A Noisy-Label-Learning Formulation for Immune Repertoire Classification and Disease-Associated Immune Receptor Sequence Identification

Assuming $N$ Individuals’ repertoires are denoted as $\{R_{1},\ldots,R_{N}\}$ and the corresponding repertoire-level concepts are denoted as $\{Y_{1},\ldots,Y_{N}\}$. $Y\in\{0,1\}$, where 1 represents that subject is positive, and 0 represents negative (To simplify the discussion, we assume the task is binary classification, although our method can be easily extended to multi-class or regression). Each repertoire consists of a large amount of sequences $\{s_{1},\ldots,s_{M}\}$ and their corresponding frequency $\{\rho_{1},\ldots,\rho_{M}\}$. Each sequence also has underlying corresponding sequence-level labels $y$, where $y\in\{0,1\}$, where 1 represents that the TCR is associated with the disease of interest, and 0 represents that it’s not. We assume the sequence-level label is unavailable during training. Only a relatively small amount of them are known and used for evaluation. We have two objectives:

• •

  Repertoire classification, i.e., a mapping function $F:R\mapsto Y$.

• •

  Disease-associated sequence identification, i.e., a mapping function $f:s\mapsto y$

Many previous methods model the repertoire classification problem as MIL, and some of them identify disease-associated sequence as a side feature. Our work attempts to learn the antigen-driven responses directly. However, the corresponding antigen of most of the sequences within repertoires is unknown. It’s hard to obtain enough labeled sequences for the training of a deep model. Considering the characteristics of this problem, we transform the repertoire-level labels to noisy sequence-level labels, i.e., letting $Y=\tilde{y}$. $\tilde{y}$ is the noisy sequence label and may not be the same as the ground-truth $y$, especially when the sequence is from the repertoire of a patient. We are to train a sequence-level model $f:s\mapsto y$, which predicts whether an input sequence belongs to a sequence-level concept, i.e., disease-irrelevant or disease-associated.

A T-cell receptor is profiled by the CDR3 sequence, V/D/J gene usage, and its productive frequency. The frequency is the read count of the productive CDR3 Amino Acid (AA) sequence over the total number of productive reads in each repertoire. We then introduce both datasets.

For the experiments on the CMV dataset, We choose the hyper-parameters using the validation set. Specifically, $\alpha$ in EMA is set to 0.99, and $\beta$ in label smoothing is set to 0.7. In terms of the model structure, there is 1 layer of 1-head attention, the dimension of the embedding token is 16, and the dropout rate is 0. The optimizer is Adam optimizer Kingma and Ba (2015) with a learning rate of 0.005 and a batch size of 256. We train the model for 15 epochs using the original targets to warm the model up. The validation set is used for early stopping. For the experiments on the Cancer dataset, We choose the hyper-parameters using the validation set. Specifically, $\alpha$ in EMA is set to 0.95, and $\beta$ in label smoothing is set to 0.4. In terms of the model structure, there are 2 layers of 4-head attention, the dimension of the embedding token is 192, and the dropout rate is 0.1. The optimizer is Adam optimizer Kingma and Ba (2015) with a learning rate of 0.0005 and a batch size of 256. We train the model for 8 epochs using the original targets to warm the model up. The validation set is used for early stopping.

We first verify the repertoire classification and disease-associated TCR sequence abilities of our model on the CMV dataset. For the classification task, we compare our method with:

• •

  Logistic regression as a baseline linear classifier.

• •

  Burden test in Emerson et al. (2017) as a baseline statistical method.

• •

  Logistic multiple instance learning (Log. MIL) Ostmeyer et al. (2020b) applies logistic regression to each k-mer representation.

• •

  DeepRC Widrich et al. (2020) is a modern Hopfield network that models the repertoire classification as MIL.

It can be seen from Table 1 that even though our method is only fed with sequence and has no access to the whole repertoire, competitive results are achieved.

We then evaluate the sequence-level predictions to explore whether our model learns the pair-wise TCR–disease relationship. As shown in the first row in Fig. 3, our model surprisingly assigns accurate association scores on the previously known CMV-associated sequences that are identified by Emerson et al. (2017). It demonstrates prediction accuracy competitive with experimental results in a majority of cases. It is also worth noting that there are a small number of false negatives in the test set because healthy donors may still have disease-associated sequences. Therefore, the reported AUC values tend to be lower than the real performance. We also release those sequences with high confidence but not in the associated sequences set in the supplementary material for future experimental verification.

We further test our model on a more challenging task, i.e., on repertoires that are not even seen during training. The results in the second row of Fig. 3 show that it is also possible to make predictions on unseen hypervariable TCR sequences.

We further verify the disease-associated TCR sequence identification ability of our model on the Cancer dataset. We mainly compare our method on the cancer dataset with DeepCAT, which deploys CNN models after PCA encoding of the AA biochemical indices, AutoCAT Wong and Li (2022), which extends DeepCAT by allowing the use of immune repertoire samples, and TCR-BERT + Linear Regression, i.e., the linear classifier on top of the embedding from TCR-BERT.

DeepCAT also attempts to directly model the sequence-disease relationship. However, we suggest that the constructed Cancer dataset is noisy by making the observation in Fig. 5. DeepCAT trains one model for each length, and our method takes all sequences as input. Thus, besides the overall AUC, we also report the prediction results of our method on 12-17 AA long test sequences for comparison with DeepCAT.

From Table 2, our method consistently outperforms DeepCAT across all sequence lengths. The effectiveness of our robustness training method verifies the existence of noisy labels in the Cancer dataset.

To explore whether our assumption about the noisy labels is mostly from the positive class, we try to empirically prove it in this section.

As shown in Arpit et al. (2017), deep models would learn easy and simple patterns first before fitting the noise. The conclusion is reached by training a deep model on a noisy dataset and making the observation that the clean samples are fitted before the noisy samples. Similarly, we train the model only using ERM and original labels and observe the model’s prediction confidence (the softmax probabilities on the corresponding class) on samples in negative and positive classes, respectively. As shown in Fig. 5, the model starts to produce higher confidence on negative samples from the early training stage. Besides, the training iterations for the model to overfit the positive samples are more than that of the negative samples. Note that the original labels are balanced on both datasets. So this observation verifies that there are more noisy positive labels than noisy negative labels.

To verify the effectiveness of different components of our method, we conduct ablation experiments on the CMV and Cancer datasets. We design two variants of our method:

• •

  w/o ASA: removing the asymmetric self-adaptive training strategy.

• •

  w/o CT: removing the co-training strategy.

It can be seen from Table 3 that the two components both bring performance gain. It is worth noting that the asymmetric self-adaptive strategy brings nearly no extra computation, facilitating the adaptation of our method. What’s more, the asymmetric self-adaptive technique ensures more stable training, as shown in the training curve in Fig. 4(a).

We also compare the choice of two important hyper-parameters in Fig. 4(b) and (c). It can be found that the $\alpha$ in EMA should be carefully chosen. Increasing $\alpha$ would make the original labels remain longer, gradually degenerating into the standard ERM. While decreasing $\alpha$ would make the training targets quickly approximate the model’s prediction and the training loss close to zero.

Repertoire-based machine learning methods and applications focus on the classification and prediction of a donor’s immune status, such as disease status, recent vaccination, or past exposure to a particular pathogen. Thus, the main application area is immunodiagnostics.

In order to capture antigen-associated sequences at a repertoire level, there exists a range of approaches: 1). Public adaptive immune receptor-based classification. Emerson et al. Emerson et al. (2017) identified TCRβ sequences associated with cytomegalovirus (CMV) positive serostatus using Fisher’s exact test. Only 164 sequences were found in positive individuals, demonstrating that the detectable signal of pathogen exposure may be small. A similarly small number of TCRβ sequences that are associated with systemic lupus erythematosus and rheumatoid arthritis are distinguished from healthy individuals Liu et al. (2019). 2). Sequence similarity cluster-based classification. Using GIANA Zhang et al. (2021) to cluster large-scale TCR datasets provided candidate antigen-specific receptors and provided a new solution to repertoire classification. This study is significant in that it identified sequence clusters that distinguish individuals. 3). K-mer-based classification. Many repertoire-based approaches rely on k-mer encoding, where each repertoire represents a 100-element vector corresponding to the distribution of CDR3β k-mers in the repertoire Thomas et al. (2014). They first cluster them in accordance with their physicochemical properties before classifying individuals using SVM approaches. 4). MIL–based classification methods predict sequences associated with the antigen within a repertoire and then compute a repertoire-level label from the set of sequence-level predictions. Ostmeyer et al. Ostmeyer et al. (2017) first developed an approach that utilized MIL for diagnosing multiple sclerosis (MS), which is traditionally difficult to distinguish from other neurological diseases. In addition, they have demonstrated that ovarian cancer-associated repertoires from women can be distinguished from cancer-free women Ostmeyer et al. (2020a). With the aim of advancing cancer screening, Beshnova et al. Beshnova et al. (2020) extended this work to identify cancer-associated TCRs. Recently, Widrich et al. Widrich et al. (2020) developed an attention-based MIL deep learning approach that accurately predicts CMV serostatus and additionally used a transformer-like attention mechanism extracting those sequence motifs that are connected to disease classes.

Multiple instance learning is a typical weakly supervised learning problem. Current MIL algorithms have three paradigms, i.e., instance-space paradigm, bag-space paradigm, and embedded-space paradigm Wang et al. (2018), categorized based on which level to learn the discriminative information (instance-level or bag-level).The instance-space paradigm focus on learning instance information, which learns the instance classifier at the first stage and then achieves the bag-level classifier by aggregating instance-level results. The bag-space paradigm and embedded-space paradigm (entire-bag-embedding MIL), on the other hand, extract discriminative information from the whole bag. In immune repertoire classification, current existing methods mostly belong to the embedded-space paradigm Widrich et al. (2020); Ostmeyer et al. (2020b). However, the nature of the huge instance size ($10^{7}-10^{8}$) and extremely low witness rate of the immune repertoire challenge the performance of entire-bag-embedding methods in practice,

Most deep learning methods assume perfect label information, which is impractical in many real-world scenarios. Learning with Noisy Label (LNL) aims to alleviate the problem since weak supervision can be obtained more efficiently.

Recently, several LNL methods have attracted much attention and obtained much better empirical performance Song et al. (2020). Sample selection methods select possible mislabeled samples and exclude them from training. For example, Jiang et al. (2018) uses a pre-trained network to filter samples with big losses, which tend to be noisy, and a student only trained by the selected clean dataset. Han et al. (2018) maintains two networks, and each selects certain small-loss samples and uses them as training signals for its peer. On top of sample selection, one can also utilize possible mislabeled data with semi-supervised learning techniques. For example, DivideMix Li et al. (2020a) first divides samples into clean and noisy using the Gaussian mixture model. Then it deploys a semi-supervised learning method to leverage both subsets. RoCL Zhou et al. (2021) uses the EMA of loss value for sample selection and label correction. Furthermore, it uses supervised training for selected clean samples and uses semi-supervised learning for selected noisy samples.