arXiv subjects

Zexun Chen

Publications and source records attributed to Zexun Chen.

10 recordsLinked to original sources

arXiv2026

Effort-Centric Fairness in Lending Decisions

Algorithmic credit scoring must satisfy fairness and explanation requirements, yet prevailing predictive-parity criteria assess only outcomes at the decision point. They can therefore overlook whether rejected applicants face unequal burdens in reaching future approval, a phenomenon we call masked inequality. We develop an effort-centric framework that measures an applicant's effort as the minimum weighted cost of feasible changes required to cross the approval boundary. The framework distinguishes feature-independent actions from additive structural shifts that propagate through a causal model and defines parity by comparing average minimum effort across protected groups. We derive tractable local expressions for general differentiable classifiers and exact expressions for logistic regression, embed them in an in-processing fairness objective, and bound changes in portfolio credit risk. The same optimisation yields actionable pathways to approval. Using mortgage data with continuous and discrete features, we find that rejected female applicants require greater effort even when standard predictive-parity criteria are satisfied. Feature-independent regularisation reduces the effort gap by more than 50\% with modest predictive changes. Causal regularisation yields reductions above 90\% at the tested positive penalty weights, but with larger predictive and risk-return trade-offs. Expected and unexpected losses remain broadly stable under feature-independent regularisation and increase under causal regularisation; RAROC declines but remains positive. These results show that effort parity complements predictive fairness by revealing and mitigating hidden barriers to future credit access while making the associated operational trade-offs explicit.

q-fin.ST↗

arXiv2026

When is multivariate kriging worthwhile? A design-geometry analysis of heterotopic multi-output Gaussian processes

Simulation experiments, multi-fidelity computer models and monitoring networks often produce several related outputs observed at different input locations, a sampling pattern known as heterotopic. Whether a joint multivariate kriging metamodel then predicts better than separate univariate metamodels has remained unresolved: careful simulation comparisons on common designs report little or no benefit from multivariate kriging, yet the multi-fidelity and geostatistical literatures are built on the premise that auxiliary outputs help. We show that, for separable multi-output Gaussian processes, the answer is governed by the geometry of the output-specific designs. We introduce model-free diagnostics that can be computed before fitting, namely directed coverage, directed proximity and borrowing potential indices. We derive an exact identity for the oracle prediction gain of joint modelling and bound this gain using local geometry under radial functions. We further prove that the estimability of cross-output dependence is controlled by a kernel-weighted cross-design interaction mass, and extend this result component by component to the linear model of coregionalisation. One consequence is that interleaved and separated designs are not statistically equivalent, even when both have zero overlap. We combine these results into a first-order net benefit criterion for deciding when joint modelling is worthwhile. Controlled synthetic experiments, an M/M/1 queueing illustration and a case study of a multi-pollutant monitoring network turn this criterion into practical guidance.

stat.ME↗

arXiv2026

Bridging Structured Knowledge and Data: A Unified Framework with Finance Applications

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function approximation. SKINNs jointly estimate neural network parameters and economically meaningful structural parameters in a single optimization problem, enforcing theoretical consistency not only on observed data but over a broader input domain through collocation, and therefore nesting approaches such as functional GMM, Bayesian updating, transfer learning, PINNs, and surrogate modeling. SKINNs define a class of M-estimators that are consistent and asymptotically normal with root-N convergence, sandwich covariance, and recovery of pseudo-true parameters under misspecification. We establish identification of structural parameters under joint flexibility, derive generalization and target-risk bounds under distributional shift in a convex proxy, and provide a restricted-optimal characterization of the weighting parameter that governs the bias-variance tradeoff. In an illustrative financial application to option pricing, SKINNs improve out-of-sample valuation and hedging performance, particularly at longer horizons and during high-volatility regimes, while recovering economically interpretable structural parameters with improved stability relative to conventional calibration. More broadly, SKINNs provide a general econometric framework for combining model-based reasoning with high-dimensional, data-driven estimation.

stat.ML↗

arXiv2024

Peer-induced Fairness: A Causal Approach for Algorithmic Fairness Auditing

With the European Union's Artificial Intelligence Act taking effect on 1 August 2024, high-risk AI applications must adhere to stringent transparency and fairness standards. This paper addresses a crucial question: how can we scientifically audit algorithmic fairness? Current methods typically remain at the basic detection stage of auditing, without accounting for more complex scenarios. We propose a novel framework, ``peer-induced fairness'', which combines the strengths of counterfactual fairness and peer comparison strategy, creating a reliable and robust tool for auditing algorithmic fairness. Our framework is universal, adaptable to various domains, and capable of handling different levels of data quality, including skewed distributions. Moreover, it can distinguish whether adverse decisions result from algorithmic discrimination or inherent limitations of the subjects, thereby enhancing transparency. This framework can serve as both a self-assessment tool for AI developers and an external assessment tool for auditors to ensure compliance with the EU AI Act. We demonstrate its utility in small and medium-sized enterprises access to finance, uncovering significant unfairness-41.51% of micro-firms face discrimination compared to non-micro firms. These findings highlight the framework's potential for broader applications in ensuring equitable AI-driven decision-making.

stat.AP↗

arXiv2023

Dynamic predictability and spatio-temporal contexts in human mobility

Human travelling behaviours are markedly regular, to a large extent, predictable, and mostly driven by biological necessities (\eg sleeping, eating) and social constructs (\eg school schedules, synchronisation of labour). Not surprisingly, such predictability is influenced by an array of factors ranging in scale from individual (\eg preference, choices) and social (\eg household, groups) all the way to global scale (\eg mobility restrictions in a pandemic). In this work, we explore how spatio-temporal patterns in individual-level mobility, which we refer to as \emph{predictability states}, carry a large degree of information regarding the nature of the regularities in mobility. Our findings indicate the existence of contextual and activity signatures in predictability states, pointing towards the potential for more sophisticated, data-driven approaches to short-term, higher-order mobility predictions beyond frequentist/probabilistic methods.

physics.soc-ph↗

arXiv2021

Contrasting social and non-social sources of predictability in human mobility

Social structures influence a variety of human behaviors including mobility patterns, but the extent to which one individual's movements can predict another's remains an open question. Further, latent information about an individual's mobility can be present in the mobility patterns of both social and non-social ties, a distinction that has not yet been addressed. Here we develop a "colocation" network to distinguish the mobility patterns of an ego's social ties from those of non-social colocators, individuals not socially connected to the ego but who nevertheless arrive at a location at the same time as the ego. We apply entropy and predictability measures to analyse and bound the predictive information of an individual's mobility pattern and the flow of that information from their top social ties and from their non-social colocators. While social ties generically provide more information than non-social colocators, we find that significant information is present in the aggregation of non-social colocators: 3-7 colocators can provide as much predictive information as the top social tie, and colocators can replace up to 85% of the predictive information about an ego, compared with social ties that can replace up to 94% of the ego's predictability. The presence of predictive information among non-social colocators raises privacy concerns: given the increasing availability of real-time mobility traces from smartphones, individuals sharing data may be providing actionable information not just about their own movements but the movements of others whose data are absent, both known and unknown individuals.

physics.soc-ph↗

arXiv2021

Remarks on multivariate Gaussian Process

Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to estimation, detection, and many statistical or machine learning models. With the fast development of Gaussian process applications, it is necessary to consolidate the fundamentals of vector-valued stochastic processes, in particular multivariate Gaussian processes, which is the essential theory for many applied problems with multiple correlated responses. In this paper, we propose a precise definition of multivariate Gaussian processes based on Gaussian measures on vector-valued function spaces, and provide an existence proof. In addition, several fundamental properties of multivariate Gaussian processes, such as strict stationarity and independence, are introduced. We further derive multivariate Brownian motion including Itô lemma as a special case of a multivariate Gaussian process, and present a brief introduction to multivariate Gaussian process regression as a useful statistical learning method for multi-output prediction problems.

math.ST↗

arXiv2021

Tuning Fairness by Balancing Target Labels

The issue of fairness in machine learning models has recently attracted a lot of attention as ensuring it will ensure continued confidence of the general public in the deployment of machine learning systems. We focus on mitigating the harm incurred by a biased machine learning system that offers better outputs (e.g. loans, job interviews) for certain groups than for others. We show that bias in the output can naturally be controlled in probabilistic models by introducing a latent target output. This formulation has several advantages: first, it is a unified framework for several notions of group fairness such as Demographic Parity and Equality of Opportunity; second, it is expressed as a marginalisation instead of a constrained problem; and third, it allows the encoding of our knowledge of what unbiased outputs should be. Practically, the second allows us to avoid unstable constrained optimisation procedures and to reuse off-the-shelf toolboxes. The latter translates to the ability to control the level of fairness by directly varying fairness target rates. In contrast, existing approaches rely on intermediate, arguably unintuitive, control parameters such as covariance thresholds.

stat.ML↗

arXiv2019

Multivariate Gaussian and Student$-t$ Process Regression for Multi-output Prediction

Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, re-formulation is not always workable and is difficult to apply to other distributions because not all matrix-variate distributions can be transformed to respective multivariate distributions, such as the case for matrix-variate Student$-t$ distribution. In this paper, we propose a unified framework which is used not only to introduce a novel multivariate Student$-t$ process regression model (MV-TPR) for multi-output prediction, but also to reformulate the multivariate Gaussian process regression (MV-GPR) that overcomes some limitations of the existing methods. Both MV-GPR and MV-TPR have closed-form expressions for the marginal likelihoods and predictive distributions under this unified framework and thus can adopt the same optimization approaches as used in the conventional GPR. The usefulness of the proposed methods is illustrated through several simulated and real data examples. In particular, we verify empirically that MV-TPR has superiority for the datasets considered, including air quality prediction and bike rent prediction. At last, the proposed methods are shown to produce profitable investment strategies in the stock markets.

stat.ML↗

arXiv2017

How priors of initial hyperparameters affect Gaussian process regression models

The hyperparameters in Gaussian process regression (GPR) model with a specified kernel are often estimated from the data via the maximum marginal likelihood. Due to the non-convexity of marginal likelihood with respect to the hyperparameters, the optimization may not converge to the global maxima. A common approach to tackle this issue is to use multiple starting points randomly selected from a specific prior distribution. As a result the choice of prior distribution may play a vital role in the predictability of this approach. However, there exists little research in the literature to study the impact of the prior distributions on the hyperparameter estimation and the performance of GPR. In this paper, we provide the first empirical study on this problem using simulated and real data experiments. We consider different types of priors for the initial values of hyperparameters for some commonly used kernels and investigate the influence of the priors on the predictability of GPR models. The results reveal that, once a kernel is chosen, different priors for the initial hyperparameters have no significant impact on the performance of GPR prediction, despite that the estimates of the hyperparameters are very different to the true values in some cases.

stat.ML↗