pwc-archive/papers-with-abstracts huggingface dataset:
Uncertainty Quantification With Noise Injection in Neural Networks: A Bayesian Perspective
Authors: Xueqiong Yuan, Jipeng Li, Ercan Engin Kuruoglu
Date: 2025-01-21 00:00:00
Tasks: Bayesian Inference, Uncertainty Quantification

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.
Quantitative Error Bounds for Scaling Limits of Stochastic Iterative Algorithms
Authors: Xiaoyu Wang, Mikolaj J. Kasprzak, Jeffrey Negrea, Solesne Bourguin, Jonathan H. Huggins
Date: 2025-01-21 00:00:00

Stochastic iterative algorithms, including stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD), are widely utilized for optimization and sampling in large-scale and high-dimensional problems in machine learning, statistics, and engineering. Numerous works have bounded the parameter error in, and characterized the uncertainty of, these approximations. One common approach has been to use scaling limit analyses to relate the distribution of algorithm sample paths to a continuous-time stochastic process approximation, particularly in asymptotic setups. Focusing on the univariate setting, in this paper, we build on previous work to derive non-asymptotic functional approximation error bounds between the algorithm sample paths and the Ornstein-Uhlenbeck approximation using an infinite-dimensional version of Stein's method of exchangeable pairs. We show that this bound implies weak convergence under modest additional assumptions and leads to a bound on the error of the variance of the iterate averages of the algorithm. Furthermore, we use our main result to construct error bounds in terms of two common metrics: the L\'{e}vy-Prokhorov and bounded Wasserstein distances. Our results provide a foundation for developing similar error bounds for the multivariate setting and for more sophisticated stochastic approximation algorithms.
Dual NUP Representations and Min-Maximization in Factor Graphs
Authors: Yun-Peng Li, Hans-Andrea Loeliger
Date: 2025-01-21 00:00:00

Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor graphs with convex-dual variables and pertinent NUP representations. In particular, in a state space setting, we propose a new iterative forward-backward algorithm that is dual to a recently proposed backward-forward algorithm.
A note on the relations between mixture models, maximum-likelihood and entropic optimal transport
Authors: Titouan Vayer, Etienne Lasalle
Date: 2025-01-21 00:00:00

This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek to present this already known result in a concise and hopefully simple manner. We give an illustration with Gaussian mixture models by showing that the standard EM algorithm is a specific block-coordinate descent on an optimal transport loss.
Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands
Authors: Lars van der Laan, Aurelien Bibaut, Nathan Kallus, Alex Luedtke
Date: 2025-01-21 00:00:00
Tasks: Causal Inference, Model Selection, valid

We propose a unified framework for automatic debiased machine learning (autoDML) to perform inference on smooth functionals of infinite-dimensional M-estimands, defined as population risk minimizers over Hilbert spaces. By automating debiased estimation and inference procedures in causal inference and semiparametric statistics, our framework enables practitioners to construct valid estimators for complex parameters without requiring specialized expertise. The framework supports Neyman-orthogonal loss functions with unknown nuisance parameters requiring data-driven estimation, as well as vector-valued M-estimands involving simultaneous loss minimization across multiple Hilbert space models. We formalize the class of parameters efficiently estimable by autoDML as a novel class of nonparametric projection parameters, defined via orthogonal minimum loss objectives. We introduce three autoDML estimators based on one-step estimation, targeted minimum loss-based estimation, and the method of sieves. For data-driven model selection, we derive a novel decomposition of model approximation error for smooth functionals of M-estimands and propose adaptive debiased machine learning estimators that are superefficient and adaptive to the functional form of the M-estimand. Finally, we illustrate the flexibility of our framework by constructing autoDML estimators for the long-term survival under a beta-geometric model.
Hypergraph Representations of scRNA-seq Data for Improved Clustering with Random Walks
Authors: Wan He, Daniel I. Bolnick, Samuel V. Scarpino, Tina Eliassi-Rad
Date: 2025-01-20 00:00:00
Tasks: Hypergraph representations

Analysis of single-cell RNA sequencing data is often conducted through network projections such as coexpression networks, primarily due to the abundant availability of network analysis tools for downstream tasks. However, this approach has several limitations: loss of higher-order information, inefficient data representation caused by converting a sparse dataset to a fully connected network, and overestimation of coexpression due to zero-inflation. To address these limitations, we propose conceptualizing scRNA-seq expression data as hypergraphs, which are generalized graphs in which the hyperedges can connect more than two vertices. In the context of scRNA-seq data, the hypergraph nodes represent cells and the edges represent genes. Each hyperedge connects all cells where its corresponding gene is actively expressed and records the expression of the gene across different cells. This hypergraph conceptualization enables us to explore multi-way relationships beyond the pairwise interactions in coexpression networks without loss of information. We propose two novel clustering methods: (1) the Dual-Importance Preference Hypergraph Walk (DIPHW) and (2) the Coexpression and Memory-Integrated Dual-Importance Preference Hypergraph Walk (CoMem-DIPHW). They outperform established methods on both simulated and real scRNA-seq datasets. The improvement brought by our proposed methods is especially significant when data modularity is weak. Furthermore, CoMem-DIPHW incorporates the gene coexpression network, cell coexpression network, and the cell-gene expression hypergraph from the single-cell abundance counts data altogether for embedding computation. This approach accounts for both the local level information from single-cell level gene expression and the global level information from the pairwise similarity in the two coexpression networks.
Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds
Authors: Florent Bouchard, Nils Laurent, Salem Said, Nicolas Le Bihan
Date: 2025-01-20 00:00:00

In this paper, the issue of averaging data on a manifold is addressed. While the Fr\'echet mean resulting from Riemannian geometry appears ideal, it is unfortunately not always available and often computationally very expensive. To overcome this, R-barycenters have been proposed and successfully applied to Stiefel and Grassmann manifolds. However, R-barycenters still suffer severe limitations as they rely on iterative algorithms and complicated operators. We propose simpler, yet efficient, barycenters that we call RL-barycenters. We show that, in the setting relevant to most applications, our framework yields astonishingly simple barycenters: arithmetic means projected onto the manifold. We apply this approach to the Stiefel and Grassmann manifolds. On simulated data, our approach is competitive with respect to existing averaging methods, while computationally cheaper.
An accuracy-runtime trade-off comparison of scalable Gaussian process approximations for spatial data
Authors: Filippo Rambelli, Fabio Sigrist
Date: 2025-01-20 00:00:00
Tasks: Gaussian Processes, parameter estimation, Time Series Analysis

Gaussian processes (GPs) are flexible, probabilistic, non-parametric models widely employed in various fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost having $\mathcal{O}(N^3)$ time and $\mathcal{O}(N^2)$ memory complexity which makes them prohibitive for large data sets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations concerning likelihood evaluation, parameter estimation, and prediction taking into account the computational time required to perform these tasks. In other words, we analyze the trade-off between accuracy and runtime on multiple simulated and large-scale real-world data sets. We find that Vecchia approximations consistently emerge as the most accurate in almost all experiments.
Transductive Conformal Inference for Full Ranking
Authors: Jean-Baptiste Fermanian, Pierre Humbert, Gilles Blanchard
Date: 2025-01-20 00:00:00
Tasks: Conformal Prediction, Prediction, valid

We introduce a method based on Conformal Prediction (CP) to quantify the uncertainty of full ranking algorithms. We focus on a specific scenario where $n+m$ items are to be ranked by some ``black box'' algorithm. It is assumed that the relative (ground truth) ranking of $n$ of them is known. The objective is then to quantify the error made by the algorithm on the ranks of the $m$ new items among the total $(n+m)$. In such a setting, the true ranks of the $n$ original items in the total $(n+m)$ depend on the (unknown) true ranks of the $m$ new ones. Consequently, we have no direct access to a calibration set to apply a classical CP method. To address this challenge, we propose to construct distribution-free bounds of the unknown conformity scores using recent results on the distribution of conformal p-values. Using these scores upper bounds, we provide valid prediction sets for the rank of any item. We also control the false coverage proportion, a crucial quantity when dealing with multiple prediction sets. Finally, we empirically show on both synthetic and real data the efficiency of our CP method for state-of-the-art algorithms such as RankNet or LambdaMart.
The "Law" of the Unconscious Contrastive Learner: Probabilistic Alignment of Unpaired Modalities
Authors: Yongwei Che, Benjamin Eysenbach
Date: 2025-01-20 00:00:00

While internet-scale data often comes in pairs (e.g., audio/image, image/text), we often want to perform inferences over modalities unseen together in the training data (e.g., audio/text). Empirically, this can often be addressed by learning multiple contrastive embedding spaces between existing modality pairs, implicitly hoping that unseen modality pairs will end up being aligned. This theoretical paper proves that this hope is well founded, under certain assumptions. Starting with the proper Bayesian approach of integrating out intermediate modalities, we show that directly comparing the representations of data from unpaired modalities can recover the same likelihood ratio. Our analysis builds on prior work on the geometry and probabilistic interpretation of contrastive representations, showing how these representations can answer many of the same inferences as probabilistic graphical models. Our analysis suggests two new ways of using contrastive representations: in settings with pre-trained contrastive models, and for handling language ambiguity in reinforcement learning. Our numerical experiments study the importance of our assumptions and demonstrate these new applications.
Physics-Informed Machine Learning for Efficient Reconfigurable Intelligent Surface Design
Authors: Zhen Zhang, Jun Hui Qiu, Jun Wei Zhang, Hui Dong Li, Dong Tang, Qiang Cheng, Wei Lin
Date: 2025-01-20 00:00:00
Tasks: Physics-informed machine learning

Reconfigurable intelligent surface (RIS) is a two-dimensional periodic structure integrated with a large number of reflective elements, which can manipulate electromagnetic waves in a digital way, offering great potentials for wireless communication and radar detection applications. However, conventional RIS designs highly rely on extensive full-wave EM simulations that are extremely time-consuming. To address this challenge, we propose a machine-learning-assisted approach for efficient RIS design. An accurate and fast model to predict the reflection coefficient of RIS element is developed by combining a multi-layer perceptron neural network (MLP) and a dual-port network, which can significantly reduce tedious EM simulations in the network training. A RIS has been practically designed based on the proposed method. To verify the proposed method, the RIS has also been fabricated and measured. The experimental results are in good agreement with the simulation results, which validates the efficacy of the proposed method in RIS design.
High-dimensional point forecast combinations for emergency department demand
Authors: Peihong Guo, Wen Ye Loh, Kenwin Maung, Esther Li Wen Choo, Borame Lee Dickens, Kelvin Bryan Tan, John Abishgenadan, Pei Ma, Jue Tao Lim
Date: 2025-01-20 00:00:00

Current work on forecasting emergency department (ED) admissions focuses on disease aggregates or singular disease types. However, given differences in the dynamics of individual diseases, it is unlikely that any single forecasting model would accurately account for each disease and for all time, leading to significant forecast model uncertainty. Yet, forecasting models for ED admissions to-date do not explore the utility of forecast combinations to improve forecast accuracy and stability. It is also unknown whether improvements in forecast accuracy can be yield from (1) incorporating a large number of environmental and anthropogenic covariates or (2) forecasting total ED causes by aggregating cause-specific ED forecasts. To address this gap, we propose high-dimensional forecast combination schemes to combine a large number of forecasting individual models for forecasting cause-specific ED admissions over multiple causes and forecast horizons. We use time series data of ED admissions with an extensive set of explanatory lagged variables at the national level, including meteorological/ambient air pollutant variables and ED admissions of all 16 causes studied. We show that the simple forecast combinations yield forecast accuracies of around 3.81%-23.54% across causes. Furthermore, forecast combinations outperform individual forecasting models, in more than 50% of scenarios (across all ED admission categories and horizons) in a statistically significant manner. Inclusion of high-dimensional covariates and aggregating cause-specific forecasts to provide all-cause ED forecasts provided modest improvements in forecast accuracy. Forecasting cause-specific ED admissions can provide fine-scale forward guidance on resource optimization and pandemic preparedness and forecast combinations can be used to hedge against model uncertainty when forecasting across a wide range of admission categories.
Generalizable Spectral Embedding with an Application to UMAP
Authors: Nir Ben-Ari, Amitai Yacobi, Uri Shaham
Date: 2025-01-20 00:00:00
Tasks: Dimensionality Reduction

Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability (i.e., out-of-sample extension), scalability, and eigenvectors separation. In this paper, we introduce GrEASE: Generalizable and Efficient Approximate Spectral Embedding, a novel deep-learning approach designed to address these limitations. GrEASE incorporates an efficient post-processing step to achieve eigenvectors separation, while ensuring both generalizability and scalability, allowing for the computation of the Laplacian's eigenvectors on unseen data. This method expands the applicability of SE to a wider range of tasks and can enhance its performance in existing applications. We empirically demonstrate GrEASE's ability to consistently approximate and generalize SE, while ensuring scalability. Additionally, we show how GrEASE can be leveraged to enhance existing methods. Specifically, we focus on UMAP, a leading visualization technique, and introduce NUMAP, a generalizable version of UMAP powered by GrEASE. Our codes are publicly available.
Sparse L0-norm based Kernel-free Quadratic Surface Support Vector Machines
Authors: Ahmad Mousavi, Ramin Zandvakili
Date: 2025-01-20 00:00:00
Tasks: Computational Efficiency

Kernel-free quadratic surface support vector machine (SVM) models have gained significant attention in machine learning. However, introducing a quadratic classifier increases the model's complexity by quadratically expanding the number of parameters relative to the dimensionality of the data, exacerbating overfitting. Hence, we propose sparse $\ell_0$-norm based Kernel-free quadratic surface SVMs, designed to mitigate overfitting and enhance interpretability. Given the intractable nature of these models, we present a penalty decomposition algorithm to obtain first-order optimality points efficiently. We demonstrate that the subproblems in our framework either admit closed-form solutions or can leverage duality theory to improve computational efficiency. Through empirical evaluations on real-world datasets, we demonstrate the efficacy and robustness of our approach, showcasing its potential to advance Kernel-free quadratic surface SVMs in practical applications while addressing overfitting concerns. All the implemented models and experiment codes are available at https://github.com/raminzandvakili/L0-QSVM.
A Metric Topology of Deep Learning for Data Classification
Authors: Jwo-Yuh Wu, Liang-Chi Huang, Wen-Hsuan Li, Chun-Hung Liu
Date: 2025-01-20 00:00:00
Tasks: Deep Learning

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this paper, we investigate DL for data classification through the prism of metric topology. Considering that conventional Euclidean metric over the network parameter space typically fails to discriminate DL networks according to their classification outcomes, we propose from a probabilistic point of view a meaningful distance measure, whereby DL networks yielding similar classification performances are close. The proposed distance measure defines such an equivalent relation among network parameter vectors that networks performing equally well belong to the same equivalent class. Interestingly, our proposed distance measure can provably serve as a metric on the quotient set modulo the equivalent relation. Then, under quite mild conditions it is shown that, apart from a vanishingly small subset of networks likely to predict non-unique labels, our proposed metric space is compact, and coincides with the well-known quotient topological space. Our study contributes to fundamental understanding of DL, and opens up new ways of studying DL using fruitful metric space theory.
An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks
Authors: Jiaqi Luo, Yahong Yang, Yuan Yuan, Shixin Xu, Wenrui Hao
Date: 2025-01-20 00:00:00

This paper introduces Residual-based Smote (RSmote), an innovative local adaptive sampling technique tailored to improve the performance of Physics-Informed Neural Networks (PINNs) through imbalanced learning strategies. Traditional residual-based adaptive sampling methods, while effective in enhancing PINN accuracy, often struggle with efficiency and high memory consumption, particularly in high-dimensional problems. RSmote addresses these challenges by targeting regions with high residuals and employing oversampling techniques from imbalanced learning to refine the sampling process. Our approach is underpinned by a rigorous theoretical analysis that supports the effectiveness of RSmote in managing computational resources more efficiently. Through extensive evaluations, we benchmark RSmote against the state-of-the-art Residual-based Adaptive Distribution (RAD) method across a variety of dimensions and differential equations. The results demonstrate that RSmote not only achieves or exceeds the accuracy of RAD but also significantly reduces memory usage, making it particularly advantageous in high-dimensional scenarios. These contributions position RSmote as a robust and resource-efficient solution for solving complex partial differential equations, especially when computational constraints are a critical consideration.
Conditional Feature Importance with Generative Modeling Using Adversarial Random Forests
Authors: Kristin Blesch, Niklas Koenen, Jan Kapar, Pegah Golchian, Lukas Burk, Markus Loecher, Marvin N. Wright
Date: 2025-01-19 00:00:00
Tasks: Explainable artificial intelligence, Explainable Artificial Intelligence (XAI), Feature Importance

This paper proposes a method for measuring conditional feature importance via generative modeling. In explainable artificial intelligence (XAI), conditional feature importance assesses the impact of a feature on a prediction model's performance given the information of other features. Model-agnostic post hoc methods to do so typically evaluate changes in the predictive performance under on-manifold feature value manipulations. Such procedures require creating feature values that respect conditional feature distributions, which can be challenging in practice. Recent advancements in generative modeling can facilitate this. For tabular data, which may consist of both categorical and continuous features, the adversarial random forest (ARF) stands out as a generative model that can generate on-manifold data points without requiring intensive tuning efforts or computational resources, making it a promising candidate model for subroutines in XAI methods. This paper proposes cARFi (conditional ARF feature importance), a method for measuring conditional feature importance through feature values sampled from ARF-estimated conditional distributions. cARFi requires only little tuning to yield robust importance scores that can flexibly adapt for conditional or marginal notions of feature importance, including straightforward extensions to condition on feature subsets and allows for inferring the significance of feature importances through statistical tests.