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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>SEVAL — Imbalanced Semi-Supervised Learning via Label Refinement and Threshold Adjustment</title>
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</head>
<body>
<!-- ═══ TOPBAR ═══ -->
<nav class="topbar">
<span class="topbar-brand">SEVAL · TMLR 2026</span>
<div class="topbar-links">
<a class="topbar-btn primary" href="https://openreview.net/forum?id=HbAMQiyK48" target="_blank">Paper</a>
<a class="topbar-btn" href="https://arxiv.org/abs/2407.05370" target="_blank">arXiv</a>
<a class="topbar-btn" href="https://github.com/ZerojumpLine/SEVAL" target="_blank">Code</a>
</div>
</nav>
<!-- ═══ HERO ═══ -->
<div class="hero">
<div class="venue-tag">Transactions on Machine Learning Research · June 2026</div>
<h1>Imbalanced Semi-Supervised Learning via <em>Label Refinement</em> and <em>Threshold Adjustment</em></h1>
<p class="author-line">
<a href="mailto:zejuli@fudan.edu.cn">Zeju Li</a><sup>1,2</sup> 
<a href="mailto:ying-qiu.zheng@ndcn.ox.ac.uk">Ying-Qiu Zheng</a><sup>2</sup> 
<a href="mailto:chen.chen2@sheffield.ac.uk">Chen Chen</a><sup>3,4,5</sup> 
<a href="mailto:saad.jbabdi@ndcn.ox.ac.uk">Saad Jbabdi</a><sup>2</sup>
</p>
<p class="affil-line">
<sup>1</sup> Fudan University ·
<sup>2</sup> FMRIB Centre, University of Oxford ·
<sup>3</sup> University of Sheffield<br/>
<sup>4</sup> University of Oxford ·
<sup>5</sup> Imperial College London
</p>
<div class="hero-links">
<a class="hero-btn filled" href="https://openreview.net/forum?id=HbAMQiyK48" target="_blank">
<svg width="15" height="15" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><path d="M14 2H6a2 2 0 0 0-2 2v16a2 2 0 0 0 2 2h12a2 2 0 0 0 2-2V8z"/><polyline points="14 2 14 8 20 8"/></svg>
Paper (OpenReview)
</a>
<a class="hero-btn outline" href="https://arxiv.org/abs/2407.05370" target="_blank">
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arXiv
</a>
<a class="hero-btn outline" href="https://github.com/ZerojumpLine/SEVAL" target="_blank">
<svg width="15" height="15" viewBox="0 0 24 24" fill="currentColor"><path d="M12 2C6.477 2 2 6.477 2 12c0 4.418 2.865 8.166 6.839 9.489.5.092.682-.217.682-.483 0-.237-.008-.868-.013-1.703-2.782.604-3.369-1.342-3.369-1.342-.454-1.154-1.11-1.462-1.11-1.462-.908-.62.069-.608.069-.608 1.003.07 1.531 1.03 1.531 1.03.892 1.529 2.341 1.087 2.91.831.092-.646.35-1.086.636-1.336-2.22-.253-4.555-1.11-4.555-4.943 0-1.091.39-1.984 1.029-2.683-.103-.253-.446-1.27.098-2.647 0 0 .84-.269 2.75 1.025A9.578 9.578 0 0 1 12 6.836a9.59 9.59 0 0 1 2.504.337c1.909-1.294 2.747-1.025 2.747-1.025.546 1.377.202 2.394.1 2.647.64.699 1.028 1.592 1.028 2.683 0 3.842-2.339 4.687-4.566 4.935.359.309.678.919.678 1.852 0 1.336-.012 2.415-.012 2.743 0 .267.18.578.688.48C19.138 20.163 22 16.418 22 12c0-5.523-4.477-10-10-10z"/></svg>
Code
</a>
</div>
</div>
<hr class="rule" />
<!-- ═══ ABSTRACT ═══ -->
<div class="content">
<section>
<div class="section-label">Abstract</div>
<p class="abstract-text">
Semi-supervised learning (SSL) algorithms often struggle to perform well when trained on imbalanced
data. In such scenarios, the generated pseudo-labels tend to exhibit a bias toward the majority class,
and models relying on these pseudo-labels can further amplify this bias. Existing imbalanced SSL
algorithms explore pseudo-labeling strategies based on either <em>pseudo-label refinement</em> (PLR)
or <em>threshold adjustment</em> (THA), aiming to mitigate the bias through heuristic-driven designs.
However, through a careful statistical analysis, we find that existing strategies are suboptimal: most
PLR algorithms are either overly empirical or rely on the unrealistic assumption that models remain
well-calibrated throughout training, while most THA algorithms depend on flawed metrics for
pseudo-label selection.
</p>
<p class="abstract-text">
To address these shortcomings, we first derive the theoretically optimal form of pseudo-labels under
class imbalance. This foundation leads to our key contribution: <strong>SEVAL</strong> (SEmi-supervised
learning with pseudo-label optimization based on VALidation data), a unified framework that learns both
PLR and THA parameters from a held-out partition of the labeled training data — no additional annotation
required. By jointly optimizing these components, SEVAL adapts to specific task requirements while
ensuring per-class pseudo-label reliability. Our experiments demonstrate that SEVAL outperforms
state-of-the-art SSL methods across diverse imbalanced scenarios while remaining compatible with
any pseudo-label-based SSL algorithm.
</p>
</section>
<!-- ═══ THEORY I ═══ -->
<section>
<div class="section-label">Theory</div>
<h2>Why existing label refinement is fundamentally suboptimal</h2>
<p>
Pseudo-label refinement methods adjust the model's logit vector $\hat{\boldsymbol{z}}^{\mathcal{U}}$
by a class-specific offset $\boldsymbol{\pi} \in \mathbb{R}^C$ before assigning pseudo-labels.
The two dominant strategies — Distribution Alignment (DA) and Logit Adjustment (LA) — both
fail for different reasons. We derive the correct target from first principles.
</p>
<h3>The theoretically optimal classifier under class imbalance</h3>
<p>
Assume the test distribution $\mathcal{T}$ shares class-conditional distributions with the
training set $\mathcal{X}$ but has different class priors:
$P^{\mathcal{X}}(X|Y) = P^{\mathcal{T}}(X|Y)$, $P^{\mathcal{X}}(Y) \neq P^{\mathcal{T}}(Y)$.
This prior-shift assumption is standard in class-imbalanced settings.
</p>
<div class="thm">
<div class="thm-label">Proposition 1 — Optimal Classifier under Prior Shift</div>
<p>
Given a classifier $f^*(X)$ optimised on $P^{\mathcal{X}}(X,Y)$, the optimal Bayes classifier
on the test distribution satisfies
$$f^{\mathcal{T}}(X) \propto \frac{f^*(X)\, P^{\mathcal{T}}(Y)}{P^{\mathcal{X}}(Y)}.$$
</p>
</div>
<div class="thm corollary">
<div class="thm-label">Corollary 1</div>
<p>
The same optimal classifier is also optimal on the resampled unlabelled distribution
$\displaystyle\frac{P^{\mathcal{U}}(X,Y)\,P^{\mathcal{T}}(Y)}{P^{\mathcal{U}}(Y)}$.
</p>
</div>
<p>
The key implication: pseudo-label offsets should be calibrated to the <em>test</em> distribution
$P^{\mathcal{T}}(Y)$, not to the unlabeled training distribution $P^{\mathcal{U}}(Y)$.
When $P^{\mathcal{T}}(Y)$ is uniform (the standard evaluation assumption), the optimal
classifier should maximise <strong>class-averaged likelihood</strong>.
</p>
<div class="thm remark">
<div class="thm-label">Remark 1</div>
<p>
The optimal Bayes classifier on $P^{\mathcal{U}}(X,Y)$ should have maximised
class-averaged likelihood, when $P^{\mathcal{T}}(Y)$ is uniform.
</p>
</div>
<p>
From this lens, both DA and LA are provably suboptimal. DA aligns pseudo-label priors to
$P^{\mathcal{U}}(Y)$ — the wrong distribution — leading to increased false negatives for minority
classes without improving true positives. LA subtracts a fixed log-prior offset, which is
theoretically justified only when $f^*(X)$ is perfectly calibrated. Neural networks during SSL
are systematically uncalibrated, and their logit distributions shift throughout training,
so the optimal offset must shift accordingly. LA has no mechanism to track this.
</p>
<figure class="fig">
<img src="figs/Fig_Analysis.png" alt="Limitations of DA and LA" />
<figcaption>
<strong>Figure 1.</strong> Two-class imbalanced classification illustrating the failure modes of
existing PLR methods. <strong>(a)</strong> DA imposes constraints based on the distribution of
$\mathcal{U}$. Even when $\mathcal{U}$ is estimable, enforcing proportional predictions increases
false negatives without improving true positives, penalising minority classes.
<strong>(b)</strong> LA refines the boundary using fixed log-prior offsets. As training proceeds,
logit distributions shift (Case 1 → Case 2), but LA's offsets remain static — the decision boundary
falls behind. <strong>(c)</strong> SEVAL directly optimises the class-averaged likelihood from
held-out data and updates parameters via a curriculum.
</figcaption>
</figure>
</section>
<!-- ═══ THEORY II ═══ -->
<section>
<h2>Why dynamic thresholding optimises the wrong metric</h2>
<p>
Class-specific thresholds $\boldsymbol{\tau} \in \mathbb{R}^C$ filter which unlabelled samples
are included as pseudo-labels. Choosing good thresholds directly controls pseudo-label noise —
and lower noise yields better models:
</p>
<div class="thm theorem">
<div class="thm-label">Theorem 1 — Noise Rate Bound</div>
<p>
Let $\hat{f}$ be trained on $\hat{\mathcal{U}}$ with noise rate
$\rho = 1 - P_{\hat{\mathcal{U}}}(y = \hat{y})$ and $|\hat{\mathcal{U}}| = M$ fixed.
For any $\delta > 0$, with probability $\geq 1-\delta$:
$$R_{\mathcal{L},\mathcal{U}}(\hat{f}) \leq \min_{f \in \mathcal{F}} R_{\mathcal{L},\mathcal{U}}(f)
+ \frac{4L\,\mathfrak{R}(\mathcal{F})}{1 - 2\rho} + 2\sqrt{\frac{\log(1/\delta)}{2M}}.$$
</p>
<p>
Reducing $\rho$ tightens the bound. The goal of thresholding is to select the subset
that minimises pseudo-label noise.
</p>
</div>
<p>
The overall pseudo-label accuracy decomposes two ways. Only one is actionable:
</p>
<div class="two-col">
<div class="thm side-by-side-item">
<div class="thm-label">Via Precision — accessible</div>
<p>
$$P(y = \hat{y}) = \sum_{j}\underbrace{P(y=j \mid \hat{y}=j)}_{\textbf{Precision}} \cdot P(\hat{y}=j)$$
$P(\hat{y}=j)$ is directly computable from model predictions.
</p>
</div>
<div class="thm side-by-side-item">
<div class="thm-label">Via Recall — inaccessible</div>
<p>
$$P(y = \hat{y}) = \sum_{j}\underbrace{P(\hat{y}=j \mid y=j)}_{\textbf{Recall}} \cdot P(y=j)$$
$P(y=j)$ requires the true labels of unlabelled samples — unavailable.
</p>
</div>
</div>
<div class="thm remark">
<div class="thm-label">Remark 2 — The Key Insight</div>
<p>
A better thresholding vector $\boldsymbol{\tau}$ should be derived from class-wise
<strong>Precision</strong>, not class-wise <strong>Recall</strong>.
</p>
</div>
<p>
Yet FlexMatch, FreeMatch, and Adsh — the leading dynamic thresholding methods — all set
thresholds based on maximum class probability $P'_c$, which is a per-class estimate of
<strong>Recall</strong>. They lower thresholds for classes with small $P'_c$,
implicitly assuming Recall and Precision are always in a trade-off. This assumption
breaks in two important and common cases: a class can have simultaneously high Recall
and high Precision (in which case these methods restrict sampling unnecessarily), or
low Recall and low Precision (in which case they admit too many noisy samples).
</p>
<figure class="fig">
<img src="figs/Fig2_Thres.png" alt="Threshold analysis on two-moons" />
<figcaption>
<strong>Figure 2.</strong> Two-moons experiments illustrating all four Recall × Precision regimes.
FlexMatch (Recall-based) correctly handles Cases 1 and 2, but systematically fails in
<em>Case 3</em> (high Recall & high Precision — selects too few) and <em>Case 4</em>
(low Recall & low Precision — selects too many noisy samples). SEVAL's Precision-derived
thresholds handle all four cases correctly. Empirically, Case 3 is frequent for minority
classes in imbalanced SSL.
</figcaption>
</figure>
<h3>Optimal thresholds equalise per-class Precision</h3>
<p>
Maximising total pseudo-label accuracy subject to a fixed budget $M$ leads to the constrained
optimisation:
$$\max_{\boldsymbol{\tau}} \sum_{c=1}^C \mathcal{A}(\tau_c, c)\,\mathcal{S}(\tau_c, c),
\quad \text{s.t.} \quad \sum_{c=1}^C \mathcal{S}(\tau_c, c) = M,$$
where $\mathcal{A}(\tau_c, c)$ is the Precision of selected samples for class $c$ and
$\mathcal{S}(\tau_c, c)$ is their count. Applying Lagrange multipliers and a smoothness
approximation yields a clean optimality condition:
</p>
<div class="thm remark">
<div class="thm-label">Remark 3 — Optimality Condition</div>
<p>
At the optimal $\boldsymbol{\tau}$, per-class Precision $\mathcal{A}(\tau_c, c)$ must be
equal across all classes. The optimal threshold vector aligns Precision to a common
target level $t$. This is a multi-class analogue of the <strong>Neyman–Pearson Lemma</strong>.
</p>
</div>
</section>
<!-- ═══ METHOD ═══ -->
<section>
<div class="section-label">Method</div>
<h2>SEVAL: learning both components from held-out data</h2>
<p>
SEVAL optimises PLR offsets $\boldsymbol{\pi}$ and THA thresholds $\boldsymbol{\tau}$
simultaneously from a small held-out partition $\mathcal{V}$ of the labelled training data.
No additional annotation is required: the training set $\mathcal{X}$ is simply split equally
into $\mathcal{X}'$ (for SSL) and $\mathcal{V}'$ (for curriculum learning).
PLR and THA address complementary stages of the pseudo-labeling pipeline and can be optimised
in parallel with network training, incurring at most 50% theoretical overhead.
</p>
<figure class="fig">
<img src="figs/Fig1_Method.png" alt="SEVAL overview" />
<figcaption>
<strong>Figure 3. SEVAL overview.</strong> Existing methods estimate offsets from class priors of
labelled samples (DA/LA) and thresholds from maximum class probability $P'_c$ (FlexMatch/FreeMatch).
SEVAL instead learns a <em>curriculum</em> of logit offsets $\boldsymbol{\pi}^*$ and class-specific
thresholds $\boldsymbol{\tau}^*$ directly from held-out data $\mathcal{V}$, updated via
exponential moving average throughout training.
</figcaption>
</figure>
<h3>Learning the offsets</h3>
<p>
PLR offsets are found by minimising the class-averaged cross-entropy on $\mathcal{V}$:
$$\boldsymbol{\pi}^* = \arg\min_{\boldsymbol{\pi}} \sum_{j=1}^C \frac{1}{C k_j}
\sum_{i=1}^K \mathbf{1}(y_i = j)\,\mathcal{L}(y_i,\, \sigma(\boldsymbol{z}_i^{\mathcal{V}} - \log\boldsymbol{\pi})).$$
Crucially, this does not require knowing $P^{\mathcal{U}}(X,Y)$ — only labelled held-out data.
Because $\boldsymbol{\pi}^*$ is tied to the current model parameters, it is also applied at
test time, outperforming LA without any calibration assumption.
</p>
<h3>Learning the thresholds</h3>
<p>
THA thresholds are set by searching for the value $\tau_c$ that brings each class's
Precision (estimated on $\mathcal{V}$) to the target level $t$:
$$\tau_c^* = \begin{cases} \arg\min_{\tau_c}|\mathcal{A}(\tau_c, c) - t| & \text{if } \alpha_c < t \\ 0 & \text{otherwise}\end{cases}$$
When a class is already sufficiently accurate ($\alpha_c \geq t$), all its samples are included.
For imbalanced $\mathcal{V}$, class-frequency weights normalise the cost function.
Group-based optimisation handles classes with very few samples ($k_c < 10$).
The single hyper-parameter $t$ replaces the per-class threshold vector, and
$\boldsymbol{\pi}$ and $\boldsymbol{\tau}$ are updated via exponential moving average
throughout training to ensure curriculum stability.
</p>
<div class="insight-trio">
<div class="insight">
<div class="insight-tag">No extra data</div>
<h4>Built from the training split</h4>
<p>$\mathcal{X}$ is partitioned into two equal halves. The curriculum is learned on one half and applied to the full dataset after training begins.</p>
</div>
<div class="insight">
<div class="insight-tag">Plug-and-play</div>
<h4>Works with any SSL algorithm</h4>
<p>SEVAL modifies only $\boldsymbol{q}$ and $\boldsymbol{\tau}$. No changes to the loss function, data augmentation, or architecture are needed.</p>
</div>
<div class="insight">
<div class="insight-tag">Data-efficient</div>
<h4>Stable with as few as 10 samples</h4>
<p>Group-based threshold optimisation guarantees stability under scarce per-class data. Performance is flat from 10 to 500 validation samples per class.</p>
</div>
</div>
</section>
<!-- ═══ RESULTS ═══ -->
<section>
<div class="section-label">Experiments</div>
<h2>State-of-the-art results across imbalanced SSL benchmarks</h2>
<p>
We evaluate on CIFAR-10-LT, CIFAR-100-LT, STL-10-LT (imbalance ratios up to 150),
and the real-world Semi-Aves benchmark (200 bird species, natural long tail ranging from
53 to 15 samples per class). All comparisons share identical codebases and hyperparameter
settings. Results below are test accuracy (%) averaged over three seeds.
</p>
<div class="table-wrap">
<table>
<thead>
<tr>
<th>Algorithm</th>
<th>Type</th>
<th>CIFAR-10-LT<br/><small style="font-weight:400">γ=100, n₁=500</small></th>
<th>CIFAR-100-LT<br/><small style="font-weight:400">γ=10, n₁=50</small></th>
<th>STL-10-LT<br/><small style="font-weight:400">γ=20, n₁=150</small></th>
</tr>
</thead>
<tbody>
<tr><td>FixMatch</td><td>—</td><td>67.8</td><td>45.2</td><td>47.6</td></tr>
<tr><td> + DARP</td><td>PLR</td><td>74.5</td><td>49.4</td><td>58.1</td></tr>
<tr><td> + FlexMatch</td><td>THA</td><td>74.0</td><td>49.9</td><td>48.3</td></tr>
<tr><td> + FreeMatch</td><td>THA</td><td>73.8</td><td>49.8</td><td>63.5</td></tr>
<tr class="ours"><td> + SEVAL-PL</td><td>PLR+THA</td><td class="best">77.7</td><td class="best">50.8</td><td class="best">67.4</td></tr>
<tr><td> + DASO</td><td>LTL+PLR</td><td>76.0</td><td>49.2</td><td>65.7</td></tr>
<tr><td> + ACR</td><td>LTL+PLR+THA</td><td>80.2</td><td>50.6</td><td>65.6</td></tr>
<tr class="ours"><td> + SEVAL</td><td>LTL+PLR+THA</td><td class="best">82.8</td><td class="best">51.4</td><td class="best">67.4</td></tr>
</tbody>
</table>
</div>
<p style="font-size:0.82rem; color: var(--muted); margin-top:10px;">
SEVAL-PL (PLR+THA only, without any long-tailed learning component) already outperforms most
hybrid methods. Full SEVAL sets a new state of the art in every category. See the paper for
Semi-Aves results, varied imbalance ratios, low-label regimes ($n_1 = 4$), and ablations.
</p>
</section>
<!-- ═══ CITATION ═══ -->
<section>
<div class="section-label">Citation</div>
<h2>If you find this work useful</h2>
<pre>@article{li2026seval,
title = {Imbalanced Semi-Supervised Learning via Label Refinement
and Threshold Adjustment},
author = {Li, Zeju and Zheng, Ying-Qiu and Chen, Chen and Jbabdi, Saad},
journal = {Transactions on Machine Learning Research},
year = {2026},
url = {https://openreview.net/forum?id=HbAMQiyK48}
}</pre>
</section>
</div><!-- /content -->
<!-- ═══ FOOTER ═══ -->
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<div class="footer-inner">
<p>
Published in <a href="https://openreview.net/forum?id=HbAMQiyK48" target="_blank">Transactions on Machine Learning Research</a>, June 2026.
</p>
<p>
<a href="https://arxiv.org/abs/2407.05370" target="_blank">arXiv preprint</a> ·
<a href="https://github.com/ZerojumpLine/SEVAL" target="_blank">GitHub</a> ·
<a href="mailto:zejuli@fudan.edu.cn">zejuli@fudan.edu.cn</a>
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