F.2 Baselines Details
While numerous branches of noisy labeled learning have been explored for classification tasks, our focus in this study centers on the challenging domain of noisy label regression.
To comprehensively investigate this task, we have conducted an extensive review of the various branches and have selected a set of fourteen baselines that are adaptable to regression.
It is worth noting that C-Mixup [Yao et al., 2022 ] was originally proposed as a regression baseline.
In the following section, we provide an overview of these selected baselines, offering a broad coverage of diverse approaches to address the noisy label regression problem.
Additionally, we present detailed descriptions of the experimental settings for each baseline.

D2L [Ma et al., 2018 ] for intrinsic dimension exploration. Following the paper, we set k=20 and m=10 for Local Intrinsic Dimensionality (LID) estimation
and set the LID estimation window as five following the official implementation.

CDR [Xia et al., 2021 ] for model weight parameter selection, and RDI [Hu et al., 2020 ] for regularizing the paramter distance from the initialization.
At RDI, we use search space \lambda\in[0.25,0.5,1,2,4,8] .

C-Mixup [Yao et al., 2022 ] for regularization via continuous mixup.
C-Mixup-batch is used in all experiments because of the excessive memory requirement for pairwise distance matrix P .
We set the beta distribution variable \alpha as 1.5.
The bandwidth variable \sigma is searched over [0.01, 0.1, 1], following Yao et al. [ 2022 ] .

SELFIE [Song et al., 2019 ] and AUX [Hu et al., 2020 ] for refurbishing.
To apply SELFIE to the continuous label, we redefine the concept of uncertainty F(x;q) and
refurbished labels y^{refurb} with the mean and standard deviation.

 F(x;q)=\frac{\sigma(H_{x}(q))}{(\max{(Y)}-\min{(Y)})}<\epsilon (7)

 y^{refurb}=\mu(H_{x}(q)) (8)

where H_{x}(q) is the prediction history of x from before q epochs, \epsilon is the uncertainty threshold.

For SELFIE, we train 1/4 of the total training epochs for the warm-up phase, following Song et al. [ 2019 ] .
The variable q is searched over half of the warm-up epochs and around.
The variable \epsilon is searched over [0.05, 0.10, 0.15, 0.20], following Song et al. [ 2019 ] .

For AUX [Hu et al., 2020 ] , we regularize the auxiliary variable by weight decay 0.0005, reducing the weight by 0.1 at 1/2 and 3/4 of the total training epochs.
The learning rate of the auxiliary variable is set to 0.1 and 0.01.
The variable \lambda is searched over [0.25, 0.5, 1, 2, 4, 8].

SPR [Wang et al., 2022 ] performs penalized regression for selection. It requires some adaptation to regression by ignoring the \ell_{q} penalty as there is no longer a linearity gap between the scalar output and the final fully connected layer that requires reducing.
Also, we use our fragmentation splits \{4,8\} to bin the regression data for SPR’s parallel optimization.

Sigua [Han et al., 2020 ] and CNLCU-S/H [Xia et al., 2022 ] for small loss selection.
For Sigua, we use \delta(t)\in[0.3,0.4] and \gamma=0.01 and set T_{k} as 5% of the total training epochs.
For CNLCU-S/H, we search \sigma and \tau_{\min} in [0.01, 0.1, 1, 10] and set T_{k} as 5%.

BMM [Arazo et al., 2019 ] for selection based on beta mixture model fitting on the loss distribution.
BMM does hard sampling and trains using the selected samples.
DY-S is a dynamic soft loss. We implemented two versions; the first uses a convex combination as in Reed et al. [ 2015 ] ((1-w)\tilde{y}^{c}-w\hat{y})^{2} . Second, instead of bootstrapping, we dynamically weight the loss using the BMM probability to create a cost-sensitive loss, (1-w)\ell .
The w is the mixture clean probability, \hat{y} is the model prediction, \tilde{y}^{c} is the assigned noisy label, and \ell is the loss.

SuperLoss [Castells et al., 2020 ] regularization parameter \lambda is searched over [0.01, 0.1, 1, 10] while \tau uses an exponential running average with a fixed smoothing parameter \alpha=0.9 .

[Incompatible] CRUST [Mirzasoleiman et al., 2020 ] for clean coreset selection.
It aims to select a coreset based on class-wisely gradient clustering .
For regression, we initially viewed all data as a single class and proceeded with coreset selection, but the results were unsatisfactory.
Therefore, we report results based only on the discretized version, demonstrating comparable performances.
We select 1/2 of the total dataset as a coreset.
The distance threshold in calculating clusters is searched over [1, 2, 4].

[Incompatible] OrdRegr [Garg and Manwani, 2020 ] for loss correction.
Since no official implementation is provided, we implemented it with cross-entropy loss for ordinal regression.
Importantly, we failed to find accurate noise rate estimation using their suggested methods.
Even when considering the transition matrix with the actual noise rate, the loss correction algorithm proved ineffective in our benchmark tests.