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Register a new userMuddling Labels for Regularization, a novel approach to generalization
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Generalization is a central problem in Machine Learning. Indeed most prediction methods require careful calibration of hyperparameters usually carried out on a hold-out textit{validation} dataset to achieve generalization. The main goal of this paper is to introduce a novel approach to achieve generalization without any data splitting, which is based on a new risk measure which directly quantifies a models tendency to overfit. To fully understand the intuition and advantages of this new approach, we illustrate it in the simple linear regression model ($Y=Xbeta+xi$) where we develop a new criterion. We highlight how this criterion is a good proxy for the true generalization risk. Next, we derive different procedures which tackle several structures simultaneously (correlation, sparsity,...). Noticeably, these procedures textbf{concomitantly} train the model and calibrate the hyperparameters. In addition, these procedures can be implemented via classical gradient descent methods when the criterion is differentiable w.r.t. the hyperparameters. Our numerical experiments reveal that our procedures are computationally feasible and compare favorably to the popular approach (Ridge, LASSO and Elastic-Net combined with grid-search cross-validation) in term of generalization. They also outperform the baseline on two additional tasks: estimation and support recovery of $beta$. Moreover, our procedures do not require any expertise for the calibration of the initial parameters which remain the same for all the datasets we experimented on.
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Deep Learning (DL) is considered the state-of-the-art in computer vision, speech recognition and natural language processing. Until recently, it was also widely accepted that DL is irrelevant for learning tasks on tabular data, especially in the small sample regime where ensemble methods are acknowledged as the gold standard. We present a new end-to-end differentiable method to train a standard FFNN. Our method, textbf{Muddling labels for Regularization} (texttt{MLR}), penalizes memorization through the generation of uninformative labels and the application of a differentiable close-form regularization scheme on the last hidden layer during training. texttt{MLR} outperforms classical NN and the gold standard (GBDT, RF) for regression and classification tasks on several datasets from the UCI database and Kaggle covering a large range of sample sizes and feature to sample ratios. Researchers and practitioners can use texttt{MLR} on its own as an off-the-shelf DL{} solution or integrate it into the most advanced ML pipelines.
Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such predictions should 1) scale correctly with data complexity; 2) scale correctly with training set size; 3) capture differences between architectures; 4) capture differences between optimization algorithms; 5) be quantitatively not too far from the true error (in particular, be non-vacuous); 6) be efficiently computable; and 7) be rigorous. We focus on generalization error upper bounds, and introduce a categorisation of bounds depending on assumptions on the algorithm and data. We review a wide range of existing approaches, from classical VC dimension to recent PAC-Bayesian bounds, commenting on how well they perform against the desiderata. We next use a function-based picture to derive a marginal-likelihood PAC-Bayesian bound. This bound is, by one definition, optimal up to a multiplicative constant in the asymptotic limit of large training sets, as long as the learning curve follows a power law, which is typically found in practice for deep learning problems. Extensive empirical analysis demonstrates that our marginal-likelihood PAC-Bayes bound fulfills desiderata 1-3 and 5. The results for 6 and 7 are promising, but not yet fully conclusive, while only desideratum 4 is currently beyond the scope of our bound. Finally, we comment on why this function-based bound performs significantly better than current parameter-based PAC-Bayes bounds.
The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is accurate. However, it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator. In this paper, we leverage the fact that VAEs rely on amortized inference and propose techniques for amortized inference regularization (AIR) that control the smoothness of the inference model. We demonstrate that, by applying AIR, it is possible to improve VAE generalization on both inference and generative performance. Our paper challenges the belief that amortized inference is simply a mechanism for approximating maximum likelihood training and illustrates that regularization of the amortization family provides a new direction for understanding and improving generalization in VAEs.
The insights revealed from process mining heavily rely on the quality of event logs. Activities extracted from healthcare information systems with the free-text nature may lead to inconsistent labels. Such inconsistency would then lead to redundancy of activity labels, which refer to labels that have different syntax but share the same behaviours. The identifications of these labels from data-driven process discovery are difficult and rely heavily on resource-intensive human review. Existing work achieves low accuracy either redundant activity labels are in low occurrence frequency or the existence of numerical data values as attributes in event logs. However, these phenomena are commonly observed in healthcare information systems. In this paper, we propose an approach to detect redundant activity labels using control-flow relations and numerical data values from event logs. Natural Language Processing is also integrated into our method to assess semantic similarity between labels, which provides users with additional insights. We have evaluated our approach through synthetic logs generated from the real-life Sepsis log and a case study using the MIMIC-III data set. The results demonstrate that our approach can successfully detect redundant activity labels. This approach can add value to the preprocessing step to generate more representative event logs for process mining tasks in the healthcare domain.
This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations within the input, analogous to the way the standard convolution uses the spatial neighborhood of a pixel on the grid. The convolution has an intuitive interpretation, is efficient and scalable and can also be used on data with varying graph structure. Furthermore, this generalization can be applied to many standard regression or classification problems, by learning the the underlying graph. We empirically demonstrate the performance of the proposed CNN on MNIST, and challenge the state-of-the-art on Merck molecular activity data set.
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