The conditional survival function of a time-to-event outcome subject to censoring and truncation is a common target of estimation in survival analysis. This parameter may be of scientific interest and also often appears as a nuisance in nonparametric and semiparametric problems. In addition to classical parametric and semiparametric methods (e.g., based on the Cox proportional hazards model), flexible machine learning approaches have been developed to estimate the conditional survival function. However, many of these methods are either implicitly or explicitly targeted toward risk stratification rather than overall survival function estimation. Others apply only to discrete-time settings or require inverse probability of censoring weights, which can be as difficult to estimate as the outcome survival function itself. Here, we employ a decomposition of the conditional survival function in terms of observable regression models in which censoring and truncation play no role. This allows application of an array of flexible regression and classification methods rather than only approaches that explicitly handle the complexities inherent to survival data. We outline estimation procedures based on this decomposition, empirically assess their performance, and demonstrate their use on data from an HIV vaccine trial.
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The paper analyses properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the directional distance function models, and even permits their generalisations. The modelling is not constrained to non-negative data and is flexible enough to accommodate variants of standard models over arbitrary data. Mathematical tools developed in the paper allow systematic analysis of the models from the point of view of ten desirable properties. It is shown that some of the properties are satisfied (resp., fail) for all models in the general scheme, while others have a more nuanced behaviour and must be assessed individually in each model. Our results can help researchers and practitioners navigate among the different models and apply the models to mixed data.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Generative models are now capable of producing highly realistic images that look nearly indistinguishable from the data on which they are trained. This raises the question: if we have good enough generative models, do we still need datasets? We investigate this question in the setting of learning general-purpose visual representations from a black-box generative model rather than directly from data. Given an off-the-shelf image generator without any access to its training data, we train representations from the samples output by this generator. We compare several representation learning methods that can be applied to this setting, using the latent space of the generator to generate multiple "views" of the same semantic content. We show that for contrastive methods, this multiview data can naturally be used to identify positive pairs (nearby in latent space) and negative pairs (far apart in latent space). We find that the resulting representations rival those learned directly from real data, but that good performance requires care in the sampling strategy applied and the training method. Generative models can be viewed as a compressed and organized copy of a dataset, and we envision a future where more and more "model zoos" proliferate while datasets become increasingly unwieldy, missing, or private. This paper suggests several techniques for dealing with visual representation learning in such a future. Code is released on our project page: //ali-design.github.io/GenRep/
Graph Neural Networks (GNNs) are widely used for analyzing graph-structured data. Most GNN methods are highly sensitive to the quality of graph structures and usually require a perfect graph structure for learning informative embeddings. However, the pervasiveness of noise in graphs necessitates learning robust representations for real-world problems. To improve the robustness of GNN models, many studies have been proposed around the central concept of Graph Structure Learning (GSL), which aims to jointly learn an optimized graph structure and corresponding representations. Towards this end, in the presented survey, we broadly review recent progress of GSL methods for learning robust representations. Specifically, we first formulate a general paradigm of GSL, and then review state-of-the-art methods classified by how they model graph structures, followed by applications that incorporate the idea of GSL in other graph tasks. Finally, we point out some issues in current studies and discuss future directions.
Zero-shot Learning (ZSL), which aims to predict for those classes that have never appeared in the training data, has arisen hot research interests. The key of implementing ZSL is to leverage the prior knowledge of classes which builds the semantic relationship between classes and enables the transfer of the learned models (e.g., features) from training classes (i.e., seen classes) to unseen classes. However, the priors adopted by the existing methods are relatively limited with incomplete semantics. In this paper, we explore richer and more competitive prior knowledge to model the inter-class relationship for ZSL via ontology-based knowledge representation and semantic embedding. Meanwhile, to address the data imbalance between seen classes and unseen classes, we developed a generative ZSL framework with Generative Adversarial Networks (GANs). Our main findings include: (i) an ontology-enhanced ZSL framework that can be applied to different domains, such as image classification (IMGC) and knowledge graph completion (KGC); (ii) a comprehensive evaluation with multiple zero-shot datasets from different domains, where our method often achieves better performance than the state-of-the-art models. In particular, on four representative ZSL baselines of IMGC, the ontology-based class semantics outperform the previous priors e.g., the word embeddings of classes by an average of 12.4 accuracy points in the standard ZSL across two example datasets (see Figure 4).
The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.
Deep learning techniques have received much attention in the area of image denoising. However, there are substantial differences in the various types of deep learning methods dealing with image denoising. Specifically, discriminative learning based on deep learning can ably address the issue of Gaussian noise. Optimization models based on deep learning are effective in estimating the real noise. However, there has thus far been little related research to summarize the different deep learning techniques for image denoising. In this paper, we offer a comparative study of deep techniques in image denoising. We first classify the deep convolutional neural networks (CNNs) for additive white noisy images; the deep CNNs for real noisy images; the deep CNNs for blind denoising and the deep CNNs for hybrid noisy images, which represents the combination of noisy, blurred and low-resolution images. Then, we analyze the motivations and principles of the different types of deep learning methods. Next, we compare the state-of-the-art methods on public denoising datasets in terms of quantitative and qualitative analysis. Finally, we point out some potential challenges and directions of future research.
Meta-learning extracts the common knowledge acquired from learning different tasks and uses it for unseen tasks. It demonstrates a clear advantage on tasks that have insufficient training data, e.g., few-shot learning. In most meta-learning methods, tasks are implicitly related via the shared model or optimizer. In this paper, we show that a meta-learner that explicitly relates tasks on a graph describing the relations of their output dimensions (e.g., classes) can significantly improve the performance of few-shot learning. This type of graph is usually free or cheap to obtain but has rarely been explored in previous works. We study the prototype based few-shot classification, in which a prototype is generated for each class, such that the nearest neighbor search between the prototypes produces an accurate classification. We introduce "Gated Propagation Network (GPN)", which learns to propagate messages between prototypes of different classes on the graph, so that learning the prototype of each class benefits from the data of other related classes. In GPN, an attention mechanism is used for the aggregation of messages from neighboring classes, and a gate is deployed to choose between the aggregated messages and the message from the class itself. GPN is trained on a sequence of tasks from many-shot to few-shot generated by subgraph sampling. During training, it is able to reuse and update previously achieved prototypes from the memory in a life-long learning cycle. In experiments, we change the training-test discrepancy and test task generation settings for thorough evaluations. GPN outperforms recent meta-learning methods on two benchmark datasets in all studied cases.
This paper surveys the machine learning literature and presents machine learning as optimization models. Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings. Particularly, mathematical optimization models are presented for commonly used machine learning approaches for regression, classification, clustering, and deep neural networks as well new emerging applications in machine teaching and empirical model learning. The strengths and the shortcomings of these models are discussed and potential research directions are highlighted.
The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.
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