Models trained with empirical risk minimization (ERM) are prone to be biased towards spurious correlations between target labels and bias attributes, which leads to poor performance on data groups lacking spurious correlations. It is particularly challenging to address this problem when access to bias labels is not permitted. To mitigate the effect of spurious correlations without bias labels, we first introduce a novel training objective designed to robustly enhance model performance across all data samples, irrespective of the presence of spurious correlations. From this objective, we then derive a debiasing method, Disagreement Probability based Resampling for debiasing (DPR), which does not require bias labels. DPR leverages the disagreement between the target label and the prediction of a biased model to identify bias-conflicting samples-those without spurious correlations-and upsamples them according to the disagreement probability. Empirical evaluations on multiple benchmarks demonstrate that DPR achieves state-of-the-art performance over existing baselines that do not use bias labels. Furthermore, we provide a theoretical analysis that details how DPR reduces dependency on spurious correlations.

Real-world datasets often exhibit a long-tailed distribution, where vast majority of classes known as tail classes have only few samples. Traditional methods tend to overfit on these tail classes. Recently, a new approach called Imbalanced SAM (ImbSAM) is proposed to leverage the generalization benefits of Sharpness-Aware Minimization (SAM) for long-tailed distributions. The main strategy is to merely enhance the smoothness of the loss function for tail classes. However, we argue that improving generalization in long-tail scenarios requires a careful balance between head and tail classes. We show that neither SAM nor ImbSAM alone can fully achieve this balance. For SAM, we prove that although it enhances the model's generalization ability by escaping saddle point in the overall loss landscape, it does not effectively address this for tail-class losses. Conversely, while ImbSAM is more effective at avoiding saddle points in tail classes, the head classes are trained insufficiently, resulting in significant performance drops. Based on these insights, we propose Stage-wise Saddle Escaping SAM (SSE-SAM), which uses complementary strengths of ImbSAM and SAM in a phased approach. Initially, SSE-SAM follows the majority sample to avoid saddle points of the head-class loss. During the later phase, it focuses on tail-classes to help them escape saddle points. Our experiments confirm that SSE-SAM has better ability in escaping saddles both on head and tail classes, and shows performance improvements.

In the context of uncertainty quantification (UQ) the curse of dimensionality, whereby quantification efficiency degrades drastistically with parameter dimension, is particular extreme with highly parameterized models such as neural networks (NNs). Fortunately, in many cases, these models are overparameterized in the sense that the number of parameters can be reduced with negligible effects on accuracy and sometimes improvements in generalization [1]. Furthermore, NNs often have parameterizations that have fungible parameters such that permutations of the values and connections lead to equivalent output responses. This suggests methods that simultaneously sparsify and characterize the uncertainty of a model, while handling and taking advantage of the symmetries inherent in the model, are potentially advantageous approaches. Although Markov chain Monte Carlo (MCMC) methods [2] have been the reference standard to generate samples for UQ methods, they can be temperamental and do not scale well for high dimensional models. More recently, there has been widespread use of variational inference methods (VI), which cast the parameter posterior sampling problem as an optimization of a surrogate posterior guided by a suitable objective, such as the Kullback-Liebler (KL) divergence between the predictive posterior and true posterior induced by the data. In particular, there is now a family of model ensemble methods based on Stein's identity [3], such as Stein variational gradient descent (SVGD) [4], projected SVGD [5], and Stein variational Newton's method [6]. These methods have advantages over MCMC methods by virtue of propagating in parallel a coordinated ensemble of particles that represent the empirical posterior.

Graphical model estimation from modern multi-omics data requires a balance between statistical estimation performance and computational scalability. We introduce a novel pseudolikelihood-based graphical model framework that reparameterizes the target precision matrix while preserving sparsity pattern and estimates it by minimizing an $\ell_1$-penalized empirical risk based on a new loss function. The proposed estimator maintains estimation and selection consistency in various metrics under high-dimensional assumptions. The associated optimization problem allows for a provably fast computation algorithm using a novel operator-splitting approach and communication-avoiding distributed matrix multiplication. A high-performance computing implementation of our framework was tested in simulated data with up to one million variables demonstrating complex dependency structures akin to biological networks. Leveraging this scalability, we estimated partial correlation network from a dual-omic liver cancer data set. The co-expression network estimated from the ultrahigh-dimensional data showed superior specificity in prioritizing key transcription factors and co-activators by excluding the impact of epigenomic regulation, demonstrating the value of computational scalability in multi-omic data analysis. %derived from the gene expression data.

Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube or the Gaussian distribution. For general target distributions with potentially unnormalized densities, leveraging the low-discrepancy property of QMC to improve accuracy remains challenging. We propose training a transport map to push forward the uniform distribution on the unit hypercube to approximate the target distribution. Inspired by normalizing flows, the transport map is constructed as a composition of simple, invertible transformations. To ensure that RQMC achieves its superior error rate, the transport map must satisfy specific regularity conditions. We introduce a flexible parametrization for the transport map that not only meets these conditions but is also expressive enough to model complex distributions. Our theoretical analysis establishes that the proposed transport QMC estimator achieves faster convergence rates than standard Monte Carlo, under mild and easily verifiable growth conditions on the integrand. Numerical experiments confirm the theoretical results, demonstrating the effectiveness of the proposed method in Bayesian inference tasks.

Unimodality constitutes a key property indicating grouping behavior of the data around a single mode of its density. We propose a method that partitions univariate data into unimodal subsets through recursive splitting around valley points of the data density. For valley point detection, we introduce properties of critical points on the convex hull of the empirical cumulative density function (ecdf) plot that provide indications on the existence of density valleys. Next, we apply a unimodal data modeling approach that provides a statistical model for each obtained unimodal subset in the form of a Uniform Mixture Model (UMM). Consequently, a hierarchical statistical model of the initial dataset is obtained in the form of a mixture of UMMs, named as the Unimodal Mixture Model (UDMM). The proposed method is non-parametric, hyperparameter-free, automatically estimates the number of unimodal subsets and provides accurate statistical models as indicated by experimental results on clustering and density estimation tasks.

The advancement of Spatial Transcriptomics (ST) has facilitated the spatially-aware profiling of gene expressions based on histopathology images. Although ST data offers valuable insights into the micro-environment of tumors, its acquisition cost remains expensive. Therefore, directly predicting the ST expressions from digital pathology images is desired. Current methods usually adopt existing regression backbones along with patch-sampling for this task, which ignores the inherent multi-scale information embedded in the pyramidal data structure of digital pathology images, and wastes the inter-spot visual information crucial for accurate gene expression prediction. To address these limitations, we propose M2OST, a many-to-one regression Transformer that can accommodate the hierarchical structure of the pathology images via a decoupled multi-scale feature extractor. Unlike traditional models that are trained with one-to-one image-label pairs, M2OST uses multiple images from different levels of the digital pathology image to jointly predict the gene expressions in their common corresponding spot. Built upon our many-to-one scheme, M2OST can be easily scaled to fit different numbers of inputs, and its network structure inherently incorporates nearby inter-spot features, enhancing regression performance. We have tested M2OST on three public ST datasets and the experimental results show that M2OST can achieve state-of-the-art performance with fewer parameters and floating-point operations (FLOPs).

Frames Per Second (FPS) significantly affects the gaming experience. Providing players with accurate FPS estimates prior to purchase benefits both players and game developers. However, we have a limited understanding of how to predict a game's FPS performance on a specific device. In this paper, we first conduct a comprehensive analysis of a wide range of factors that may affect game FPS on a global-scale dataset to identify the determinants of FPS. This includes player-side and game-side characteristics, as well as country-level socio-economic statistics. Furthermore, recognizing that accurate FPS predictions require extensive user data, which raises privacy concerns, we propose a federated learning-based model to ensure user privacy. Each player and game is assigned a unique learnable knowledge kernel that gradually extracts latent features for improved accuracy. We also introduce a novel training and prediction scheme that allows these kernels to be dynamically plug-and-play, effectively addressing cold start issues. To train this model with minimal bias, we collected a large telemetry dataset from 224 countries and regions, 100,000 users, and 835 games. Our model achieved a mean Wasserstein distance of 0.469 between predicted and ground truth FPS distributions, outperforming all baseline methods.

We study the dynamics of gradient flow in high dimensions for the multi-spiked tensor problem, where the goal is to estimate $r$ unknown signal vectors (spikes) from noisy Gaussian tensor observations. Specifically, we analyze the maximum likelihood estimation procedure, which involves optimizing a highly nonconvex random function. We determine the sample complexity required for gradient flow to efficiently recover all spikes, without imposing any assumptions on the separation of the signal-to-noise ratios (SNRs). More precisely, our results provide the sample complexity required to guarantee recovery of the spikes up to a permutation. Our work builds on our companion paper [Ben Arous, Gerbelot, Piccolo 2024], which studies Langevin dynamics and determines the sample complexity and separation conditions for the SNRs necessary for ensuring exact recovery of the spikes (where the recovered permutation matches the identity). During the recovery process, the correlations between the estimators and the hidden vectors increase in a sequential manner. The order in which these correlations become significant depends on their initial values and the corresponding SNRs, which ultimately determines the permutation of the recovered spikes.

As several studies have shown, predicting credit risk is still a major concern for the financial services industry and is receiving a lot of scholarly interest. This area of study is crucial because it aids financial organizations in determining the probability that borrowers would default, which has a direct bearing on lending choices and risk management tactics. Despite the progress made in this domain, there is still a substantial knowledge gap concerning consumer actions that take place prior to the filing of credit card applications. The objective of this study is to predict customer responses to mail campaigns and assess the likelihood of default among those who engage. This research employs advanced machine learning techniques, specifically logistic regression and XGBoost, to analyze consumer behavior and predict responses to direct mail campaigns. By integrating different data preprocessing strategies, including imputation and binning, we enhance the robustness and accuracy of our predictive models. The results indicate that XGBoost consistently outperforms logistic regression across various metrics, particularly in scenarios using categorical binning and custom imputation. These findings suggest that XGBoost is particularly effective in handling complex data structures and provides a strong predictive capability in assessing credit risk.