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Register a new userNeuMiss networks: differentiable programming for supervised learning with missing values
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Thomas Moreau
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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The presence of missing values makes supervised learning much more challenging. Indeed, previous work has shown that even when the response is a linear function of the complete data, the optimal predictor is a complex function of the observed entries and the missingness indicator. As a result, the computational or sample complexities of consistent approaches depend on the number of missing patterns, which can be exponential in the number of dimensions. In this work, we derive the analytical form of the optimal predictor under a linearity assumption and various missing data mechanisms including Missing at Random (MAR) and self-masking (Missing Not At Random). Based on a Neumann-series approximation of the optimal predictor, we propose a new principled architecture, named NeuMiss networks. Their originality and strength come from the use of a new type of non-linearity: the multiplication by the missingness indicator. We provide an upper bound on the Bayes risk of NeuMiss networks, and show that they have good predictive accuracy with both a number of parameters and a computational complexity independent of the number of missing data patterns. As a result they scale well to problems with many features, and remain statistically efficient for medium-sized samples. Moreover, we show that, contrary to procedures using EM or imputation, they are robust to the missing data mechanism, including difficult MNAR settings such as self-masking.
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We propose a novel theoretical framework to understand contrastive self-supervised learning (SSL) methods that employ dual pairs of deep ReLU networks (e.g., SimCLR). First, we prove that in each SGD update of SimCLR with various loss functions, including simple contrastive loss, soft Triplet loss and InfoNCE loss, the weights at each layer are updated by a emph{covariance operator} that specifically amplifies initial random selectivities that vary across data samples but survive averages over data augmentations. To further study what role the covariance operator plays and which features are learned in such a process, we model data generation and augmentation processes through a emph{hierarchical latent tree model} (HLTM) and prove that the hidden neurons of deep ReLU networks can learn the latent variables in HLTM, despite the fact that the network receives emph{no direct supervision} from these unobserved latent variables. This leads to a provable emergence of hierarchical features through the amplification of initially random selectivities through contrastive SSL. Extensive numerical studies justify our theoretical findings. Code is released in https://github.com/facebookresearch/luckmatters/tree/master/ssl.
This paper introduces the Differentiable Algorithm Network (DAN), a composable architecture for robot learning systems. A DAN is composed of neural network modules, each encoding a differentiable robot algorithm and an associated model; and it is trained end-to-end from data. DAN combines the strengths of model-driven modular system design and data-driven end-to-end learning. The algorithms and models act as structural assumptions to reduce the data requirements for learning; end-to-end learning allows the modules to adapt to one another and compensate for imperfect models and algorithms, in order to achieve the best overall system performance. We illustrate the DAN methodology through a case study on a simulated robot system, which learns to navigate in complex 3-D environments with only local visual observations and an image of a partially correct 2-D floor map.
There has been a growing concern about the fairness of decision-making systems based on machine learning. The shortage of labeled data has been always a challenging problem facing machine learning based systems. In such scenarios, semi-supervised learning has shown to be an effective way of exploiting unlabeled data to improve upon the performance of model. Notably, unlabeled data do not contain label information which itself can be a significant source of bias in training machine learning systems. This inspired us to tackle the challenge of fairness by formulating the problem in a semi-supervised framework. In this paper, we propose a semi-supervised algorithm using neural networks benefiting from unlabeled data to not just improve the performance but also improve the fairness of the decision-making process. The proposed model, called SSFair, exploits the information in the unlabeled data to mitigate the bias in the training data.
In many application settings, the data have missing entries which make analysis challenging. An abundant literature addresses missing values in an inferential framework: estimating parameters and their variance from incomplete tables. Here, we consider supervised-learning settings: predicting a target when missing values appear in both training and testing data. We show the consistency of two approaches in prediction. A striking result is that the widely-used method of imputing with a constant, such as the mean prior to learning is consistent when missing values are not informative. This contrasts with inferential settings where mean imputation is pointed at for distorting the distribution of the data. That such a simple approach can be consistent is important in practice. We also show that a predictor suited for complete observations can predict optimally on incomplete data,through multiple imputation.Finally, to compare imputation with learning directly with a model that accounts for missing values, we analyze further decision trees. These can naturally tackle empirical risk minimization with missing values, due to their ability to handle the half-discrete nature of incomplete variables. After comparing theoretically and empirically different missing values strategies in trees, we recommend using the missing incorporated in attribute method as it can handle both non-informative and informative missing values.
Graph convolutional network (GCN) provides a powerful means for graph-based semi-supervised tasks. However, as a localized first-order approximation of spectral graph convolution, the classic GCN can not take full advantage of unlabeled data, especially when the unlabeled node is far from labeled ones. To capitalize on the information from unlabeled nodes to boost the training for GCN, we propose a novel framework named Self-Ensembling GCN (SEGCN), which marries GCN with Mean Teacher - another powerful model in semi-supervised learning. SEGCN contains a student model and a teacher model. As a student, it not only learns to correctly classify the labeled nodes, but also tries to be consistent with the teacher on unlabeled nodes in more challenging situations, such as a high dropout rate and graph collapse. As a teacher, it averages the student model weights and generates more accurate predictions to lead the student. In such a mutual-promoting process, both labeled and unlabeled samples can be fully utilized for backpropagating effective gradients to train GCN. In three article classification tasks, i.e. Citeseer, Cora and Pubmed, we validate that the proposed method matches the state of the arts in the classification accuracy.
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