Multi-domain learning (MDL) aims at obtaining a model with minimal average risk across multiple domains. Our empirical motivation is automated microscopy data, where cultured cells are imaged after being exposed to known and unknown chemical perturbations, and each dataset displays significant experimental bias. This paper presents a multi-domain adversarial learning approach, MuLANN, to leverage multiple datasets with overlapping but distinct class sets, in a semi-supervised setting. Our contributions include: i) a bound on the average- and worst-domain risk in MDL, obtained using the H-divergence; ii) a new loss to accommodate semi-supervised multi-domain learning and domain adaptation; iii) the experimental validation of the approach, improving on the state of the art on two standard image benchmarks, and a novel bioimage dataset, Cell. Advances in technology have enabled large scale dataset generation by life sciences laboratories. These datasets contain information about overlapping but non-identical known and unknown experimental conditions. A challenge is how to best leverage information across multiple datasets on the same subject, and to make discoveries that could not have been obtained from any individual dataset alone.Transfer learning provides a formal framework for addressing this challenge, particularly crucial in cases where data acquisition is expensive and heavily impacted by experimental settings. One such field is automated microscopy, which can capture thousands of images of cultured cells after exposure to different experimental perturbations (e.g from chemical or genetic sources). A goal is to classify mechanisms by which perturbations affect cellular processes based on the similarity of cell images. In principle, it should be possible to tackle microscopy image classification as yet another visual object recognition task. However, two major challenges arise compared to mainstream visual object recognition problems BID51 . First, biological images are heavily impacted by experimental choices, such as microscope settings and experimental reagents. Second, there is no standardized set of labeled perturbations, and datasets often contain labeled examples for a subset of possible classes only. This has limited microscopy image classification to single datasets and does not leverage the growing number of datasets collected by the life sciences community. These challenges make it desirable to learn models across many microscopy datasets, that achieve both good robustness w.r.t. experimental settings and good class coverage, all the while being robust to the fact that datasets contain samples from overlapping but distinct class sets.Multi-domain learning (MDL) aims to learn a model of minimal risk from datasets drawn from distinct underlying distributions BID20 , and is a particular case of transfer learning BID46 . As such, it contrasts with the so-called domain adaptation (DA) problem BID7 BID5 BID22 BID46 . DA aims at learning a model with minimal risk on a distribution called "target" by leveraging other distributions called "sources". Notably, most DA methods assume that target classes are identical to source classes, or a subset thereof in the case of partial DA BID77 .The expected benefits of MDL, compared to training a separate model on each individual dataset, are two-fold. First , MDL leverages more (labeled and unlabeled) information, allowing better generalization while accommodating the specifics of each domain BID20 BID72 . Thus , MDL models have a higher chance of ab initio performing well on a new domain − a problem referred to as domain generalization BID44 or zero-shot domain adaptation BID74 . Second , MDL enables knowledge transfer between domains: in unsupervised and semi-supervised settings, concepts learned on one domain are applied to another, significantly reducing the need for labeled examples from the latter BID46 . Learning a single model from samples drawn from n distributions raises the question of available learning guarantees regarding the model error on each distribution. BID32 introduced the notion of H-divergence to measure the distance between source and target marginal distributions in DA. BID4 have shown that a finite sample estimate of this divergence can be used to bound the target risk of the learned model.The contributions of our work are threefold. First, we extend the DA guarantees to MDL (Sec. 3.1), showing that the risk of the learned model over all considered domains is upper bounded by the oracle risk and the sum of the H-divergences between any two domains. Furthermore, an upper bound on the classifier imbalance (the difference between the individual domain risk, and the average risk over all domains) is obtained, thus bounding the worst-domain risk. Second, we propose the approach Multi-domain Learning Adversarial Neural Network (MULANN), which extends Domain Adversarial Neural Networks (DANNs) BID22 to semi-supervised DA and MDL. Relaxing the DA assumption , MULANN handles the so-called class asymmetry issue (when each domain may contain varying numbers of labeled and unlabeled examples of a subset of all possible classes), through designing a new loss (Sec. 3.2). Finally, MULANN is empirically validated in both DA and MDL settings (Sec. 4), as it significantly outperforms the state of the art on three standard image benchmarks BID52 BID35 , and a novel bioimage benchmark, CELL, where the state of the art involves extensive domain-dependent pre-processing.Notation. Let X denote an input space and Y = {1, . . . , L} a set of classes. For i = 1, . . . , n, dataset S i is an iid sample drawn from distribution D i on X × Y. The marginal distribution of D i on X is denoted by D X i . Let H be a hypothesis space; for each h in H (h : X → Y) we define the risk under distribution D i as i (h) = P x,y∼Di (h(x) = y). h i (respectively h ) denotes the oracle hypothesis according to distribution D i (resp. with minimal total risk over all domains): DISPLAYFORM0 In the semi-supervised setting, the label associated with an instance might be missing. In the following, "domain" and "distribution" will be used interchangeably, and the "classes of a domain" denote the classes for which labeled or unlabeled examples are available in this domain. This paper extends the use of domain adversarial learning to multi-domain learning, establishing how the H-divergence can be used to bound both the risk across all domains and the worst-domain risk (imbalance on a specific domain). The stress is put on the notion of class asymmetry, that is, when some domains contain labeled or unlabeled examples of classes not present in other domains. Showing the significant impact of class asymmetry on the state of the art, this paper also introduces MULANN, where a new loss is meant to resist the contractive effects of the adversarial domain discriminator and to repulse (a fraction of) unlabeled examples from labeled ones in each domain.The merits of the approach are satisfactorily demonstrated by comparison to DANN and MADA on DIGITS, RoadSigns and OFFICE, and results obtained on the real-world CELL problem establish a new baseline for the microscopy image community.A perspective for further study is to bridge the gap between the proposed loss and importance sampling techniques, iteratively exploiting the latent representation to identify orphan samples and adapt the loss while learning. Further work will also focus on how to identify and preserve relevant domain-specific behaviours while learning in a domain adversarial setting (e.g., if different cell types have distinct responses to the same class of perturbations).
Adversarial Domain adaptation and Multi-domain learning: a new loss to handle multi- and single-domain classes in the semi-supervised setting.
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