Inductive bias

Résumé

The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered. Inductive bias is anything which makes the algorithm learn one pattern instead of another pattern (e.g. step-functions in decision trees instead of continous function in a linear regression model). In machine learning, one aims to construct algorithms that are able to learn to predict a certain target output. To achieve this, the learning algorithm is presented some training examples that demonstrate the intended relation of input and output values. Then the learner is supposed to approximate the correct output, even for examples that have not been shown during training. Without any additional assumptions, this problem cannot be solved since unseen situations might have an arbitrary output value. The kind of necessary assumptions about the nature of the target function are subsumed in the phrase induc

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https://en.wikipedia.org/wiki/Inductive_bias

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A Plug-and-Play Deep Image Prior

Volkan Cevher, Fabian Ricardo Latorre Gomez, Thomas Sanchez, Zhaodong Sun

Deep image priors (DIP) offer a novel approach for the regularization that leverages the inductive bias of a deep convolutional architecture in inverse problems. However, the quality of DIP approaches often degrades when the number of iterations exceeds a certain threshold due to overfitting. To mitigate this effect, this work incorporates a plug-and-play prior scheme which can accommodate additional regularization steps within a DIP framework. Our modification is achieved using an augmented Lagrangian formulation of the problem, and is solved using an Alternating Direction Method of Multipliers (ADMM) variant, which can capture existing DIP approaches as a special case. We show experimentally that our ADMM-based DIP pairing outperforms competitive baselines in PSNR while exhibiting less overfitting.

IEEE2021

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PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees

Martin Josifoski, Andreas Krause

Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

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Auto-tuning deep forest for shear stiffness prediction of headed stud connectors

Yuqing Liu

The shear stiffness of headed stud connector is a critical parameter for the calculation of deflection and inter-facial shear force for steel-concrete composite structure. Thus, this study presented a promising data-driven model auto-tuning Deep Forest (ATDF) to precisely predict the stud shear stiffness, where the novel Deep For-est algorithm is integrated with the Sequential Model-Based Optimization method to achieve automatic hyper -parameter optimization. Six variables having causal relationships with shear stiffness were extracted via mechanism and model analysis, including the effect of weld collar that cannot be considered in existing models and subsequently constituting a database of 425 push-out tests. Then the ATDF model was trained by combining the advantages of deep learning, ensemble learning, and auto-tuning techniques. It was approved to significantly outperform representative benchmark models with R values of 0.91 and 0.87 for training and testing sets. The ATDF was subjected to attribute importance analysis, which quantified the stud diameter and concrete elastic modulus as the most significant variables for shear stiffness, with the stud elastic modulus having the minimal effect. The model uncertainty of ATDF was further evaluated, revealing that it had the lowest bias and variability than those in existing empirical or semi-empirical models. Finally, the reliability analysis was conducted and the partial factors of ATDF under specified target reliability were derived.

2022

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