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1. Generalization Guarantees for Neural Architecture Search with Train-Validation Split

   Oymak, Samet; Li, Mingchen; Soltanolkotabi, Mahdi (January 2021, ICML 2021)

   Neural Architecture Search (NAS) is a popular method for automatically designing optimized architectures for high-performance deep learning. In this approach, it is common to use bilevel optimization where one optimizes the model weights over the training data (lower-level problem) and various hyperparameters such as the configuration of the architecture over the validation data (upper-level problem). This paper explores the statistical aspects of such problems with train-validation splits. In practice, the lower-level problem is often overparameterized and can easily achieve zero loss. Thus, a-priori it seems impossible to distinguish the right hyperparameters based on training loss alone which motivates a better understanding of the role of train-validation split. To this aim this work establishes the following results: • We show that refined properties of the validation loss such as risk and hyper-gradients are indicative of those of the true test loss. This reveals that the upper-level problem helps select the most generalizable model and prevent overfitting with a near-minimal validation sample size. Importantly, this is established for continuous spaces – which are highly relevant for popular differentiable search schemes. • We establish generalization bounds for NAS problems with an emphasis on an activation search problem. When optimized with gradient-descent, we show that the train-validation procedure returns the best (model, architecture) pair even if all architectures can perfectly fit the training data to achieve zero error. • Finally, we highlight rigorous connections between NAS, multiple kernel learning, and low-rank matrix learning. The latter leads to novel algorithmic insights where the solution of the upper problem can be accurately learned via efficient spectral methods to achieve near-minimal risk. 

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2. Generalization Guarantees for Neural Architecture Search with Train-Validation Split

   Oymak, Samet; Li, Mingchen; Soltanolkotabi, Mahdi (July 2021, International Conference on Machine Learning)

   null (Ed.)

   Neural Architecture Search (NAS) is a popular method for automatically designing optimized architectures for high-performance deep learning. In this approach, it is common to use bilevel optimization where one optimizes the model weights over the training data (lower-level problem) and various hyperparameters such as the configuration of the architecture over the validation data (upper-level problem). This paper explores the statistical aspects of such problems with train-validation splits. In practice, the lower-level problem is often overparameterized and can easily achieve zero loss. Thus, a-priori it seems impossible to distinguish the right hyperparameters based on training loss alone which motivates a better understanding of the role of train-validation split. To this aim this work establishes the following results: • We show that refined properties of the validation loss such as risk and hyper-gradients are indicative of those of the true test loss. This reveals that the upper-level problem helps select the most generalizable model and prevent overfitting with a near-minimal validation sample size. Importantly, this is established for continuous spaces – which are highly relevant for popular differentiable search schemes. • We establish generalization bounds for NAS problems with an emphasis on an activation search problem. When optimized with gradient-descent, we show that the train-validation procedure returns the best (model, architecture) pair even if all architectures can perfectly fit the training data to achieve zero error. • Finally, we highlight rigorous connections between NAS, multiple kernel learning, and low-rank matrix learning. The latter leads to novel algorithmic insights where the solution of the upper problem can be accurately learned via efficient spectral methods to achieve near-minimal risk. 

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3. A Multiscale Deep Learning Model for Soil Moisture Integrating Satellite and In Situ Data

   https://doi.org/10.1029/2021GL096847  

   Liu, Jiangtao; Rahmani, Farshid; Lawson, Kathryn; Shen, Chaopeng (March 2022, Geophysical Research Letters)

   Abstract Deep learning (DL) models trained on hydrologic observations can perform extraordinarily well, but they can inherit deficiencies of the training data, such as limited coverage of in situ data or low resolution/accuracy of satellite data. Here we propose a novel multiscale DL scheme learning simultaneously from satellite and in situ data to predict 9 km daily soil moisture (5 cm depth). Based on spatial cross‐validation over sites in the conterminous United States, the multiscale scheme obtained a median correlation of 0.901 and root‐mean‐square error of 0.034 m³/m³. It outperformed the Soil Moisture Active Passive satellite mission's 9 km product, DL models trained on in situ data alone, and land surface models. Our 9 km product showed better accuracy than previous 1 km satellite downscaling products, highlighting limited impacts of improving resolution. Not only is our product useful for planning against floods, droughts, and pests, our scheme is generically applicable to geoscientific domains with data on multiple scales, breaking the confines of individual data sets. 

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4. Data Twinning

   https://doi.org/10.1002/sam.11574  

   Vakayil, Akhil; Joseph, V_Roshan (February 2022, Statistical Analysis and Data Mining: The ASA Data Science Journal)

   Abstract In this work, we develop a method namedTwinningfor partitioning a dataset into statistically similar twin sets.Twinningis based onSPlit, a recently proposed model‐independent method for optimally splitting a dataset into training and testing sets.Twinningis orders of magnitude faster than theSPlitalgorithm, which makes it applicable to Big Data problems such as data compression.Twinningcan also be used for generating multiple splits of a given dataset to aid divide‐and‐conquer procedures andk‐fold cross validation. 

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5. Deep Learning Movement Intent Decoders Trained with Dataset Aggregation for Prosthetic Limb Control

   https://doi.org/10.1109/TBME.2019.2901882  

   Dantas, Henrique; Warren, David J.; Wendelken, Suzanne; Davis, Tyler; Clark, Gregory A.; Mathews, V. John (July 2019, IEEE Transactions on Biomedical Engineering)

   Significance: The performance of traditional approaches to decoding movement intent from electromyograms (EMGs) and other biological signals commonly degrade over time. Furthermore, conventional algorithms for training neural network-based decoders may not perform well outside the domain of the state transitions observed during training. The work presented in this paper mitigates both these problems, resulting in an approach that has the potential to substantially he quality of live of people with limb loss. Objective: This paper presents and evaluates the performance of four decoding methods for volitional movement intent from intramuscular EMG signals. Methods: The decoders are trained using dataset aggregation (DAgger) algorithm, in which the training data set is augmented during each training iteration based on the decoded estimates from previous iterations. Four competing decoding methods: polynomial Kalman filters (KFs), multilayer perceptron (MLP) networks, convolution neural networks (CNN), and Long-Short Term Memory (LSTM) networks, were developed. The performance of the four decoding methods was evaluated using EMG data sets recorded from two human volunteers with transradial amputation. Short-term analyses, in which the training and cross-validation data came from the same data set, and long-term analyses training and testing were done in different data sets, were performed. Results: Short-term analyses of the decoders demonstrated that CNN and MLP decoders performed significantly better than KF and LSTM decoders, showing an improvement of up to 60% in the normalized mean-square decoding error in cross-validation tests. Long-term analysis indicated that the CNN, MLP and LSTM decoders performed significantly better than KF-based decoder at most analyzed cases of temporal separations (0 to 150 days) between the acquisition of the training and testing data sets. Conclusion: The short-term and long-term performance of MLP and CNN-based decoders trained with DAgger, demonstrated their potential to provide more accurate and naturalistic control of prosthetic hands than alternate approaches. 

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