pwc-archive/papers-with-abstracts huggingface dataset:
Bayesian Optimization for CVaR-based portfolio optimization
Authors: Robert Millar, Jinglai Li
Date: 2025-03-22 00:00:00
Tasks: Bayesian Optimization, Portfolio Optimization

Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained minimization problems, seeking to minimize the conditional value-at-risk (a computationally intensive risk measure) under a minimum expected return constraint. The proposed algorithms utilize a new acquisition function, which drives sampling towards the optimal region. Additionally, a new two-stage procedure is developed, which significantly reduces the number of evaluations of the expensive-to-evaluate objective function. The proposed algorithm's competitive performance is demonstrated through practical examples.
Planning and Learning in Average Risk-aware MDPs
Authors: Weikai Wang, Erick Delage
Date: 2025-03-22 00:00:00
Tasks: Q-Learning

For continuing tasks, average cost Markov decision processes have well-documented value and can be solved using efficient algorithms. However, it explicitly assumes that the agent is risk-neutral. In this work, we extend risk-neutral algorithms to accommodate the more general class of dynamic risk measures. Specifically, we propose a relative value iteration (RVI) algorithm for planning and design two model-free Q-learning algorithms, namely a generic algorithm based on the multi-level Monte Carlo method, and an off-policy algorithm dedicated to utility-base shortfall risk measures. Both the RVI and MLMC-based Q-learning algorithms are proven to converge to optimality. Numerical experiments validate our analysis, confirms empirically the convergence of the off-policy algorithm, and demonstrate that our approach enables the identification of policies that are finely tuned to the intricate risk-awareness of the agent that they serve.
Time-optimal neural feedback control of nilpotent systems as a binary classification problem
Authors: Sara Bicego, Samuel Gue, Dante Kalise, Nelly Villamizar
Date: 2025-03-21 00:00:00
Tasks: Binary Classification

A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, which leads to a characterization of the time-optimal trajectory as a parameter-dependent polynomial system for the control switching sequence. A deflated Newton's method is then applied to exhaust all the real roots of the polynomial system. The root-finding procedure is informed by the Hermite quadratic form, which provides a sharp estimate on the number of real roots to be found. In the second part of the paper, the polynomial systems are sampled and solved to generate a synthetic dataset for the construction of a time-optimal deep neural network -- interpreted as a binary classifier -- via supervised learning. Numerical tests in integrators of increasing dimension assess the accuracy, robustness, and real-time-control capabilities of the approximate control law.
An Efficient Alternating Algorithm for ReLU-based Symmetric Matrix Decomposition
Authors: Qingsong Wang
Date: 2025-03-21 00:00:00

Symmetric matrix decomposition is an active research area in machine learning. This paper focuses on exploiting the low-rank structure of non-negative and sparse symmetric matrices via the rectified linear unit (ReLU) activation function. We propose the ReLU-based nonlinear symmetric matrix decomposition (ReLU-NSMD) model, introduce an accelerated alternating partial Bregman (AAPB) method for its solution, and present the algorithm's convergence results. Our algorithm leverages the Bregman proximal gradient framework to overcome the challenge of estimating the global $L$-smooth constant in the classic proximal gradient algorithm. Numerical experiments on synthetic and real datasets validate the effectiveness of our model and algorithm.
Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions
Authors: Kevine Meugang Toukam
Date: 2025-03-20 00:00:00

We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This distance is defined by penalizing the action with a costless movement of the particle that does not change the direction and speed of its trajectory. We show that for Gaussian distribution resume to measuring the Euclidean distance between their ordered vector of eigenvalues and we show a direct application in recovering Latent Gaussian distributions.
Availability of Perfect Decomposition in Statistical Linkage Learning for Unitation-based Function Concatenations
Authors: Michal Prusik, Bartosz Frej, Michal W. Przewozniczek
Date: 2025-03-18 00:00:00
Tasks: Problem Decomposition

Statistical Linkage Learning (SLL) is a part of many state-of-the-art optimizers. The purpose of SLL is to discover variable interdependencies. It has been shown that the effectiveness of SLL-using optimizers is highly dependent on the quality of SLL-based problem decomposition. Thus, understanding what kind of problems are hard or easy to decompose by SLL is important for practice. In this work, we analytically estimate the size of a population sufficient for obtaining a perfect decomposition in case of concatenations of certain unitation-based functions. The experimental study confirms the accuracy of the proposed estimate. Finally, using the proposed estimate, we identify those problem types that may be considered hard for SLL-using optimizers.
Optimal Betting: Beyond the Long-Term Growth
Authors: Levon Hakobyan, Sergey Lototsky
Date: 2025-03-23 00:00:00

While the Kelly portfolio has many desirable properties, including optimal long-term growth rate, the resulting investment strategy is rather aggressive. In this paper, we suggest a unified approach to the risk assessment of the Kelly criterion in both discrete and continuous time by introducing and analyzing the asymptotic variance that describes fluctuations of the portfolio growth, and use the results to propose two new measures for quantifying risk.
Persistence and extinction dynamics in a stochastic predator-prey model with emergent Allee effects
Authors: Carlos Granados, Leon A. Valencia
Date: 2025-03-21 00:00:00

The Allee effect describes a decline in population fitness at low densities, potentially leading to extinction. In predator-prey systems, an emergent Allee effect can arise due to interactions such as density-dependent maturation rates and predation constraints. This work studies a stochastic predator-prey model where the prey population is structured into juvenile and adult stages, with maturation following a nonlinear function. We introduce Ito-type stochastic perturbations in mortality rates to account for environmental variability. We first establish the positivity of solutions and derive sufficient conditions for the stability of the trivial equilibrium, prey extinction, and conditional predator extinction. We then analyze prey persistence under specific maturation rate functions. Finally, numerical simulations illustrate the theoretical results and their ecological implications.
Martingale property and moment explosions in signature volatility models
Authors: Eduardo Abi Jaber, Paul Gassiat, Dimitri Sotnikov
Date: 2025-03-21 00:00:00

We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of a time-extended Brownian motion. Excluding trivial cases, we demonstrate that the price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative. The proof involves a fine analysis of the explosion time of a signature stochastic differential equation. This result is of key practical relevance, as it highlights that, when used for approximation purposes, the linear combination of signature elements must be taken of odd order to preserve the martingale property. Once martingality is established, we also characterize the existence of higher moments of the price process in terms of a condition on a correlation parameter.
Malliavin Calculus for Score-based Diffusion Models
Authors: Ehsan Mirafzali, Utkarsh Gupta, Patrick Wyrod, Frank Proske, Daniele Venturi, Razvan Marinescu
Date: 2025-03-21 00:00:00

We introduce a new framework based on Malliavin calculus to derive exact analytical expressions for the score function $\nabla \log p_t(x)$, i.e., the gradient of the log-density associated with the solution to stochastic differential equations (SDEs). Our approach combines classical integration-by-parts techniques with modern stochastic analysis tools, such as Bismut's formula and Malliavin calculus, and it works for both linear and nonlinear SDEs. In doing so, we establish a rigorous connection between the Malliavin derivative, its adjoint, the Malliavin divergence (Skorokhod integral), and diffusion generative models, thereby providing a systematic method for computing $\nabla \log p_t(x)$. In the linear case, we present a detailed analysis showing that our formula coincides with the analytical score function derived from the solution of the Fokker--Planck equation. For nonlinear SDEs with state-independent diffusion coefficients, we derive a closed-form expression for $\nabla \log p_t(x)$. We evaluate the proposed framework across multiple generative tasks and find that its performance is comparable to state-of-the-art methods. These results can be generalised to broader classes of SDEs, paving the way for new score-based diffusion generative models.
Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions
Authors: Daniele Bracale, Moulinath Banerjee, Cong Shi, Yuekai Sun
Date: 2025-03-20 00:00:00

We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices and subsequently observe their respective demand that is unobservable to competitors. The demand function for each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. To address this challenge, we propose a semi-parametric least-squares estimation of the nonlinear mean function, which does not require sellers to communicate demand information. We show that when all sellers employ our policy, their prices converge at a rate of $O(T^{-1/7})$ to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of $O(T^{5/7})$ relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of $s$-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making.
Calibration Bands for Mean Estimates within the Exponential Dispersion Family
Authors: Łukasz Delong, Selim Gatti, Mario V. Wüthrich
Date: 2025-03-24 00:00:00

A statistical model is said to be calibrated if the resulting mean estimates perfectly match the true means of the underlying responses. Aiming for calibration is often not achievable in practice as one has to deal with finite samples of noisy observations. A weaker notion of calibration is auto-calibration. An auto-calibrated model satisfies that the expected value of the responses being given the same mean estimate matches this estimate. Testing for auto-calibration has only been considered recently in the literature and we propose a new approach based on calibration bands. Calibration bands denote a set of lower and upper bounds such that the probability that the true means lie simultaneously inside those bounds exceeds some given confidence level. Such bands were constructed by Yang-Barber (2019) for sub-Gaussian distributions. Dimitriadis et al. (2023) then introduced narrower bands for the Bernoulli distribution and we use the same idea in order to extend the construction to the entire exponential dispersion family that contains for example the binomial, Poisson, negative binomial, gamma and normal distributions. Moreover, we show that the obtained calibration bands allow us to construct various tests for calibration and auto-calibration, respectively.
Glivenko-Cantelli for $f$-divergence
Authors: Haoming Wang, Lek-Heng Lim
Date: 2025-03-21 00:00:00

We extend the celebrated Glivenko-Cantelli theorem, sometimes called the fundamental theorem of statistics, from its standard setting of total variation distance to all $f$-divergences. A key obstacle in this endeavor is to define $f$-divergence on a subcollection of a $\sigma$-algebra that forms a $\pi$-system but not a $\sigma$-subalgebra. This is a side contribution of our work. We will show that this notion of $f$-divergence on the $\pi$-system of rays preserves nearly all known properties of standard $f$-divergence, yields a novel integral representation of the Kolmogorov-Smirnov distance, and has a Glivenko-Cantelli theorem. We will also discuss the prospects of a Vapnik-Chervonenkis theory for $f$-divergence.
AutoBayes: A Compositional Framework for Generalized Variational Inference
Authors: Toby St Clere Smithe, Marco Perin
Date: 2025-03-24 00:00:00
Tasks: Bayesian Inference, Variational Inference

We introduce a new compositional framework for generalized variational inference, clarifying the different parts of a model, how they interact, and how they compose. We explain that both exact Bayesian inference and the loss functions typical of variational inference (such as variational free energy and its generalizations) satisfy chain rules akin to that of reverse-mode automatic differentiation, and we advocate for exploiting this to build and optimize models accordingly. To this end, we construct a series of compositional tools: for building models; for constructing their inversions; for attaching local loss functions; and for exposing parameters. Finally, we explain how the resulting parameterized statistical games may be optimized locally, too. We illustrate our framework with a number of classic examples, pointing to new areas of extensibility that are revealed.
Poisson-Process Topic Model for Integrating Knowledge from Pre-trained Language Models
Authors: Morgane Austern, Yuanchuan Guo, Zheng Tracy Ke, Tianle Liu
Date: 2025-03-22 00:00:00
Tasks: Word Embeddings

Topic modeling is traditionally applied to word counts without accounting for the context in which words appear. Recent advancements in large language models (LLMs) offer contextualized word embeddings, which capture deeper meaning and relationships between words. We aim to leverage such embeddings to improve topic modeling. We use a pre-trained LLM to convert each document into a sequence of word embeddings. This sequence is then modeled as a Poisson point process, with its intensity measure expressed as a convex combination of $K$ base measures, each corresponding to a topic. To estimate these topics, we propose a flexible algorithm that integrates traditional topic modeling methods, enhanced by net-rounding applied before and kernel smoothing applied after. One advantage of this framework is that it treats the LLM as a black box, requiring no fine-tuning of its parameters. Another advantage is its ability to seamlessly integrate any traditional topic modeling approach as a plug-in module, without the need for modifications Assuming each topic is a $\beta$-H\"{o}lder smooth intensity measure on the embedded space, we establish the rate of convergence of our method. We also provide a minimax lower bound and show that the rate of our method matches with the lower bound when $\beta\leq 1$. Additionally, we apply our method to several datasets, providing evidence that it offers an advantage over traditional topic modeling approaches.
A Statistical Theory of Contrastive Learning via Approximate Sufficient Statistics
Authors: Licong Lin, Song Mei
Date: 2025-03-21 00:00:00
Tasks: Contrastive Learning, Data Augmentation, regression, Topic Classification

Contrastive learning -- a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones -- has driven significant progress in foundation models. In this work, we develop a new theoretical framework for analyzing data augmentation-based contrastive learning, with a focus on SimCLR as a representative example. Our approach is based on the concept of \emph{approximate sufficient statistics}, which we extend beyond its original definition in \cite{oko2025statistical} for contrastive language-image pretraining (CLIP) using KL-divergence. We generalize it to equivalent forms and general f-divergences, and show that minimizing SimCLR and other contrastive losses yields encoders that are approximately sufficient. Furthermore, we demonstrate that these near-sufficient encoders can be effectively adapted to downstream regression and classification tasks, with performance depending on their sufficiency and the error induced by data augmentation in contrastive learning. Concrete examples in linear regression and topic classification are provided to illustrate the broad applicability of our results.
Efficient Knowledge Distillation via Curriculum Extraction
Authors: Shivam Gupta, Sushrut Karmalkar
Date: 2025-03-21 00:00:00
Tasks: Knowledge Distillation, Language Modeling, Language Modelling

Knowledge distillation is a technique used to train a small student network using the output generated by a large teacher network, and has many empirical advantages~\citep{Hinton2015DistillingTK}. While the standard one-shot approach to distillation only uses the output of the final teacher network, recent work~\citep{panigrahi2024progressive} has shown that using intermediate checkpoints from the teacher's training process as an implicit ``curriculum'' for progressive distillation can significantly speed up training. However, such schemes require storing these checkpoints, and often require careful selection of the intermediate checkpoints to train on, which can be impractical for large-scale training. In this paper, we show that a curriculum can be \emph{extracted} from just the fully trained teacher network, and that this extracted curriculum can give similar efficiency benefits to those of progressive distillation. Our extraction scheme is natural; we use a random projection of the hidden representations of the teacher network to progressively train the student network, before training using the output of the full network. We show that our scheme significantly outperforms one-shot distillation and achieves a performance similar to that of progressive distillation for learning sparse parities with two-layer networks, and provide theoretical guarantees for this setting. Additionally, we show that our method outperforms one-shot distillation even when using transformer-based architectures, both for sparse-parity learning, and language modeling tasks.
Nonparametric Factor Analysis and Beyond
Authors: Yujia Zheng, Yang Liu, Jiaxiong Yao, Yingyao Hu, Kun Zhang
Date: 2025-03-21 00:00:00
Tasks: Representation Learning

Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or noiseless regimes. In contrast, we study the more general case where noise can take arbitrary forms, depend on latent variables, and be non-invertibly entangled within a nonlinear function. We propose a general framework for identifying latent variables in the nonparametric noisy settings. We first show that, under suitable conditions, the generative model is identifiable up to certain submanifold indeterminacies even in the presence of non-negligible noise. Furthermore, under the structural or distributional variability conditions, we prove that latent variables of the general nonlinear models are identifiable up to trivial indeterminacies. Based on the proposed theoretical framework, we have also developed corresponding estimation methods and validated them in various synthetic and real-world settings. Interestingly, our estimate of the true GDP growth from alternative measurements suggests more insightful information on the economies than official reports. We expect our framework to provide new insight into how both researchers and practitioners deal with latent variables in real-world scenarios.
RiboFlow: Conditional De Novo RNA Sequence-Structure Co-Design via Synergistic Flow Matching
Authors: Runze Ma, Zhongyue Zhang, Zichen Wang, Chenqing Hua, Zhuomin Zhou, Fenglei Cao, Jiahua Rao, Shuangjia Zheng
Date: 2025-03-21 00:00:00

Ribonucleic acid (RNA) binds to molecules to achieve specific biological functions. While generative models are advancing biomolecule design, existing methods for designing RNA that target specific ligands face limitations in capturing RNA's conformational flexibility, ensuring structural validity, and overcoming data scarcity. To address these challenges, we introduce RiboFlow, a synergistic flow matching model to co-design RNA structures and sequences based on target molecules. By integrating RNA backbone frames, torsion angles, and sequence features in an unified architecture, RiboFlow explicitly models RNA's dynamic conformations while enforcing sequence-structure consistency to improve validity. Additionally, we curate RiboBind, a large-scale dataset of RNA-molecule interactions, to resolve the scarcity of high-quality structural data. Extensive experiments reveal that RiboFlow not only outperforms state-of-the-art RNA design methods by a large margin but also showcases controllable capabilities for achieving high binding affinity to target ligands. Our work bridges critical gaps in controllable RNA design, offering a framework for structure-aware, data-efficient generation.
An Energy-Adaptive Elastic Equivariant Transformer Framework for Protein Structure Representation
Authors: Zhongyue Zhang, Runze Ma, Yanjie Huang, Shuangjia Zheng
Date: 2025-03-21 00:00:00
Tasks: Drug Discovery, Representation Learning

Structure-informed protein representation learning is essential for effective protein function annotation and \textit{de novo} design. However, the presence of inherent noise in both crystal and AlphaFold-predicted structures poses significant challenges for existing methods in learning robust protein representations. To address these issues, we propose a novel equivariant Transformer-State Space Model(SSM) hybrid framework, termed $E^3$former, designed for efficient protein representation. Our approach uses energy function-based receptive fields to construct proximity graphs and incorporates an equivariant high-tensor-elastic selective SSM within the transformer architecture. These components enable the model to adapt to complex atom interactions and extract geometric features with higher signal-to-noise ratios. Empirical results demonstrate that our model outperforms existing methods in structure-intensive tasks, such as inverse folding and binding site prediction, particularly when using predicted structures, owing to its enhanced tolerance to data deviation and noise. Our approach offers a novel perspective for conducting biological function research and drug discovery using noisy protein structure data.