arXiv subjects

Shixiang Zhu

Publications and source records attributed to Shixiang Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set

Data-driven distributionally robust optimization (DRO) typically treats the conditional outcome law as fixed and uses ambiguity sets to capture estimation error. This paper studies latent distributional heterogeneity, where each instance has an unobserved law but contributes only one observation, so uncertainty persists even if the mixture law is known. We propose Conformal-DRO, which uses nested conformal regions to construct an ambiguity set for the future latent law. Under exchangeability, the set covers this law with probability at least $1-α$ in finite samples, without estimating underlying latent laws or their mixing mechanism. The conformal path induces a data-driven transport geometry, while $α$ determines the radius. The worst-case problem reduces to a finite linear program over conformal shells and admits sparse adversarial solutions. The resulting robust value provides a finite-sample certificate for the selected decision's expected cost.

math.OC↗

arXiv2026

Learning Polyhedral Conformal Sets for Robust Optimization

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly conservative decisions, whereas small sets risk excluding the true outcome. Recent data-driven approaches, particularly conformal prediction, offer finite-sample validity guarantees but remain largely task-agnostic, ignoring the downstream decision structure. In this paper, we propose a decision-aware conformal framework that learns uncertainty sets tailored to robust optimization objectives. Our approach parameterizes a flexible family of polyhedral sets via data-driven hyperplanes and learns their geometry by directly minimizing the induced robust loss, while preserving statistical validity through conformal calibration. To correct for data-dependent selection, we incorporate a re-calibration step on an independent dataset to restore coverage. The resulting sets capture directional and anisotropic uncertainty aligned with the decision objective while remaining computationally tractable. We provide finite-sample coverage guarantees and bounds on the sub-optimality gap to an oracle decision. This work bridges the gap between statistical validity and decision optimality, providing a principled framework for data-driven robust optimization.

cs.LG↗

arXiv2026

Beyond Prediction: Conformal Inference for Latent Distributional Parameters

Many prediction problems seek to infer an unobserved, instance-specific parameter that governs the distribution of an observable response, even though the latent parameter is unavailable for both historical and future instances. We develop LatentCP, a prior-free conformal framework that constructs uncertainty sets for latent distributional parameters using only observed context--response pairs and a specified forward model. The method first constructs a conformal prediction set in the observable response space and then retains candidate latent parameters according to the probability their induced response distributions assign to that set. This inversion provides finite-sample marginal coverage without requiring latent calibration labels, a unique inverse mapping, or knowledge of the latent mixing distribution. Because latent-set efficiency depends nonmonotonically on the response-space miscoverage rate, we further introduce a multilevel procedure that aggregates normalized incompatibility scores across several response sets and selects the aggregation distribution using an independent tuning sample. Across synthetic experiments, LatentCP maintains nominal latent coverage under weak forward identification, observational nonidentifiability, and latent heterogeneity and multimodality, where empirical-Bayes, likelihood-based, and proxy-label conformal methods can substantially under-cover. On a California wildfire real dataset, it produces spatially adaptive uncertainty sets for latent fire intensity. Independent tuning improves efficiency, while multilevel aggregation provides additional gains when different response levels contain complementary information, without sacrificing validity.

stat.ME↗

arXiv2026

Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift

Deployed decisions are often optimized once and retained because updates impose operational, regulatory, or switching costs. As operating conditions change, when should such decisions be re-optimized? We study this question for stochastic optimization when the objective's functional form is known but the decision maker's trade-offs are encoded by an unknown preference parameter. Standard distribution-shift tests are poorly aligned with this goal: they can flag detectable yet decision-irrelevant changes without determining whether the incumbent decision has become materially suboptimal. We propose \texttt{RADAR} (Regret-based Assessment of Decision Adequacy and Risk), a decision-focused framework that uses inverse optimization to infer latent preferences and tests the deployed decision's optimality gap under the current distribution. By targeting regret, \texttt{RADAR} ignores decision-irrelevant shifts while detecting changes that warrant re-optimization. We develop two-sample and sequential changepoint procedures and establish asymptotic guarantees for Type-I error and power. Across synthetic optimization problems, a semi-synthetic capacity allocation task, and police-zone planning, \texttt{RADAR} more reliably distinguishes harmful from harmless shifts than decision-agnostic alternatives.

stat.ML↗

arXiv2026

Generalized Hypercube Queueing Models with Overlapping Service Regions

Motivated by the operations of the Atlanta Police Department, where heavy workloads and staffing shortages increasingly require units to patrol across overlapping service regions, we develop a generalized hypercube queueing model, extending Larson (1974), for spatial service systems with overlapping coverage. Designing effective service regions requires capturing both workload and the operations of mobile servers such as police units. The classical hypercube model, which tracks only whether each server is busy or idle, is well suited to light traffic but inadequate for congested systems with server-specific queues and restricted service regions. We model the system as a Markov chain on a nonnegative integer-valued state space and develop a sparse truncated hyperlattice approximation for efficient steady-state computation and performance evaluation. We further characterize the workloads attainable under stable dispatch policies, establish conditions for stabilizability, and identify dispatch policies that optimally balance workloads. We validate the model through simulation and apply it to the Atlanta Police Department, where rising workloads, staffing shortages, and boundary effects create significant operational challenges. Using real 911 calls-for-service data, our analysis indicates that a police operations system with permitted overlapping patrols can significantly mitigate these problems, leading to more effective deployment of the police force. Although the paper focuses on police districting applications, the generalized hypercube queueing model is applicable to other mobile server models in the general setup.

math.PR↗

arXiv2026

Balancing Optimality and Diversity: Human-Centered Decision Making through Generative Curation

Many decision-support systems recommend actions by optimizing measurable objectives, even when a human decision-maker retains final authority and considers additional criteria that are difficult to specify in advance. We study how an algorithm should curate a small portfolio of quantitatively strong alternatives in such settings. We introduce generative curation, a framework that learns a recommendation policy to maximize the expected desirability of the action ultimately selected by the decision-maker. For policies that generate quantitatively competitive actions, we decompose expected portfolio desirability into quantitative performance and a qualitative curation gain. Under a Gaussian process model of residual desirability, this gain is characterized by the Gaussian width induced by the covariance kernel, yielding a decision-theoretic notion of diversity based on qualitative nonredundancy rather than generic geometric separation. We establish diminishing returns to portfolio size and characterize regimes in which optimal policies are balanced, endpoint-concentrated, or space-filling. We develop neural generative and sequential optimization approaches applicable to continuous and combinatorial action spaces. Controlled synthetic experiments demonstrate substantial regret reductions relative to optimization- and distance-based benchmarks, while an Atlanta police redistricting case study illustrates the framework's applicability to a complex operational planning problem.

cs.LG↗

arXiv2026

Hierarchical Probabilistic Conformal Prediction for Distributed Energy Resources Adoption

The rapid growth of distributed energy resources (DERs) presents both opportunities and operational challenges for electric grid management. Accurately predicting DER adoption is critical for proactive infrastructure planning, but the inherent uncertainty and spatial disparity of DER growth complicate traditional forecasting approaches. Moreover, the hierarchical structure of distribution grids demands that predictions satisfy statistical guarantees at both the circuit and substation levels, a non-trivial requirement for reliable decision-making. In this paper, we propose a novel uncertainty quantification framework for DER adoption predictions that ensures validity across hierarchical grid structures. Leveraging a multivariate Hawkes process to model DER adoption dynamics and a tailored split conformal prediction algorithm, we introduce a new nonconformity score that preserves statistical guarantees under aggregation while maintaining prediction efficiency. We establish theoretical validity under mild conditions and demonstrate through empirical evaluation on customer-level solar panel installation data from Indianapolis, Indiana that our method consistently outperforms existing baselines in both predictive accuracy and uncertainty calibration.

stat.AP↗

arXiv2026

Calibrating Decision Robustness via Inverse Conformal Risk Control

Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient protection or overly conservative and costly solutions. Recent approaches using conformal prediction construct data-driven uncertainty sets with finite-sample coverage guarantees, but they still fix coverage targets a priori and offer little guidance for selecting robustness levels. We propose a new framework that provides distribution-free, finite-sample guarantees on both miscoverage and regret for any family of robust predict-then-optimize policies. Our method constructs valid estimators that trace out the miscoverage--regret Pareto frontier, enabling decision-makers to reliably evaluate and calibrate robustness levels according to their cost--risk preferences. The framework is simple to implement, broadly applicable across classical optimization formulations, and achieves sharper finite-sample performance. This paper offers a principled data-driven methodology for guiding robustness selection and empowers practitioners to balance robustness and conservativeness in high-stakes decision-making.

stat.ML↗

arXiv2026

Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness

Missing value imputation is a fundamental task in machine learning, with most existing methods assuming that all missing entries correspond to unobserved regular values. In many real-world datasets, however, missingness may arise from two distinct sources: some entries are meaningfully missing (intrinsically absent and semantically valid), while others are missing due to the observation process and should be imputed. We formalize this distinction as a selective imputation problem, where the goal is to jointly infer which missing entries should be preserved and which should be recovered. To address this challenge, we propose Diff-Joint, a diffusion-based framework that jointly models tabular data together with a latent missingness mask. The method alternates between conditional sampling and uncertainty-aware aggregation to iteratively refine both imputed values and missingness labels. Empirical results on synthetic and real-world datasets demonstrate that Diff-Joint effectively identifies meaningfully missing entries while achieving competitive imputation accuracy and improved downstream task performance.

cs.LG↗

arXiv2026

Large-Scale Resilience Planning for Wildfire-Prone Electricity-System via Adaptive Robust Optimization

Wildfire risk poses a growing challenge for electric utilities, as powerline failures can ignite wildfires while large fires can disrupt grid operations. Utilities increasingly rely on operational interventions such as Public Safety Power Shutoffs (PSPS) and fast-trip protection to mitigate ignition risk, but these measures can cause widespread service disruptions if deployed indiscriminately. Infrastructure planning decisions--such as feeder sectionalization and protection configuration--play a key role in determining how effectively these interventions can be targeted. We develop a planning framework for wildfire resilience that jointly optimizes long-term infrastructure configuration and short-term operational response under uncertain ignition risk. The problem is formulated as a tri-level optimization model capturing the interaction between infrastructure planning, wildfire risk realization, and adaptive operational decisions. To represent system-wide ignition uncertainty, we construct a data-driven uncertainty set that combines segment-level prediction intervals with group-level uncertainty budgets. Leveraging the model structure, we reformulate the problem as a tractable robust optimization model and develop a scalable column-and-constraint generation algorithm. Synthetic experiments and a large-scale case study on an investor-owned utility distribution system show that coordinated planning of sectionalization and operational mitigation strategies can substantially reduce wildfire risk while maintaining service reliability.

math.OC↗

arXiv2026

Mamoda2.5: Enhancing Unified Multimodal Model with DiT-MoE

We present Mamoda2.5, a unified AR-Diffusion framework that seamlessly integrates multimodal understanding and generation within a single architecture. To efficiently enhance the model's generation capability, we equip the Diffusion Transformer backbone with a fine-grained Mixture-of-Experts (MoE) design (128 experts, Top-8 routing), yielding a 25B-parameter model that activates only 3B parameters, significantly reducing training costs while scaling up the model capacity. Mamoda2.5 achieves top-tier generation performance on VBench 2.0 and sets a new record in video editing quality, surpassing evaluated open-source models and matching the performance of current top-tier proprietary models, including the Kling O1 on OpenVE-Bench. Furthermore, we introduce a joint few-step distillation and reinforcement learning framework that compresses the 30-step editing model into a 4-step model and greatly accelerates model inference. Compared to open-source baselines, Mamoda2.5 achieves up to $95.9\times$ faster video editing inference. In real-world applications, Mamoda2.5 has been successfully deployed for content moderation and creative restoration tasks in advertising scenarios, achieving a 98% success rate in internal advertising video editing scenario.

cs.CV↗

arXiv2026

Learning to Test: Physics-Informed Representation for Dynamical Instability Detection

Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate under stochastically varying environmental inputs, so stability is not a static property but must be reassessed as the context distribution shifts. Repeated large-scale DAE simulation, however, is computationally prohibitive in high-dimensional or real-time settings. This paper proposes a test-oriented learning framework for stability assessment under distribution shift. Rather than re-estimating physical parameters or repeatedly solving the underlying DAE, we learn a physics-informed latent representation of contextual variables that captures stability-relevant structure and is regularized toward a tractable reference distribution. Trained on baseline data from a certified safe regime, the learned representation enables deployment-time safety monitoring to be formulated as a distributional hypothesis test in latent space, with controlled Type I error. By integrating neural dynamical surrogates, uncertainty-aware calibration, and uniformity-based testing, our approach provides a scalable and statistically grounded method for detecting instability risk in stochastic constrained dynamical systems without repeated simulation.

cs.LG↗

arXiv2026

Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making

Decision-focused learning (DFL) integrates predictive models with downstream optimization, directly training machine learning models to minimize decision errors. While DFL has been shown to provide substantial advantages when compared to a counterpart that treats the predictive and prescriptive models separately, it has also been shown to struggle in high-dimensional and risk-sensitive settings, limiting its applicability in real-world settings. To address this limitation, this paper introduces decision-focused generative learning (Gen-DFL), a novel framework that leverages generative models to adaptively model uncertainty and improve decision quality. Instead of relying on fixed uncertainty sets, Gen-DFL learns a structured representation of the optimization parameters and samples from the tail regions of the learned distribution to enhance robustness against worst-case scenarios. This approach mitigates over-conservatism while capturing complex dependencies in the parameter space. The paper shows, theoretically, that Gen-DFL achieves improved worst-case performance bounds compared to traditional DFL. Empirically, it evaluates Gen-DFL on various scheduling and logistics problems, demonstrating its strong performance against existing DFL methods.

cs.LG↗

arXiv2026

Score-Based Change-Point Detection and Region Localization for Spatio-Temporal Point Processes

We study sequential change-point detection for spatio-temporal point processes, where actionable detection requires not only identifying when a distributional change occurs but also localizing where it manifests in space. While classical quickest change detection methods provide strong guarantees on detection delay and false-alarm rates, existing approaches for point-process data predominantly focus on temporal changes and do not explicitly infer affected spatial regions. We propose a likelihood-free, score-based detection framework that jointly estimates the change time and the change region in continuous space-time without assuming parametric knowledge of the pre- or post-change dynamics. The method leverages a localized and conditionally weighted Hyvärinen score to quantify event-level deviations from nominal behavior and aggregates these scores using a spatio-temporal CUSUM-type statistic over a prescribed class of spatial regions. Operating sequentially, the procedure outputs both a stopping time and an estimated change region, enabling real-time detection with spatial interpretability. We establish theoretical guarantees on false-alarm control, detection delay, and spatial localization accuracy, and demonstrate the effectiveness of the proposed approach through simulations and real-world spatio-temporal event data.

stat.ME↗

arXiv2025

Conformalized Decision Risk Assessment

In many operational settings, decision-makers must commit to actions before uncertainty resolves, but existing optimization tools rarely quantify how consistently a chosen decision remains optimal across plausible scenarios. This paper introduces CREDO -- Conformalized Risk Estimation for Decision Optimization, a distribution-free framework that quantifies the probability that a prescribed decision remains (near-)optimal across realizations of uncertainty. CREDO reformulates decision risk through the inverse feasible region -- the set of outcomes under which a decision is optimal -- and estimates its probability using inner approximations constructed from conformal prediction balls generated by a conditional generative model. This approach yields finite-sample, distribution-free lower bounds on the probability of decision optimality. The framework is model-agnostic and broadly applicable across a wide range of optimization problems. Extensive numerical experiments demonstrate that CREDO provides accurate, efficient, and reliable evaluations of decision optimality across various optimization settings.

stat.ML↗

arXiv2025

Global-Decision-Focused Neural ODEs for Proactive Grid Resilience Management

Extreme hazard events such as wildfires and hurricanes increasingly threaten power systems, causing widespread outages and disrupting critical services. Recently, predict-then-optimize approaches have gained traction in grid operations, where system functionality forecasts are first generated and then used as inputs for downstream decision-making. However, this two-stage method often results in a misalignment between prediction and optimization objectives, leading to suboptimal resource allocation. To address this, we propose predict-all-then-optimize-globally (PATOG), a framework that integrates outage prediction with globally optimized interventions. At its core, our global-decision-focused (GDF) neural ODE model captures outage dynamics while optimizing resilience strategies in a decision-aware manner. Unlike conventional methods, our approach ensures spatially and temporally coherent decision-making, improving both predictive accuracy and operational efficiency. Experiments on synthetic and real-world datasets demonstrate significant improvements in outage prediction consistency and grid resilience.

cs.LG↗

arXiv2025

TimeAutoDiff: A Unified Framework for Generation, Imputation, Forecasting, and Time-Varying Metadata Conditioning of Heterogeneous Time Series Tabular Data

We present TimeAutoDiff, a unified latent-diffusion framework for four fundamental time-series tasks: unconditional generation, missing-data imputation, forecasting, and time-varying-metadata conditional generation. The model natively supports heterogeneous features including continuous, binary, and categorical variables. We unify all tasks using a masked-modeling strategy in which a binary mask specifies which time-series cells are observed and which must be generated. TimeAutoDiff combines a lightweight variational autoencoder, which maps mixed-type features into a continuous latent sequence, with a diffusion model that learns temporal dynamics in this latent space. Two architectural choices provide strong speed and scalability benefits. The diffusion model samples an entire latent trajectory at once rather than denoising one timestep at a time, greatly reducing reverse-diffusion calls. In addition, the VAE compresses along the feature axis, enabling efficient modeling of wide tables in a low-dimensional latent space. Empirical evaluation shows that TimeAutoDiff matches or surpasses strong baselines in synthetic sequence fidelity and consistently improves imputation and forecasting performance. Metadata conditioning enables realistic scenario exploration, allowing users to edit metadata sequences and produce coherent counterfactual trajectories that preserve cross-feature dependencies. Ablation studies highlight the importance of the VAE's feature encoding and key components of the denoiser. A distance-to-closest-record audit further indicates that the model generalizes without excessive memorization. Code is available at https://github.com/namjoonsuh/TimeAutoDiff

cs.LG↗

arXiv2025

Impact of power outages on the adoption of residential solar photovoltaic in a changing climate

Residential solar photovoltaic (PV) systems are a cornerstone of residential decarbonization and energy resilience. However, most existing systems are PV-only and cannot provide backup power during grid failures. Here, we present a high-resolution analysis of 377,726 households in Indianapolis, US, quantifying how power outages influence the installation of PV-only systems between 2014 and 2023. Using a two-part econometric panel model, we estimate the causal effect of power outage exposure and project future risks under a middle of the road climate scenario (RCP 4.5). We find that each additional hour of annual outage duration per household lowers the new-installation rate by 0.012 percentage points per year, equivalent to a 31% decline relative to the historical mean (2014-2023). With outage duration and frequency projected to double by 2040, these results reveal a potential vicious cycle between grid unreliability and slower decarbonization, calling for policies that integrate grid resilience and clean-energy goals.

econ.GN↗