to learn the structure of the $E.\ coli$ genome, and demonstrate its use in simulated ancient DNA (aDNA) read mapping and identification of structural variations. Furthermore, we illustrate the potential of using this type of model for metagenomic species identification. We show how incorporating a domain-specific noise model can enhance embedding robustness, and how a supervised contrastive learning setting can be adopted when a linear reference genome is available, by introducing a distance thresholding parameter $\Gamma$. The model can also be trained fully self-supervised on read data, enabling analysis without the need to construct a full genome assembly using specialized algorithms. Small prediction heads based on a pre-trained embedding are shown to perform on par with BWA-aln, the current gold standard approach for aDNA mapping, in terms of accuracy and runtime for short genomes. Given the method's favorable scaling properties with respect to total genome size, inference using our approach is highly promising for metagenomic applications and for mapping to genomes comparable in size to the human genome.
Multi-omic Causal Discovery using Genotypes and Gene Expression
Authors: Stephen Asiedu, David Watson
Date: 2025-05-21 00:00:00
Tasks: Causal Discovery, Drug Discovery

Causal discovery in multi-omic datasets is crucial for understanding the bigger picture of gene regulatory mechanisms, but remains challenging due to high dimensionality, differentiation of direct from indirect relationships, and hidden confounders. We introduce GENESIS (GEne Network inference from Expression SIgnals and SNPs), a constraint-based algorithm that leverages the natural causal precedence of genotypes to infer ancestral relationships in transcriptomic data. Unlike traditional causal discovery methods that start with a fully connected graph, GENESIS initialises an empty ancestrality matrix and iteratively populates it with direct, indirect or non-causal relationships using a series of provably sound marginal and conditional independence tests. By integrating genotypes as fixed causal anchors, GENESIS provides a principled ``head start'' to classical causal discovery algorithms, restricting the search space to biologically plausible edges. We test GENESIS on synthetic and real-world genomic datasets. This framework offers a powerful avenue for uncovering causal pathways in complex traits, with promising applications to functional genomics, drug discovery, and precision medicine.
CoT Information: Improved Sample Complexity under Chain-of-Thought Supervision
Authors: Awni Altabaa, Omar Montasser, John Lafferty
Date: 2025-05-21 00:00:00

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* $\mathcal{I}_{\mathcal{D}, h_\star}^{\mathrm{CoT}}(\epsilon; \calH)$, which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error $\epsilon$ scales as $d/\mathcal{I}_{\mathcal{D}, h_\star}^{\mathrm{CoT}}(\epsilon; \calH)$, where $d$ is a measure of hypothesis class complexity, which can be much faster than standard $d/\epsilon$ rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.
PO-Flow: Flow-based Generative Models for Sampling Potential Outcomes and Counterfactuals
Authors: Dongze Wu, David I. Inouye, Yao Xie
Date: 2025-05-21 00:00:00
Tasks: Causal Inference, counterfactual, Image Generation

We propose PO-Flow, a novel continuous normalizing flow (CNF) framework for causal inference that jointly models potential outcomes and counterfactuals. Trained via flow matching, PO-Flow provides a unified framework for individualized potential outcome prediction, counterfactual predictions, and uncertainty-aware density learning. Among generative models, it is the first to enable density learning of potential outcomes without requiring explicit distributional assumptions (e.g., Gaussian mixtures), while also supporting counterfactual prediction conditioned on factual outcomes in general observational datasets. On benchmarks such as ACIC, IHDP, and IBM, it consistently outperforms prior methods across a range of causal inference tasks. Beyond that, PO-Flow succeeds in high-dimensional settings, including counterfactual image generation, demonstrating its broad applicability.
Oh SnapMMD! Forecasting Stochastic Dynamics Beyond the Schrödinger Bridge's End
Authors: Renato Berlinghieri, Yunyi Shen, Jialong Jiang, Tamara Broderick
Date: 2025-05-21 00:00:00

Scientists often want to make predictions beyond the observed time horizon of "snapshot" data following latent stochastic dynamics. For example, in time course single-cell mRNA profiling, scientists have access to cellular transcriptional state measurements (snapshots) from different biological replicates at different time points, but they cannot access the trajectory of any one cell because measurement destroys the cell. Researchers want to forecast (e.g.) differentiation outcomes from early state measurements of stem cells. Recent Schr\"odinger-bridge (SB) methods are natural for interpolating between snapshots. But past SB papers have not addressed forecasting -- likely since existing methods either (1) reduce to following pre-set reference dynamics (chosen before seeing data) or (2) require the user to choose a fixed, state-independent volatility since they minimize a Kullback-Leibler divergence. Either case can lead to poor forecasting quality. In the present work, we propose a new framework, SnapMMD, that learns dynamics by directly fitting the joint distribution of both state measurements and observation time with a maximum mean discrepancy (MMD) loss. Unlike past work, our method allows us to infer unknown and state-dependent volatilities from the observed data. We show in a variety of real and synthetic experiments that our method delivers accurate forecasts. Moreover, our approach allows us to learn in the presence of incomplete state measurements and yields an $R^2$-style statistic that diagnoses fit. We also find that our method's performance at interpolation (and general velocity-field reconstruction) is at least as good as (and often better than) state-of-the-art in almost all of our experiments.
Exponential Convergence of CAVI for Bayesian PCA
Authors: Arghya Datta, Philippe Gagnon, Florian Maire
Date: 2025-05-22 00:00:00
Tasks: Dimensionality Reduction, Uncertainty Quantification, Variational Inference

Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is allowing uncertainty quantification. The parameters of BPCA are typically learned using mean-field variational inference, and in particular, the coordinate ascent variational inference (CAVI) algorithm. So far, the convergence speed of CAVI for BPCA has not been characterized. In our paper, we fill this gap in the literature. Firstly, we prove a precise exponential convergence result in the case where the model uses a single principal component (PC). Interestingly, this result is established through a connection with the classical $\textit{power iteration algorithm}$ and it indicates that traditional PCA is retrieved as points estimates of the BPCA parameters. Secondly, we leverage recent tools to prove exponential convergence of CAVI for the model with any number of PCs, thus leading to a more general result, but one that is of a slightly different flavor. To prove the latter result, we additionally needed to introduce a novel lower bound for the symmetric Kullback--Leibler divergence between two multivariate normal distributions, which, we believe, is of independent interest in information theory.
Integral Imprecise Probability Metrics
Authors: Siu Lun Chau, Michele Caprio, Krikamol Muandet
Date: 2025-05-22 00:00:00
Tasks: Uncertainty Quantification

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty (EU) -- due to incomplete knowledge -- requires richer representations than those offered by classical probability. Imprecise probability (IP) theory offers such models, capturing ambiguity and partial belief. This has driven growing interest in imprecise probabilistic machine learning (IPML), where inference and decision-making rely on broader uncertainty models -- highlighting the need for metrics beyond classical probability. This work introduces the Integral Imprecise Probability Metric (IIPM) framework, a Choquet integral-based generalisation of classical Integral Probability Metric (IPM) to the setting of capacities -- a broad class of IP models encompassing many existing ones, including lower probabilities, probability intervals, belief functions, and more. Theoretically, we establish conditions under which IIPM serves as a valid metric and metrises a form of weak convergence of capacities. Practically, IIPM not only enables comparison across different IP models but also supports the quantification of epistemic uncertainty within a single IP model. In particular, by comparing an IP model with its conjugate, IIPM gives rise to a new class of EU measures -- Maximum Mean Imprecision -- which satisfy key axiomatic properties proposed in the Uncertainty Quantification literature. We validate MMI through selective classification experiments, demonstrating strong empirical performance against established EU measures, and outperforming them when classical methods struggle to scale to a large number of classes. Our work advances both theory and practice in IPML, offering a principled framework for comparing and quantifying epistemic uncertainty under imprecision.
Graph-Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry
Authors: Masanari Kimura
Date: 2025-05-22 00:00:00

Label shift adaptation aims to recover target class priors when the labelled source distribution $P$ and the unlabelled target distribution $Q$ share $P(X \mid Y) = Q(X \mid Y)$ but $P(Y) \neq Q(Y)$. Classical black-box shift estimators invert an empirical confusion matrix of a frozen classifier, producing a brittle point estimate that ignores sampling noise and similarity among classes. We present Graph-Smoothed Bayesian BBSE (GS-B$^3$SE), a fully probabilistic alternative that places Laplacian-Gaussian priors on both target log-priors and confusion-matrix columns, tying them together on a label-similarity graph. The resulting posterior is tractable with HMC or a fast block Newton-CG scheme. We prove identifiability, $N^{-1/2}$ contraction, variance bounds that shrink with the graph's algebraic connectivity, and robustness to Laplacian misspecification. We also reinterpret GS-B$^3$SE through information geometry, showing that it generalizes existing shift estimators.