Selection via Proxy (SVP)

• SVP is a methodological paradigm that employs surrogate proxies to perform selection, allocation, or inference, enabling efficient and cost-effective solutions.
• It is applied in domains like crowdsourcing, machine learning, federated systems, and causal inference, improving both accuracy and resource utilization.
• Empirical results show up to 32% error reduction and 10–50× compute speedup, underscoring SVP's practical efficacy in diverse computational tasks.

Selection via Proxy (SVP) is a methodological paradigm in which selection, allocation, or inference tasks are performed not directly on the primary objects or data, but via suitably chosen proxies—simpler, cheaper, or more accessible surrogates that partially capture relevant information. SVP has emerged across diverse research areas, including crowdsourcing, data-efficient machine learning, federated systems, collaborative filtering, fairness-constrained sampling, causal inference with unmeasured confounders, and even computational geometry. All forms of SVP share the core idea: rather than querying or aggregating over expensive, noisy, or inaccessible “targets,” the system selects, weights, or filters proxies—such as more informative workers, calculated subsamples, compact representations, or data-driven variable surrogates—to achieve rigorous, resource-efficient solutions. Below, key SVP frameworks, algorithms, and theoretical insights are summarized across canonical exemplar domains.

1. Crowdsourcing: Proxy Voting and Weighted Aggregation

The PCS (“Proxy Crowdsourcing”) framework crystallizes the classical SVP idea in human computation settings (Cohensius et al., 2018). A fixed budget of question–answer pairs is allocated between:

• Leaders ("proxies"): A small set (m) of workers label the entire dataset of n items (producing answer vectors $x_i\in X^n$).
• Followers: A larger set (k) of workers answer a small, random subset (s of n) items.

Each follower “delegates” her unit weight to the leader(s) whose full answer vector most closely matches her partial vector (measured e.g. by Hamming or $L_1$ distance). If multiple leaders tie, the follower's weight is divided among them. Leader $i$'s total weight $w_i$ is the sum or fractional total of followers for whom $i$ is a nearest-neighbor proxy. Final aggregation occurs over leaders, weighted by these proxy assignments:

• For categorical tasks: weighted plurality.
• For continuous tasks: weighted mean.

PCS consistently outperforms unweighted aggregation in error (7–32% improvement across datasets and tasks), with theoretical guarantees that more competent leaders exponentially dominate proxy assignment as budget or competence gaps grow. Empirically, optimal resource allocation is typically β ≈ 1/3–1/2 on followers and $\alpha \approx 0.2$ for question subset ratio (Cohensius et al., 2018).

2. Machine Learning: Data Selection and NAS via Proxy

SVP principles underpin efficient data selection and subsampling across supervised learning, active/coreset selection, and neural architecture search (NAS).

2.1. Proxy Model Data Selection

In deep learning, full-sized models are computationally expensive to train or evaluate for each data subset selection. SVP replaces the full target with a much faster, downscaled proxy model (e.g., a shallower or narrower neural net). The proxy is used in the selection phase (e.g., for uncertainty or representativeness ranking), after which the chosen data is used to train the full model (Coleman et al., 2019). Despite higher proxy error rates, selection by proxy maintains:

• Spearman correlation $>0.8$ between proxy and target ranking.
• Only 0.1–0.3% degradation in final accuracy with 7–51$\times$ runtime speedup for active or core-set selection on datasets including CIFAR-10/100, ImageNet, and Amazon Review (Coleman et al., 2019).

2.2. Proxy Data in NAS and AutoML

For NAS, SVP techniques construct entropy-informed proxy datasets: select subsets that balance “easy” (low-entropy) and “hard” (high-entropy) examples (entropy measured by pre-trained model predictions) (Na et al., 2021). Sampling by entropy binning, the SVP algorithm preserves architectural search quality while reducing compute by 10–20$\times$. On CIFAR-10, using only 3% of the data is sufficient to match full-data DARTS search performance. On ImageNet, search time drops from days to 7.5 hours with negligible loss in test error (Na et al., 2021).

Automated data selection for AutoML (ASP) further extends SVP by dynamically mixing multiple per-example metrics (gradient norm, loss, entropy, forgetting) and sampling with replacement from the full pool, sustaining robust, high rank correlation and up to 10$\times$ speedup without accuracy loss (Yao et al., 2023).

3. Statistical Selection: Precision/Recall Guarantees via Proxy

When filtering large datasets for rare events (e.g., video, scientific curation), SVP formalizes approximate selection with guaranteed minimum precision or recall, subject to limited expensive “oracle” (ground-truth) queries (Kang et al., 2020). The algorithm uses:

1. A proxy model to score all records.
2. A small importance-weighted sample for oracle labeling.
3. Empirical confidence intervals to choose a proxy threshold guaranteeing target precision/recall with failure rate $\leq \delta$.
4. A corrected proxy-selected set, adding back any positively labeled “missed” records below threshold.

The approach provides up to 30$\times$ higher recall or precision at the same oracle cost vs. uniform sampling, with sample complexity $O(\varepsilon^{-2}\log(1/\delta))$ for additive error $\varepsilon$ (Kang et al., 2020).

4. Federated and Distributed Systems: Proxy-based Client Selection

In federated learning for recommender systems, ProxyRL-FRS introduces dual-branch local models (ProxyNCF): one branch trains conventionally, the other predicts local client "contribution" (e.g., estimated loss) in a single, low-cost forward pass (Qu et al., 14 Aug 2025). The server uses these proxy contributions as state for a staleness-aware actor-critic RL client selector, balancing immediate accuracy and embedding freshness. This delivers both faster convergence and improved NDCG/HR over previous random or brute-force client selection, as confirmed on datasets such as MovieLens-1M, Fashion, and Video Games (Qu et al., 14 Aug 2025).

5. Causal Inference: Proxy Variable Selection for Unmeasured Confounders

SVP appears in methods for unbiased causal effect estimation when confounders are unobserved but proxy variables are present (Xie et al., 2024). In linear SEMs with multiple treatments and confounders, valid proxies (Negative Control Exposures/Outcomes) are sought by data-driven rank and independence constraints:

• Second-order rank tests (Trek separation): search variable sets whose covariance matrices exhibit specific rank deficiencies, indicating sufficient “decoupling” from unmeasured components.
• Higher-order “Generalized Independent Noise” (GIN) tests: exploit non-Gaussianity via empirical independence metrics.

Upon identifying proxy sets, the causal effect is consistently estimated via a determinant ratio of observed covariances. Both theoretical identifiability and $\sqrt{n}$-consistency are achieved, outperforming naive regression or brute-force negative control search (Xie et al., 2024).

6. SVP in Fair Sampling, Recommender Evaluation, and Interaction

• Fair and Balanced Sampling: SVP can be used to enforce balanced sample collection with respect to sensitive groups, using learned proxies constrained to limit group-membership disclosure to a user-defined level $\alpha$. Optimal proxy-based sampling weights are derived via QP to ensure $\beta$-balance (Deng et al., 2023).
• Collaborative Filtering Subsampling: For algorithm evaluation under data subsampling, SVP-CF samples interactions in proportion to proxy gradient norms, preserving the relative ranking of algorithm performance (NDCG, Recall) after subsampling even at 40% of the data (Sachdeva et al., 2021).
• MR/AR Object Selection: In human-computer interaction, Reality Proxy realizes SVP by mapping physical objects to AI-enriched proxies, supporting attribute-based, hierarchical, or semantic selection and manipulation (Liu et al., 23 Jul 2025).

7. Design Patterns, Limitations, and Theoretical Underpinnings

SVP effectiveness depends on the calibration and informativeness of the proxy, the alignment of proxy and target objectives, and—often—the soundness of the weighting or selection function transferring proxy information to the main aggregation or filtering task. Theoretical justification in various domains includes:

• Exponential concentration of follower weights to higher-competence leaders in crowdsourcing (Cohensius et al., 2018).
• Precision and recall guarantees by confidence bounds and importance sampling (Kang et al., 2020).
• Rank/covariance-based identifiability in causal inference, or clipping/filtering strategies to bound error from imprecise proxies (Xie et al., 2024, Deng et al., 2023). Empirically, SVP is robust so long as the proxy retains high ranking correlation or sufficient discriminative structure with respect to the target metric; degradation becomes more likely if proxies are underspecified, adversarial, or too simplistic for the true input-output relation.

Application Domain	SVP Mechanism	Key Performance/Guarantee
Crowdsourcing	Followers select leader	7–32% error reduction at fixed budget
Data Subselection/NAS	Proxy model/data subset	2–50$\times$ speedup, $<0.1$–$0.3$\% error
Statistical Filtering	Proxy+oracle, CIs	$1-\delta$ precision/recall guarantee
Federated Recommendation	Proxy-predicted contribution, RL	+16.5% NDCG/HR, faster convergence
Causal Inference	Rank/GIN proxy selection	Consistent, unbiased causal effect estimate
Fair Sampling	Proxy with $\alpha$-disclosure	$(\alpha, \beta)$-bounded imbalance

SVP is now a foundational design pattern throughout scalable, resource-constrained, or privacy-restricted machine intelligence and data science (Cohensius et al., 2018, Coleman et al., 2019, Na et al., 2021, Qu et al., 14 Aug 2025, Xie et al., 2024, Deng et al., 2023). Variants and generalizations span from combinatorial optimization to adaptive querying and interaction abstraction, with ongoing research focused on tighter theoretical bounds, multi-stage proxies, and adaptive proxy learning.