Multidimensional Sequential Screening

• Multidimensional sequential screening is a framework of adaptive methods that sequentially identify and classify latent components in high-dimensional systems.
• It integrates techniques from variable selection, adaptive experimental design, optimal stopping theory, and mechanism design to enhance screening power and control errors.
• Practical algorithms like MAQuA and SCS demonstrate its efficacy in reducing resource use while boosting detection accuracy in applications ranging from mental health diagnostics to economic analysis.

Multidimensional sequential screening refers to a class of methodologies, algorithms, and mechanism design principles developed to identify, classify, or extract information about multiple latent components, variables, or private types in a system via adaptive, sequential data collection or interrogation. This paradigm arises in domains including high-dimensional variable selection, mental health diagnostics, sequential hypothesis testing, economic mechanism design with multidimensional private information, and adversarial or strategic classification. The unifying characteristics are: the presence of high-dimensional or multivariate latent structure, sequential/interadaptive sampling or interaction, and a focus on optimizing information acquisition, screening power, or incentive compatibility under stringent resource or information constraints.

1. Mathematical Frameworks for Multidimensional Sequential Screening

Multidimensional sequential screening is mathematically instantiated in several distinct but related frameworks:

• Sequential variable selection and multiple testing: High-dimensional signal recovery or top-m selection using sequential thresholding, confidence sequence methods, or stagewise variable elimination. The primarily goal is to recover the support (indices) of strong effects among many candidates, efficiently and with explicit error control (Malloy et al., 2011, Toyoda et al., 20 Aug 2025).
• Adaptive experimental design and bifurcation algorithms: Sequential group-splitting and subgroup testing procedures (such as multidimensional sequential bifurcation) are applied to efficiently identify active variables or effects in simulation or experimental systems under first-order or sparsity assumptions (Woods et al., 2015, Liang et al., 2022).
• Bayesian and optimal stopping theory: Multidimensional sequential detection is formulated as an optimal stopping problem for a high-dimensional posterior process, with continuation and stopping regions characterized by variational inequalities and exhibiting structured geometric properties under concavity assumptions (Ekström et al., 2020, Wang, 2015).
• Mechanism design and dynamic screening: In economics, multidimensional sequential screening concerns designing history-dependent allocation and price mechanisms for agents with correlated, multi-good private information, where the designer seeks to maximize revenue or information extraction over time (Gao, 29 Dec 2025).
• Strategic and adversarial screening: Sequential deployment of classifiers or tests, where agents may behave strategically to pass a sequence of hurdles, giving rise to nontrivial manipulation paths and distinct outcomes relative to simultaneous screening (Cohen et al., 2023).
• Multivariate IRT and computerized adaptive testing: Multidimensional item response models are used in intelligent adaptive screening, optimizing the sequence of probes for efficient information gain across several latent traits, as implemented in systems such as MAQuA (Varadarajan et al., 10 Aug 2025).

2. Algorithmic and Statistical Principles

Representative sequential screening algorithms share several core elements:

• Sequential elimination/partitioning: Stagewise reduction of the candidate variable or state set by applying adaptive thresholds or information criteria, often leveraging the monotonicity of certain test statistics or confidence bounds. In variable selection, this includes SCS and sequential thresholding, which rigorously guarantee containment of the true support set throughout all stages (Malloy et al., 2011, Toyoda et al., 20 Aug 2025).
• Group-wise or hierarchical screening: Algorithms like sequential bifurcation perform recursive partitioning of high-dimensional factor spaces, splitting active groups until isolated active factors are found, reducing experiment costs from exponential to linear in the dimension (Woods et al., 2015).
• Multidimensional information-optimal probing: In adaptive testing, e.g., MAQuA, the sequential selection of queries maximizes a D-optimality criterion (determinant of Fisher information matrix), optimally resolving uncertainty over multiple latent dimensions via most-informative items at each step (Varadarajan et al., 10 Aug 2025).
• Low-dimensional state reduction: In sequential multi-class diagnosis and multiresponse screening, dimensionality reduction via matrix factorization, low-rank approximation, or sufficient-statistics mapping is leveraged to render dynamic programs or criteria computationally tractable even in high dimension (Wang, 2015, Liang et al., 2022).
• Anytime validity and error control: Confidence-sequence-based approaches guarantee that the true discovery set is always preserved with high probability at any stage, with adjustable post-selection inference procedures to manage statistical errors in stopping sets (Toyoda et al., 20 Aug 2025).
• Strategic manipulation analysis: Theoretical results characterize when sequential screening can be subverted by agents zig-zagging through test sequences (with “sequential cost” strictly lower than at-once cost), and the construction of screening policies robust to such manipulation (e.g., B-shift defenses) (Cohen et al., 2023).

3. Theoretical Properties and Structural Results

Key structural features are established across diverse multidimensional sequential screening regimes:

• Dimensionality reduction under model structure: When multivariate observation or class distributions exhibit exponential-tilt or low-rank structure, the reachable set of posterior beliefs collapses to a low-dimensional manifold, enabling design of optimal or near-optimal policies in otherwise intractable multi-hypothesis testing problems (Wang, 2015).
• Frontloading and dynamic decoupling: In dynamic mechanism design, under “invariant dependency” (i.e., copula independence from initial private type), the full multidimensional sequential screening mechanism decomposes into independent one-good problems, simplifying optimal mechanism construction and surplus extraction (Gao, 29 Dec 2025).
• Concavity-induced geometric simplicity: In Bayesian sequential testing and detection, unilateral concavity of the value function (concavity in each coordinate individually) constrains stopping and continuation regions to have threshold-curve structure in each dimension, greatly simplifying geometric characterization and numerical analysis (Ekström et al., 2020).
• Screening power and sample complexity: Sequential screening achieves exponential gains in detection power over non-sequential (batch) methods in sparse regimes, as demonstrated in high-dimensional multiple testing. The required signal-noise separation and minimum sample size depend only logarithmically on the number of true signals, versus logarithmically on the ambient dimension for non-sequential approaches (Malloy et al., 2011).
• Sure screening, false coverage rate, and model selection consistency: Procedures such as TSA-SIS, SeSS, and SCS possess sure screening properties (probability of containing all true variables approaches unity), control familywise/post-screening inference error rates, and guarantee asymptotic recovery of the target support or model components under explicit signal and regularity conditions (Ma et al., 2017, Liang et al., 2022, Toyoda et al., 20 Aug 2025).

4. Practical Algorithms and Empirical Results

The following table summarizes selected practical algorithms and their domains:

Algorithm/System	Domain	Key Guarantee/Feature
MAQuA (Varadarajan et al., 10 Aug 2025)	Mental health screening	Reduces queries by 50–87% over random orderings
SCS (Toyoda et al., 20 Aug 2025)	Top-m variable selection	Anytime-validity, FCR-controlled post-screening CI
Sequential Bifurcation (Woods et al., 2015)	Design of experiments	O(p) run complexity under first-order effect assumption
SeSS (Liang et al., 2022)	Multiresponse screening	Sure screening under complex group structures
Dynamic decoupling (Gao, 29 Dec 2025)	Mechanism design	Reduction to n independent one-good sequential screens
Zig-zag screening (Cohen et al., 2023)	Strategic classification	Exploitable cost gap, B-shift optimal defense

Empirical studies confirm that such adaptive, sequential multidimensional methodologies substantially reduce burden (e.g., number of experiments or patient queries), enhance power in sparse regimes, or robustly identify active variables with provable statistical error bounds.

5. Limitations, Regularity Conditions, and Open Problems

Despite their promise, multidimensional sequential screening techniques are subject to specific limitations:

• Model assumptions: Many results rely on sparsity, first-order additivity, or degree-1 surrogacy (linear effects, positive coefficients), with screening consistency or computational tractability breaking down in the presence of strong interactions, sign-mixed effects, or high intrinsic dimension (Woods et al., 2015, Liang et al., 2022).
• Structural constraints: Results such as dynamic decoupling require precise invariant dependency conditions (copula independence), and unilateral concavity assumptions for tractable continuation region characterization (Gao, 29 Dec 2025, Ekström et al., 2020).
• Language and deployment bias: Adaptive systems trained/validated on English-only populations or fixed item pools (e.g., MAQuA) may not generalize beyond these settings; clinical validation and multi-language extension are open directions (Varadarajan et al., 10 Aug 2025).
• Strategic evasion: In sequential classifier pipelines, agents may exploit sequential zig-zag attacks unless classifiers are engineered defensively (e.g., B-shifts); optimal defense construction remains nontrivial in complex feature or non-linear settings (Cohen et al., 2023).
• Computational scalability: Complexity can become prohibitive for algorithms relying on large-dimension posterior updates, full-matrix calculations, or exhaustive search over group configurations without careful low-rank or approximate techniques (Wang, 2015, Liang et al., 2022).

6. Extensions and Cross-Domain Applications

The theoretical and methodological toolkit for multidimensional sequential screening has been integrated and extended across domains including:

• Multistudy regression and panel data screening: Adaptive methods for feature selection across multiple studies using self-normalized correlation aggregations, enabling exponentially high-dimensional settings under correlated study effects (Ma et al., 2017).
• Adaptive clinical and psychometric assessment: Multidimensional item response models with adaptive question selection and language modeling interface directly with emerging LLM-based mental health triage and remote patient assessment (Varadarajan et al., 10 Aug 2025).
• Multiresponse group-sparse models: Complex group-structured screening using PC-simple, group-lasso, and multistep screening procedures with proven selection consistency and computational tractability under sparsity and eigenvalue conditions (Liang et al., 2022).
• Adversarial learning and testing pipeline security: Strategic and adversarial sequential screening frameworks characterize and mitigate attack vectors in policy design for screening/classification pipelines (Cohen et al., 2023).
• Empirical Bayes and multivariate optimal stopping: Bayesian settings where stopping rules and belief state space are intrinsically multidimensional, leading to new variational inequality characterizations and practical solvers (Ekström et al., 2020).

Recent research continues to integrate structural, statistical, and algorithmic insights across these regimes, advancing multidimensional sequential screening as a foundational paradigm in adaptive experimentation, dynamic decision processes, and robust information extraction.