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Learning curves illustrate how generalization performance of a learner evolves with more training data. While this is a useful tool to characterize learners, not all learning curve behavior is well understood. For instance, it is sometimes assumed that the more training data provided, the better the learner performs. However, counter-examples exist for both classical machine learning algorithms and deep neural networks, where errors do not monotonically decrease with training set size. Loog et al. [12] describe this monotonicity problem, and present several regression examples where simple empirical risk minimizers display unexpected learning curve behaviors. In this paper, we will study two of these proposed problems in detail and explain what caused the odd learning curves. For the first, we use a bias-variance decomposition to show that the monotonic increase in the learning curve is caused by an increase in the variance, which we explain by a mismatch between the model and the data generating process. For the second problem, we explain the recurring increases in the learning curve by showing only two solutions are attainable by the learner. The probability of obtaining a configuration of training objects that leads to the high risk solution typically decreases as the training set size increases. However, for particular training set sizes, additional configurations that produce the high risk solution become possible. We prove that these additional configurations increase the probability of the high risk solution and therefore explain the unusual learning curve. These examples contribute to a more complete understanding of learning curves and the possibilities and reasons behind their various behaviors., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Pattern Recognition and Bioinformatics

The learning curve illustrates how the generalization performance of the learner evolves with more training data. It can predict the amount of data needed for decent accuracy and the highest achievable accuracy. However, the behavior of learning curves is not well understood. Many assume that the more training data provided, the better the learner performs. However, many counter-examples exist for both classical machine learning algorithms and deep neural networks. As presented in previous works, even the learning curves for simple problems using classical machine learning algorithms have unexpected behaviors. In this paper, we will explain what caused the odd learning curves generated while using ERM to solve two regression problems. Loog et al. [1] first proposed these two problems. As a result of our study, we conclude that the unexpected behaviors of the learning curves under these two problem settings are caused by incorrect modeling or the correlation between the expected risk and the output of the learner., CSE3000 Research Project, Computer Science and Engineering

Although it is well known that plants emit acoustic pulses under drought stress, the exact origin of the waveform of these ultrasound pulses has remained elusive. Here, we present evidence for a correlation between the characteristics of the waveform of these pulses and the dimensions of xylem conduits in plants. Using a model that relates the resonant vibrations of a vessel to its dimension and viscoelasticity, we extract the xylem radii from the waveforms of ultrasound pulses and show that these are correlated and in good agreement with optical microscopy. We demonstrate the versatility of the method by applying it to shoots of ten different vascular plant species. In particular, for Hydrangea quercifolia, we further extract vessel element lengths with our model and compare them with scanning electron cryomicroscopy. The ultrasonic, noninvasive characterization of internal conduit dimensions enables a breakthrough in speed and accuracy in plant phenotyping and stress detection., Dynamics of Micro and Nano Systems, QN/Steeneken Lab

The learning curve illustrates how the generalization performance of the learner evolves with more training data. It can predict the amount of data needed for decent accuracy and the highest achievable accuracy. However, the behavior of learning curves is not well understood. Many assume that the more training data provided, the better the learner performs. However, many counter-examples exist for both classical machine learning algorithms and deep neural networks. As presented in previous works, even the learning curves for simple problems using classical machine learning algorithms have unexpected behaviors. In this paper, we will explain what caused the odd learning curves generated while using ERM to solve two regression problems. Loog et al. [1] first proposed these two problems. As a result of our study, we conclude that the unexpected behaviors of the learning curves under these two problem settings are caused by incorrect modeling or the correlation between the expected risk and the output of the learner., CSE3000 Research Project, Computer Science and Engineering