Selective Sampling: Methods and Applications

• Selective Sampling is a family of methods that uses explicit decision rules based on uncertainty, geometry, or risk to acquire high-value, informative data.
• In matrix completion, selective sampling designs the observation set to exploit low-rank structures, achieving up to 80% accuracy gains over uniform sampling.
• In online prediction and deep learning, selective sampling accelerates training and enhances label efficiency by targeting examples near decision boundaries or ambiguous regions.

Searching arXiv for recent and foundational papers on selective sampling across domains. Selective sampling denotes a family of methods in which the learner, analyst, or training pipeline does not accept observations, labels, features, trajectories, or generated candidates uniformly, but instead uses an explicit decision rule to determine which information to acquire, retain, or enforce. Across the literature, the common principle is to replace structure-agnostic acquisition with a selection mechanism informed by uncertainty, geometry, known low-rank structure, disagreement, saliency, cost, or reward. The term therefore appears in several technically distinct settings: matrix completion with designed observations (Parkinson et al., 2019), stream-based and online label querying (Castro et al., 2023, Camilleri et al., 2021, Sekhari et al., 2023), nearest-neighbor classification under active sample placement (Joseph et al., 2013), action-recognition feature subsampling (Zhou et al., 2015), deep-network training-time example selection (Weinstein et al., 2019, Weinstein et al., 2020), selective inference after convex optimization (Harris et al., 2016), nonstationary online learning (Moroshko et al., 2014), self-labeling with active querying (Kozal et al., 2023), and selective trajectory filtering for efficient reasoning in LLMs (Ge et al., 23 Feb 2026). What unifies these formulations is not a single algorithmic template, but a shared objective: improve statistical or computational efficiency by conditioning data acquisition or reuse on an estimate of informativeness, structure, or risk.

1. Matrix and signal acquisition formulations

In matrix completion, selective sampling refers to designing the observation set $\Omega$ instead of treating it as uniformly random. The baseline low-rank recovery problem observes $P_\Omega(M)$ for an unknown matrix $M \in \mathbb{R}^{m \times n}$ with $\mathrm{rank}(M)=r$, and solves the nuclear-norm program

$$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$

Classical guarantees assume $\Omega$ is generated uniformly at random and recover $M$ when $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$ under incoherence conditions (Parkinson et al., 2019). The selective-sampling variant instead assumes that a subset of columns $M_\tau$ is known or assumed to satisfy $\mathrm{rank}(M_\tau)=k \ll t$, and uses that structural prior to choose entries adaptively.

The first mechanism is “optimal sampling” for the structured block $P_\Omega(M)$0. If $P_\Omega(M)$1 for $P_\Omega(M)$2 basis columns and coefficient matrix $P_\Omega(M)$3, then the algorithm seeks a $P_\Omega(M)$4 invertible submatrix by sampling row and column sets $P_\Omega(M)$5, $P_\Omega(M)$6, and, once invertibility is detected, samples the remaining entries needed to recover $P_\Omega(M)$7 and the basis columns exactly. The resulting observation complexity for exact recovery of the low-rank block is

$P_\Omega(M)$8

which is stated to be necessary and sufficient for perfect reconstruction of $P_\Omega(M)$9 under the rank assumption and a continuous distribution of entries (Parkinson et al., 2019). This differs qualitatively from uniform sampling, whose expected number of observed entries in the block is $M \in \mathbb{R}^{m \times n}$0. The advantage is largest when $M \in \mathbb{R}^{m \times n}$1 is large, $M \in \mathbb{R}^{m \times n}$2 is small, and $M \in \mathbb{R}^{m \times n}$3 is not too small.

A second, more practical variant starts from random observations and discovers local basis relationships column by column. It maintains a set $M \in \mathbb{R}^{m \times n}$4 of columns for which it has inferred linear dependence relations of the form

$M \in \mathbb{R}^{m \times n}$5

or more precisely

$M \in \mathbb{R}^{m \times n}$6

where $M \in \mathbb{R}^{m \times n}$7 indexes the basis columns used for column $M \in \mathbb{R}^{m \times n}$8. These relations are then incorporated as additional linear constraints in the nuclear-norm program

$M \in \mathbb{R}^{m \times n}$9

Here selective sampling is simultaneously a measurement-design problem and a feasible-set reduction mechanism: the objective remains the nuclear norm, but the constraint set encodes inferred structure (Parkinson et al., 2019).

This matrix-completion usage is notable because selective sampling is not cast as uncertainty-based querying. Instead, it is a structurally constrained sensing problem in which prior knowledge about a submatrix reduces sample complexity and narrows the admissible completion set. The numerical experiments on $\mathrm{rank}(M)=r$0 and $\mathrm{rank}(M)=r$1 synthetic matrices report large gains in relative operator-norm error: for a $\mathrm{rank}(M)=r$2 matrix with first $\mathrm{rank}(M)=r$3 columns of rank $\mathrm{rank}(M)=r$4 and total rank 6, optimal sampling gives nearly 80% average accuracy gain over uniform sampling, while the iterative selective variant gives roughly 40% (Parkinson et al., 2019).

2. Online prediction, active querying, and drift

In online prediction with expert advice, selective sampling means the forecaster predicts every round but requests the true label only on a selected subset of rounds. In the binary experts setting, outcomes $\mathrm{rank}(M)=r$5 and expert predictions $\mathrm{rank}(M)=r$6 are observed sequentially. The forecaster predicts $\mathrm{rank}(M)=r$7, then samples a Bernoulli variable $\mathrm{rank}(M)=r$8: if $\mathrm{rank}(M)=r$9, it observes $$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$0; if $$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$1, it skips the label. Exponentially weighted forecasters are updated through importance-weighted losses,

$$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$2

so that losses remain unbiased despite missing labels (Castro et al., 2023).

The central design question is how to choose $$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$3. The paper derives the smallest sampling probability $$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$4, with $$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$5 the weighted fraction of experts predicting 1, that preserves the full-information regret bound

$$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$6

A practical upper bound is

$$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$7

Thus labels are queried nearly always when experts disagree ($$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$8) and much less when consensus is strong ($$\min_X \|X\|_* \quad \text{subject to} \quad P_\Omega(X)=P_\Omega(M).$$9 or $\Omega$0) (Castro et al., 2023). In the worst case this preserves the standard adversarial regret rate, while under a stochastic gap condition $\Omega$1, expected label complexity satisfies

$\Omega$2

which yields essentially $\Omega$3 queried labels when $\Omega$4 (Castro et al., 2023). Selective sampling is therefore label-efficient but not regret-degrading.

A related but geometrically different formulation appears in online best-arm identification with selective observation. There, points $\Omega$5 arrive IID from a distribution $\Omega$6, the learner can either measure $\Omega$7 or abstain, and must identify

$\Omega$8

with probability at least $\Omega$9. The paper characterizes the trade-off between unlabeled stopping time $M$0 and label complexity $M$1, via an oracle quantity

$M$2

and proves both lower and upper bounds involving $M$3 and the oversampling factor $M$4 (Camilleri et al., 2021). The resulting optimal decision rule has a geometric form: label $M$5 if and only if it lies outside an ellipsoid $M$6, or a smooth approximation thereof. This makes selective sampling a streaming measurement-design problem with explicit geometry.

Selective sampling in online classification with function approximation generalizes further in the SAGE and RAVIOLI frameworks. A learner observes contexts $M$7, predicts multiclass labels, and queries a noisy expert label only when its current predictor’s margin is small relative to a confidence radius $M$8 derived from an online regression oracle. The query rule is

$M$9

with regret controlled by the regression oracle’s regret and query complexity governed by scale-sensitive eluder dimension or disagreement coefficient (Sekhari et al., 2023). In imitation learning, this extends to episodic sequential decision problems, where the number of queries and the regret depend on the number of times the optimal policy visits small-margin states,

$|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$0

rather than on the learner’s or noisy expert’s state visitation (Sekhari et al., 2023). A plausible implication is that selective querying becomes particularly powerful when the expert policy avoids ambiguous regions of state space.

Nonstationary selective sampling introduces drift. In binary online classification with changing comparator sequence $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$1, drift is measured by

$|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$2

The LASEC and LASEC-SS algorithms use a last-step min-max formulation with drift penalty $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$3, second-order matrices $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$4, and margin-based randomized querying

$|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$5

The resulting expected-mistake bounds depend on both cumulative hinge loss and drift $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$6, recovering stationary selective-sampling bounds as the special case $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$7 (Moroshko et al., 2014). This directly addresses the failure mode of stationary active learners whose query rates collapse after concept shifts.

3. Geometry, nearest neighbors, and principal-curve time series

In nearest-neighbor classification, selective sampling means actively choosing the locations of labeled samples rather than drawing them IID from the underlying measure. The general setup considers a metric space $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$8, probability measure $|\Omega| \gtrsim C\, r(m+n)\log^2(m+n)$9, countable label set $M_\tau$0, and deterministic target function $M_\tau$1. At stage $M_\tau$2, a candidate pool of size $M_\tau$3 is drawn IID from $M_\tau$4, and the next sample $M_\tau$5 is the candidate maximizing a heuristic $M_\tau$6, where $M_\tau$7 is the current sample set (Joseph et al., 2013).

Three heuristics are developed. The first is distance to the sample set,

$M_\tau$8

which fills sparse regions. The second uses Voronoi neighbors and the non-modal count

$M_\tau$9

so points are preferred when their affected Voronoi neighbors disagree in label, which concentrates sampling near the $\mathrm{rank}(M_\tau)=k \ll t$0-boundary. The third replaces Voronoi neighbors by a $\mathrm{rank}(M_\tau)=k \ll t$1-nearest-neighbor surrogate with analogous non-modal count (Joseph et al., 2013). Under the admissibility condition

$\mathrm{rank}(M_\tau)=k \ll t$2

the paper proves almost-sure convergence $\mathrm{rank}(M_\tau)=k \ll t$3 for points off the $\mathrm{rank}(M_\tau)=k \ll t$4-boundary, and convergence in measure under separability and measure-zero boundary assumptions (Joseph et al., 2013). Two of the heuristics have naive per-step complexity linear in the number of samples. Here selective sampling is neither label-efficient online learning nor uncertainty sampling in the probabilistic sense; it is active sample placement with convergence guarantees in general metric spaces.

A distinct geometric formulation arises in time-series classification via principal curves. Samples are pairs $\mathrm{rank}(M_\tau)=k \ll t$5, with explicit timestamps, and the classifier fits one principal curve per class using Constraint Local Principal Curve (CLPC), then concatenates them into a “governing pattern” $\mathrm{rank}(M_\tau)=k \ll t$6. Classification is preceded by a matching step that aligns the recent history $\mathrm{rank}(M_\tau)=k \ll t$7 to the governing pattern by optimizing a KL-like similarity over time shifts $\mathrm{rank}(M_\tau)=k \ll t$8: $\mathrm{rank}(M_\tau)=k \ll t$9 The label is then assigned by nearest principal curve,

$P_\Omega(M)$00

Selective sampling uses the same similarity signal: a history of similarity values is analyzed by deterministic query rules rather than Bernoulli draws (Hakimzadeh et al., 2022).

The linear query strategy counts similarity decreases and queries when the normalized decrease rate exceeds a threshold. The exponential strategy compounds penalties when consecutive decreases occur, doubling a coefficient $P_\Omega(M)$01 after each drop and halving it otherwise, then queries when the normalized accumulated penalty exceeds a threshold (Hakimzadeh et al., 2022). The authors position determinism as an explicit contrast to probabilistic selective-sampling algorithms, arguing that lower variance and reproducibility are particularly desirable in safety-critical monitoring. This suggests selective sampling can also be understood as a deterministic alarm process driven by geometric misalignment rather than probabilistic uncertainty.

4. Feature, example, and label selection in discriminative learning

In action recognition, selective sampling is feature subsampling rather than label acquisition. Dense Trajectory (DT) and improved Dense Trajectory (iDT) pipelines generate very large numbers of local spatio-temporal features from videos; the problem is to reduce feature count while retaining discriminative signal. The paper defines dense sampling, uniformly random sampling, and selective sampling over trajectories $P_\Omega(M)$02. In selective sampling, each trajectory’s retention depends on a saliency map $P_\Omega(M)$03 derived from object proposals: a trajectory with starting point $P_\Omega(M)$04 is kept if

$P_\Omega(M)$05

Two saliency mechanisms are used: EdgeBox, based on static object contours, and FusionEdgeBox, which combines static and motion objectness through

$P_\Omega(M)$06

Experiments on J-HMDB report better average recognition accuracy using 25% less features for one proposed selective-sampling method, and comparable accuracy while discarding 70% features (Zhou et al., 2015). The paper also shows strong asymmetry between DT and iDT: because iDT already suppresses camera-motion-induced background trajectories, further selective sampling can introduce harmful bias, and random sampling may preserve the original feature distribution better (Zhou et al., 2015). In this setting, selective sampling is best interpreted as saliency-biased sparsification of local descriptors prior to Fisher-vector encoding.

For deep neural networks, selective sampling becomes online sample selection inside standard supervised SGD. A large candidate mini-batch of size $P_\Omega(M)$07 is passed through the model, a score is computed for each example, and only a smaller subset of size $P_\Omega(M)$08 is used for backpropagation. The key score is the Minimal Margin Score (MMS), defined at the last linear layer. If the top two class scores for sample $P_\Omega(M)$09 are $P_\Omega(M)$10 and $P_\Omega(M)$11, then

$P_\Omega(M)$12

which is the distance in feature space to the decision boundary between the predicted class and the runner-up (Weinstein et al., 2019, Weinstein et al., 2020). Training uses the $P_\Omega(M)$13 smallest-MMS samples from the candidate batch, i.e. those nearest the current decision boundary.

This criterion is explicitly margin-based rather than loss-based. The authors contrast it with hard negative mining, which selects high-loss examples, and entropy-based selection, which can degrade when the number of classes is large because tail probabilities become noisy (Weinstein et al., 2019). On CIFAR-10 with ResNet-44, MMS-based selection combined with an aggressive learning-rate drop schedule reaches about 93.0% accuracy in roughly 44k steps versus 93.24% for baseline training in 156k steps. On CIFAR-100 with WRN-28-10, it reaches about 82.2% at around 80k steps versus 82.26% at 156k steps (Weinstein et al., 2019). The closely related margin-regularization work interprets the same geometry through multi-margin regularization (MMR), where

$P_\Omega(M)$14

and uses MMS as a selection score to accelerate training while maintaining accuracy across image benchmarks (Weinstein et al., 2020). Here selective sampling is a compute-allocation mechanism: fully labeled data are available, but only a strategically chosen subset contributes gradient signal.

5. Semi-supervised, self-labeling, and selective inference interpretations

Selective sampling in stream-based active learning is extended in SL2S by allowing a third action besides query and discard: self-label. The setup maintains a labeled set $P_\Omega(M)$15, a stream $P_\Omega(M)$16, and an ensemble of $P_\Omega(M)$17 bootstrapped base classifiers. For an incoming unlabeled $P_\Omega(M)$18, each ensemble member outputs a support vector $P_\Omega(M)$19 and predicted label $P_\Omega(M)$20. If a majority of models are confident above threshold $P_\Omega(M)$21 and all confident models agree, the sample is eligible for pseudo-labeling; otherwise, if budget remains, the oracle is queried (Kozal et al., 2023).

The paper emphasizes a failure mode of naïve self-labeling in selective sampling: dynamic class imbalance. In synthetic studies, confidence-thresholded self-labeling shifts the empirical class distribution toward easier classes even when the true distribution is balanced, and exacerbates preexisting imbalance when the seed set is already skewed (Kozal et al., 2023). Two corrective mechanisms are introduced. The first is a prior filter: for a candidate pseudo-label $P_\Omega(M)$22, estimate the recent class prior over the last $P_\Omega(M)$23 labels,

$P_\Omega(M)$24

and suppress self-labeling if $P_\Omega(M)$25. The second is a confidence- and budget-dependent multiplicity parameter for online bagging,

$P_\Omega(M)$26

which downweights self-labeled samples after the oracle budget is exhausted (Kozal et al., 2023). The resulting procedure is selective sampling in a broader sense: it jointly decides which examples receive costly labels, which receive cheap pseudo-labels, and which are ignored.

A statistically different use of the term appears in selective inference after solving convex programs. There, “selective sampling” denotes sampling from the post-selection distribution induced by conditioning on a model-selection event, such as the support and signs of a randomized LASSO solution. For a randomized convex program

$P_\Omega(M)$27

the KKT condition implies

$P_\Omega(M)$28

with $P_\Omega(M)$29 and $P_\Omega(M)$30. The paper derives a pull-back density for the conditional law of $P_\Omega(M)$31 after selection: $P_\Omega(M)$32 where $P_\Omega(M)$33 is the model density, $P_\Omega(M)$34 the randomization density, and the Jacobian term captures the geometry of the penalty (Harris et al., 2016). For polyhedral penalties such as the LASSO, curvature vanishes and the Jacobian is simple; for non-polyhedral penalties such as group LASSO and nuclear norm, curvature terms analogous to Weyl–Steiner tube formulas appear (Harris et al., 2016). After deriving the target density, the paper outlines projected Langevin sampling for the commonly occurring log-concave case. This usage belongs to post-selection inference rather than active learning, but the core idea is again selective conditioning: one samples from a distribution modified by a prior data-dependent decision.

6. Generative models, mixture components, and LLM selective thinking

In generative adversarial networks, selective sampling can mean selecting a generator rather than selecting data. A multi-generator GAN with $P_\Omega(M)$35 generators $P_\Omega(M)$36, one adversarial discriminator $P_\Omega(M)$37, and $P_\Omega(M)$38 supplementary discriminators $P_\Omega(M)$39 induces a mixture

$P_\Omega(M)$40

where $P_\Omega(M)$41 is the distribution of generator $P_\Omega(M)$42 (Barsim et al., 2018). Supplementary discriminators push generators to specialize, and the nonparametric analysis yields a value function involving negative generalized Jensen–Shannon divergences among component distributions: $P_\Omega(M)$43 After training, sampling from a specific generator $P_\Omega(M)$44 is interpreted as selective sampling from the corresponding learned mixture component (Barsim et al., 2018). In MNIST two-digit experiments, the generators often specialize to different digits or styles, so generator choice acts as unsupervised mode selection.

For LLMs, the phrase has acquired two newer meanings. The first concerns selective thinking during post-training. Ada-RS operates on multiple sampled completions $P_\Omega(M)$45 for a given context $P_\Omega(M)$46, and scores them by an adaptive length-penalized reward

$P_\Omega(M)$47

The solve rate $P_\Omega(M)$48 estimates prompt difficulty: easy prompts induce a large effective penalty for long reasoning traces, while hard prompts relax that penalty (Ge et al., 23 Feb 2026). Ada-RS then applies rejection sampling either to preference pairs,

$P_\Omega(M)$49

or to grouped candidates,

$P_\Omega(M)$50

and only retained pairs or trajectories contribute to DPO or DAPO updates (Ge et al., 23 Feb 2026). On a synthetic e-commerce benchmark with Qwen3-8B and LoRA, the method reduces average output tokens by up to 80% and thinking rate by up to 95% while maintaining or improving tool-call accuracy (Ge et al., 23 Feb 2026). This is selective sampling over training trajectories rather than over external data.

The second LLM meaning concerns inference-time decoding. Selective sampling dynamically switches between greedy decoding and high-temperature truncated sampling at each token position based on a learned sampling-risk classifier. The sampling risk at prefix $P_\Omega(M)$51 is defined as

$P_\Omega(M)$52

where $P_\Omega(M)$53 is the task reward obtained by greedy continuation, and the expectation evaluates the drop in reward if the next token is sampled instead (Troshin et al., 20 Sep 2025). A lightweight classifier on LM hidden states predicts whether the current position is safe to sample; if risky, decoding is greedy, otherwise high-temperature min-$P_\Omega(M)$54 or related sampling is used. On GSM8K, GSM-Symbolic, and Minerva Prealgebra, this improves the quality–diversity trade-off over top-$P_\Omega(M)$55, min-$P_\Omega(M)$56, top-$P_\Omega(M)$57, and entropy-based dynamic temperature, with area-under-curve gains such as $P_\Omega(M)$58 versus $P_\Omega(M)$59 on GSM-Symbolic (Troshin et al., 20 Sep 2025). Selective sampling here is explicitly token-local risk gating.

These generative formulations broaden the term considerably. Rather than choosing external measurements or labels, they choose mixture components, generated trajectories, or decoding modes. A plausible implication is that the modern LLM literature is reinterpreting selective sampling as control over where stochasticity enters the system: in data collection, in learning signals, or in decoding.

7. Conceptual structure, common trade-offs, and recurring limitations

Despite its heterogeneous uses, selective sampling exhibits a recurring triplet of design variables: a candidate set, a selection score or admissibility rule, and a post-selection objective. In matrix completion, candidates are entries or blocks, the score is structural utility under a low-rank model, and the objective is exact or improved completion (Parkinson et al., 2019). In online experts and imitation learning, candidates are labels, the score is disagreement or margin relative to uncertainty sets, and the objective is regret minimization under label efficiency (Castro et al., 2023, Sekhari et al., 2023). In deep learning, candidates are examples or features, the score is margin, loss, or saliency, and the objective is accelerated convergence or reduced memory (Zhou et al., 2015, Weinstein et al., 2019). In LLM post-training and decoding, candidates are trajectories or token-level stochastic actions, the score is reward or risk, and the objective is a better efficiency–quality or quality–diversity frontier (Ge et al., 23 Feb 2026, Troshin et al., 20 Sep 2025).

A second commonality is that selective sampling almost always imposes a structural bias on the retained subset. This is usually beneficial only when the selection score faithfully tracks informativeness. Several papers emphasize failure modes when that condition breaks. In action recognition, selective saliency helps DT but can hurt iDT by distorting an already compact feature distribution (Zhou et al., 2015). In self-labeling with selective sampling, confident pseudo-labels can skew class priors and amplify imbalance unless explicit prior-control mechanisms are used (Kozal et al., 2023). In adaptive label-efficient prediction, worst-case $P_\Omega(M)$60 label complexity remains unavoidable without a stochastic gap condition, so selective sampling cannot evade adversarial lower bounds (Castro et al., 2023). In drift settings, stationary query heuristics can stop asking for labels precisely when adaptation is most needed (Moroshko et al., 2014). In selective inference, incorrect omission of Jacobian or curvature terms yields a misspecified post-selection law (Harris et al., 2016).

A third commonality is that the gain from selective sampling often derives from a reduction in effective degrees of freedom. In constrained matrix completion, extra linear relations narrow the feasible set (Parkinson et al., 2019). In nearest-neighbor and principal-curve methods, samples concentrate around regions where decision boundaries or pattern mismatches matter most (Joseph et al., 2013, Hakimzadeh et al., 2022). In expert aggregation and online regression, queried labels focus on disagreement regions whose size is controlled by eluder dimension or disagreement coefficient (Sekhari et al., 2023). In deep networks, low-margin points function as approximate support vectors (Weinstein et al., 2019). In LLM selective thinking, only high-reward or risk-safe trajectories shape optimization or decoding (Ge et al., 23 Feb 2026, Troshin et al., 20 Sep 2025). This suggests that selective sampling is best understood not merely as subsampling, but as targeted reduction of redundancy under an explicit structural model.

The principal controversies are therefore not definitional but epistemic: what score should govern selection, and how robust is it across regimes? Some papers advocate deterministic selection for reliability (Hakimzadeh et al., 2022); others exploit stochastic querying to preserve worst-case guarantees (Castro et al., 2023, Moroshko et al., 2014). Some use model-agnostic geometry (Camilleri et al., 2021, Joseph et al., 2013); others rely on task-specific scorers or reward models (Zhou et al., 2015, Ge et al., 23 Feb 2026). Some impose strong prior structure such as low-rank subblocks (Parkinson et al., 2019); others seek universal selectors trained across domains (Sekhari et al., 2023, Troshin et al., 20 Sep 2025). Selective sampling is therefore not a single method but an organizing principle for data-dependent acquisition, retention, or conditioning. Its effectiveness is determined by the fidelity of its informativeness proxy, the geometry of the underlying problem, and the way post-selection optimization or inference accounts for the induced bias.