Abstracts

Linglong Kong, University of Alberta

Statistical Foundations for Trustworthy AI: Fairness, Uncertainty, and Online Inference

Ensuring fairness, reliability, and transparency is central to trustworthy artificial intelligence. We present statistical frameworks that address these challenges from fairness and uncertainty quantification perspectives. First, we propose a method for fair quantile prediction that leverages optimal transport and Wasserstein barycenters to enforce demographic parity across sensitive groups, capturing disparities often hidden in mean-based approaches. We extend this to Conformal Fair Quantile Prediction (CFQP), which delivers prediction intervals with exact coverage guarantees while significantly reducing group-level bias. Second, we develop online inference procedures for smoothed quantile regression, including renewable estimators and debiased lasso methods, enabling valid statistical inference with streaming, high-dimensional, or heavy-tailed data. These contributions highlight how modern statistical methodology—integrating quantile regression, conformal inference, and online learning—provides rigorous foundations for AI systems deployed in socially sensitive, high-stakes domains.

Sandesh Acharya, University of Calgary

Clustering in single-cell data using Gene-Gene Correlation Structure

Genes do not function in isolation, they form intricate networks within cells, influencing various cellular processes like differentiation, development, and response to stimuli. This interplay involves the coordinated regulation of multiple genes which contributes to the establishment or maintenance of distinct cell types. We propose that each cell type can be characterized by a set of genes which exhibit high correlations with one another. Building upon this premise, we have developed a novel bi-clustering algorithm tailored for single-cell data analysis, leveraging gene-gene correlation patterns. Our algorithm iteratively identifies clusters of genes exhibiting strong mutual correlations and segregates cells based on the expression profiles of these gene networks. As a result, this method outputs a dendrogram showing the relations between parents and daughter clusters as well as the genes that can separate them. To validate the efficacy of our approach, we have applied our algorithm to four distinct single-cell RNAseq datasets. Our results demonstrate the algorithm's ability to effectively segregate the datasets into biologically meaningful clusters. Notably, the genes identified at each iterative step serve as reliable discriminators, facilitating the accurate distinction between the clusters.

Justin Dumouchelle, University of Calgary

Neural Heuristics for Mathematical Optimization via Value Function Approximation

Mathematical optimization is an invaluable framework for modeling and solving decision-making problems with many successes in single-level deterministic problems (e.g., mixed-integer linear or nonlinear optimization). However, many real-world problems require accounting for uncertainty or the reaction of another agent. Paradigms such as stochastic programming, bilevel optimization, and robust optimization can model these situations but are much slower to solve than their deterministic counterparts, especially when discrete decisions must be made. This work demonstrates how a single framework based on value function approximation and optimizing over trained neural networks can be adapted to all three domains. Empirically, we find solutions of similar, and in some cases significantly better, quality than state-of-the-art algorithms in each field, often within a fraction of the running time. The datasets and three frameworks, Neur2SP (NeurIPS'22), Neur2RO (ICLR'24), and Neur2BiLO (NeurIPS'24), are open-sourced for further research.

Forough Fazeliasl, University of Alberta

A Bayesian Nonparametric Mechanism for Differentially Private Generative Modeling

Ensuring differential privacy in generative modeling remains a central challenge, as protecting individual-level information often comes at the cost of data utility. We present a Bayesian non- parametric framework that introduces privacy directly into the generative process by leveraging the flexibility of the Dirichlet process (DiP). Our approach enforces privacy at two comple- mentary levels. Globally, a finite-series approximation of the DiP posterior yields a Dirichlet mechanism that injects structured uncertainty into the distributional weights, providing formal (ε, δ)-differential privacy guarantees. Locally, a copula-based base measure is constructed for the DiP to perturb continuous and categorical marginals according to calibrated privacy bud- gets, while maintaining correlations across features. This dual global–local mechanism ensures that differential privacy is respected both at the distributional level and at the feature-specific level. The Bayesian nonparametric structure additionally regularizes the model, reducing over- fitting and mitigating misspecification, while stabilizing training in high-dimensional settings. Altogether, the proposed framework offers a scalable and theoretically grounded procedure for private generative modeling that preserves utility while ensuring rigorous privacy protections across diverse data modalities.

Yixin Han, University of Alberta

Towards Differentially Private One-shot Model-free Screening

Screening with privacy protection is of great importance since high-dimensional data typically retains important yet sensitive information. In this paper, we propose a Safe Differentially Private model-free variable screening framework (SDPscreen) for high-dimensional sensitive data. Our private strategy is constructed upon the (boosted) Chatterjee's rank coefficient by incorporating a one-shot peeling algorithm. Our method is fully non-parametric, enabling the detection of non-linear and non-monotone associations without imposing any bounded conditions for privacy protection. Our privatized coefficients achieve both privacy guarantees and sure screening property under mild theoretical conditions. Furthermore, we construct a private data-adaptive threshold to control the false discovery rate in the screening process. Extensive numerical experiments and a real-world application confirm that our methods outperform existing approaches in both screening accuracy and privacy efficiency.

Andrew McCormack, University of Alberta

The Unbiasedness Threshold

Applications of linear algebra in statistics abound, such as those in linear regression and principal components analysis. Moving beyond linearity, the field of algebraic statistics leverages tools from computational algebra and algebraic geometry to solve statistical problems that involve polynomial functions. In this work I examine statistical hypothesis testing for discrete data from an algebraic perspective, with a focus on questions of the existence of unbiased tests. The sample size needed for the existence of a strictly unbiased test, termed the unbiasedness threshold, is shown to be the minimum degree of a polynomial that separates the null and alternative hypothesis sets. In particular, this result implies that null hypothesis sets must be semialgebraic for there to exist a strictly unbiased test. Explicit sample size requirements for various hypotheses in a multinomial model, such as hypotheses of independence in contingency tables, are given. It is demonstrated that upper bounds for the unbiasedness threshold can be found by computing Gröbner bases, and that such upper bounds are tight when all polynomial power functions can be written as sums of squares.

Inesh Munaweera, MacEwan University

Application of Bayesian Hierarchical Models in Fisheries Ecology

Bayesian models are widely used for complex ecological data, including those collected with modern animal tracking technologies such as acoustic telemetry (AT), because of their flexibility, ability to incorporate prior knowledge, and improved estimation precision. AT systems are increasingly applied to study fish movement, habitat use, and demographic parameters. However, omnidirectional AT systems generate data with multiple sources of variability. In this talk, I present applications of Bayesian hierarchical modelling to (i) estimate individual-level Walleye movement paths in Lake Winnipeg and (ii) study variation in survival probabilities of Arctic Char in the Cambridge Bay region. In addition, I will present a Bayesian latent multinomial framework to estimate survival and population dynamics of Lake Sturgeon in the North Saskatchewan River using multi-tag mark–recapture data (external tags and PIT), explicitly accounting for individual misidentification. Finally, I will address practical modelling challenges and briefly discuss how these findings offer actionable insights for effective fisheries management.

Sankhapali Polgolla, University of Calgary

Semiparametric Location-Scale Mixture Models: Identifiability and Minimum Hellinger Distance Estimation

Semiparametric mixture models have been extensively studied in the past decades, due to its flexibility in adapting to different data structures without strong parametric assumptions. Numerous studies have explored semiparametric location-shifted mixture models, establishing their identifiability and various estimation methods. However, for the semiparametric location-scale mixture models, as a natural but broader extension of location- shifted models, investigation remains very limited. To fill the gap, our research focuses on the semiparametric two-component location-scale mixture models. This model consists of five unknown parameters, i.e. mixing proportion, two location parameters and two scale parameters, and one nuisance parameter, which is the zero symmetric density function with unit standard deviation (for the sake of identifiability) called base function. We first proved the identifiability of this model over the parameter space. Then we applied the minimum distance technique and constructed the minimum Hellinger distance estimators (MHDE) of the unknown parameters after recovering the base function. For this MHDE, we proved its asymptotic properties including its existence, continuity as a functional and consistency. The finite-sample performance of the MHDE illustrated by simulation studies and real data analysis showed that our proposed MHDE is very competitive with widely used methods for normal or light-tailed components, while it performs better than those methods for heavy-tailed components.

David Thiessen, MacEwan University

Skeptical Survey Calibration

Calibration estimators are used in survey sampling, causal inference, and missing data analysis. They involve collecting data on secondary auxiliary variables and reweighting the sample observations so that sample means of auxiliary variables match known population means. This improves the representativeness of the sample and the accuracy of the results. However, they require these auxiliary population means to be reliably known. In this talk, we consider calibration using population values which are subject to uncertainty. We propose a new estimator and show how the estimator changes depending on the assumed precision of the auxiliary population variables.