The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider when a perfect fit to training data in linear regression is compatible with accurate prediction. We give a characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. The characterization is in terms of two notions of the effective rank of the data covariance. It shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size. By studying examples of data covariance properties that this characterization shows are required for benign overfitting, we find an important role for finite-dimensional data: the accuracy of the minimum norm interpolating prediction rule approaches the best possible accuracy for a much narrower range of properties of the data distribution when the data lie in an infinite-dimensional space vs. when the data lie in a finite-dimensional space with dimension that grows faster than the sample size.
Deep learning: a statistical viewpoint
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting, that is, accurate predictions despite overfitting training data. In this article, we survey recent progress in statistical learning theory that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behaviour of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favourable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
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- NSF-PAR ID:
- 10344161
- Date Published:
- Journal Name:
- Acta Numerica
- Volume:
- 30
- ISSN:
- 0962-4929
- Page Range / eLocation ID:
- 87 to 201
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In deep learning, often the training process nds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem y = Ax+ noise with sparse x , neither minimum l_1 orl_`2 norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of l_1 and l_2 interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.more » « less
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Feature representations from pre-trained deep neural networks have been known to exhibit excellent generalization and utility across a variety of related tasks. Fine-tuning is by far the simplest and most widely used approach that seeks to exploit and adapt these feature representations to novel tasks with limited data. Despite the effectiveness of fine-tuning, itis often sub-optimal and requires very careful optimization to prevent severe over-fitting to small datasets. The problem of sub-optimality and over-fitting, is due in part to the large number of parameters used in a typical deep convolutional neural network. To address these problems, we propose a simple yet effective regularization method for fine-tuning pre-trained deep networks for the task of k-shot learning. To prevent overfitting, our key strategy is to cluster the model parameters while ensuring intra-cluster similarity and inter-cluster diversity of the parameters, effectively regularizing the dimensionality of the parameter search space. In particular, we identify groups of neurons within each layer of a deep network that shares similar activation patterns. When the network is to be fine-tuned for a classification task using only k examples, we propagate a single gradient to all of the neuron parameters that belong to the same group. The grouping of neurons is non-trivial as neuron activations depend on the distribution of the input data. To efficiently search for optimal groupings conditioned on the input data, we propose a reinforcement learning search strategy using recurrent networks to learn the optimal group assignments for each network layer. Experimental results show that our method can be easily applied to several popular convolutional neural networks and improve upon other state-of-the-art fine-tuning based k-shot learning strategies by more than10%more » « less
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Obeid, I. (Ed.)The Neural Engineering Data Consortium (NEDC) is developing the Temple University Digital Pathology Corpus (TUDP), an open source database of high-resolution images from scanned pathology samples [1], as part of its National Science Foundation-funded Major Research Instrumentation grant titled “MRI: High Performance Digital Pathology Using Big Data and Machine Learning” [2]. The long-term goal of this project is to release one million images. We have currently scanned over 100,000 images and are in the process of annotating breast tissue data for our first official corpus release, v1.0.0. This release contains 3,505 annotated images of breast tissue including 74 patients with cancerous diagnoses (out of a total of 296 patients). In this poster, we will present an analysis of this corpus and discuss the challenges we have faced in efficiently producing high quality annotations of breast tissue. It is well known that state of the art algorithms in machine learning require vast amounts of data. Fields such as speech recognition [3], image recognition [4] and text processing [5] are able to deliver impressive performance with complex deep learning models because they have developed large corpora to support training of extremely high-dimensional models (e.g., billions of parameters). Other fields that do not have access to such data resources must rely on techniques in which existing models can be adapted to new datasets [6]. A preliminary version of this breast corpus release was tested in a pilot study using a baseline machine learning system, ResNet18 [7], that leverages several open-source Python tools. The pilot corpus was divided into three sets: train, development, and evaluation. Portions of these slides were manually annotated [1] using the nine labels in Table 1 [8] to identify five to ten examples of pathological features on each slide. Not every pathological feature is annotated, meaning excluded areas can include focuses particular to these labels that are not used for training. A summary of the number of patches within each label is given in Table 2. To maintain a balanced training set, 1,000 patches of each label were used to train the machine learning model. Throughout all sets, only annotated patches were involved in model development. The performance of this model in identifying all the patches in the evaluation set can be seen in the confusion matrix of classification accuracy in Table 3. The highest performing labels were background, 97% correct identification, and artifact, 76% correct identification. A correlation exists between labels with more than 6,000 development patches and accurate performance on the evaluation set. Additionally, these results indicated a need to further refine the annotation of invasive ductal carcinoma (“indc”), inflammation (“infl”), nonneoplastic features (“nneo”), normal (“norm”) and suspicious (“susp”). This pilot experiment motivated changes to the corpus that will be discussed in detail in this poster presentation. To increase the accuracy of the machine learning model, we modified how we addressed underperforming labels. One common source of error arose with how non-background labels were converted into patches. Large areas of background within other labels were isolated within a patch resulting in connective tissue misrepresenting a non-background label. In response, the annotation overlay margins were revised to exclude benign connective tissue in non-background labels. Corresponding patient reports and supporting immunohistochemical stains further guided annotation reviews. The microscopic diagnoses given by the primary pathologist in these reports detail the pathological findings within each tissue site, but not within each specific slide. The microscopic diagnoses informed revisions specifically targeting annotated regions classified as cancerous, ensuring that the labels “indc” and “dcis” were used only in situations where a micropathologist diagnosed it as such. Further differentiation of cancerous and precancerous labels, as well as the location of their focus on a slide, could be accomplished with supplemental immunohistochemically (IHC) stained slides. When distinguishing whether a focus is a nonneoplastic feature versus a cancerous growth, pathologists employ antigen targeting stains to the tissue in question to confirm the diagnosis. For example, a nonneoplastic feature of usual ductal hyperplasia will display diffuse staining for cytokeratin 5 (CK5) and no diffuse staining for estrogen receptor (ER), while a cancerous growth of ductal carcinoma in situ will have negative or focally positive staining for CK5 and diffuse staining for ER [9]. Many tissue samples contain cancerous and non-cancerous features with morphological overlaps that cause variability between annotators. The informative fields IHC slides provide could play an integral role in machine model pathology diagnostics. Following the revisions made on all the annotations, a second experiment was run using ResNet18. Compared to the pilot study, an increase of model prediction accuracy was seen for the labels indc, infl, nneo, norm, and null. This increase is correlated with an increase in annotated area and annotation accuracy. Model performance in identifying the suspicious label decreased by 25% due to the decrease of 57% in the total annotated area described by this label. A summary of the model performance is given in Table 4, which shows the new prediction accuracy and the absolute change in error rate compared to Table 3. The breast tissue subset we are developing includes 3,505 annotated breast pathology slides from 296 patients. The average size of a scanned SVS file is 363 MB. The annotations are stored in an XML format. A CSV version of the annotation file is also available which provides a flat, or simple, annotation that is easy for machine learning researchers to access and interface to their systems. Each patient is identified by an anonymized medical reference number. Within each patient’s directory, one or more sessions are identified, also anonymized to the first of the month in which the sample was taken. These sessions are broken into groupings of tissue taken on that date (in this case, breast tissue). A deidentified patient report stored as a flat text file is also available. Within these slides there are a total of 16,971 total annotated regions with an average of 4.84 annotations per slide. Among those annotations, 8,035 are non-cancerous (normal, background, null, and artifact,) 6,222 are carcinogenic signs (inflammation, nonneoplastic and suspicious,) and 2,714 are cancerous labels (ductal carcinoma in situ and invasive ductal carcinoma in situ.) The individual patients are split up into three sets: train, development, and evaluation. Of the 74 cancerous patients, 20 were allotted for both the development and evaluation sets, while the remain 34 were allotted for train. The remaining 222 patients were split up to preserve the overall distribution of labels within the corpus. This was done in hope of creating control sets for comparable studies. Overall, the development and evaluation sets each have 80 patients, while the training set has 136 patients. In a related component of this project, slides from the Fox Chase Cancer Center (FCCC) Biosample Repository (https://www.foxchase.org/research/facilities/genetic-research-facilities/biosample-repository -facility) are being digitized in addition to slides provided by Temple University Hospital. This data includes 18 different types of tissue including approximately 38.5% urinary tissue and 16.5% gynecological tissue. These slides and the metadata provided with them are already anonymized and include diagnoses in a spreadsheet with sample and patient ID. We plan to release over 13,000 unannotated slides from the FCCC Corpus simultaneously with v1.0.0 of TUDP. Details of this release will also be discussed in this poster. Few digitally annotated databases of pathology samples like TUDP exist due to the extensive data collection and processing required. The breast corpus subset should be released by November 2021. By December 2021 we should also release the unannotated FCCC data. We are currently annotating urinary tract data as well. We expect to release about 5,600 processed TUH slides in this subset. We have an additional 53,000 unprocessed TUH slides digitized. Corpora of this size will stimulate the development of a new generation of deep learning technology. In clinical settings where resources are limited, an assistive diagnoses model could support pathologists’ workload and even help prioritize suspected cancerous cases. ACKNOWLEDGMENTS This material is supported by the National Science Foundation under grants nos. CNS-1726188 and 1925494. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. REFERENCES [1] N. Shawki et al., “The Temple University Digital Pathology Corpus,” in Signal Processing in Medicine and Biology: Emerging Trends in Research and Applications, 1st ed., I. Obeid, I. Selesnick, and J. Picone, Eds. New York City, New York, USA: Springer, 2020, pp. 67 104. https://www.springer.com/gp/book/9783030368432. [2] J. Picone, T. Farkas, I. Obeid, and Y. Persidsky, “MRI: High Performance Digital Pathology Using Big Data and Machine Learning.” Major Research Instrumentation (MRI), Division of Computer and Network Systems, Award No. 1726188, January 1, 2018 – December 31, 2021. https://www. isip.piconepress.com/projects/nsf_dpath/. [3] A. Gulati et al., “Conformer: Convolution-augmented Transformer for Speech Recognition,” in Proceedings of the Annual Conference of the International Speech Communication Association (INTERSPEECH), 2020, pp. 5036-5040. https://doi.org/10.21437/interspeech.2020-3015. [4] C.-J. Wu et al., “Machine Learning at Facebook: Understanding Inference at the Edge,” in Proceedings of the IEEE International Symposium on High Performance Computer Architecture (HPCA), 2019, pp. 331–344. https://ieeexplore.ieee.org/document/8675201. [5] I. Caswell and B. Liang, “Recent Advances in Google Translate,” Google AI Blog: The latest from Google Research, 2020. [Online]. Available: https://ai.googleblog.com/2020/06/recent-advances-in-google-translate.html. [Accessed: 01-Aug-2021]. [6] V. Khalkhali, N. Shawki, V. Shah, M. Golmohammadi, I. Obeid, and J. Picone, “Low Latency Real-Time Seizure Detection Using Transfer Deep Learning,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2021, pp. 1 7. https://www.isip. piconepress.com/publications/conference_proceedings/2021/ieee_spmb/eeg_transfer_learning/. [7] J. Picone, T. Farkas, I. Obeid, and Y. Persidsky, “MRI: High Performance Digital Pathology Using Big Data and Machine Learning,” Philadelphia, Pennsylvania, USA, 2020. https://www.isip.piconepress.com/publications/reports/2020/nsf/mri_dpath/. [8] I. Hunt, S. Husain, J. Simons, I. Obeid, and J. Picone, “Recent Advances in the Temple University Digital Pathology Corpus,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2019, pp. 1–4. https://ieeexplore.ieee.org/document/9037859. [9] A. P. Martinez, C. Cohen, K. Z. Hanley, and X. (Bill) Li, “Estrogen Receptor and Cytokeratin 5 Are Reliable Markers to Separate Usual Ductal Hyperplasia From Atypical Ductal Hyperplasia and Low-Grade Ductal Carcinoma In Situ,” Arch. Pathol. Lab. Med., vol. 140, no. 7, pp. 686–689, Apr. 2016. https://doi.org/10.5858/arpa.2015-0238-OA.more » « less
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null (Ed.)The DeepLearningEpilepsyDetectionChallenge: design, implementation, andtestofanewcrowd-sourced AIchallengeecosystem Isabell Kiral*, Subhrajit Roy*, Todd Mummert*, Alan Braz*, Jason Tsay, Jianbin Tang, Umar Asif, Thomas Schaffter, Eren Mehmet, The IBM Epilepsy Consortium◊ , Joseph Picone, Iyad Obeid, Bruno De Assis Marques, Stefan Maetschke, Rania Khalaf†, Michal Rosen-Zvi† , Gustavo Stolovitzky† , Mahtab Mirmomeni† , Stefan Harrer† * These authors contributed equally to this work † Corresponding authors: rkhalaf@us.ibm.com, rosen@il.ibm.com, gustavo@us.ibm.com, mahtabm@au1.ibm.com, sharrer@au.ibm.com ◊ Members of the IBM Epilepsy Consortium are listed in the Acknowledgements section J. Picone and I. Obeid are with Temple University, USA. T. Schaffter is with Sage Bionetworks, USA. E. Mehmet is with the University of Illinois at Urbana-Champaign, USA. All other authors are with IBM Research in USA, Israel and Australia. Introduction This decade has seen an ever-growing number of scientific fields benefitting from the advances in machine learning technology and tooling. More recently, this trend reached the medical domain, with applications reaching from cancer diagnosis [1] to the development of brain-machine-interfaces [2]. While Kaggle has pioneered the crowd-sourcing of machine learning challenges to incentivise data scientists from around the world to advance algorithm and model design, the increasing complexity of problem statements demands of participants to be expert data scientists, deeply knowledgeable in at least one other scientific domain, and competent software engineers with access to large compute resources. People who match this description are few and far between, unfortunately leading to a shrinking pool of possible participants and a loss of experts dedicating their time to solving important problems. Participation is even further restricted in the context of any challenge run on confidential use cases or with sensitive data. Recently, we designed and ran a deep learning challenge to crowd-source the development of an automated labelling system for brain recordings, aiming to advance epilepsy research. A focus of this challenge, run internally in IBM, was the development of a platform that lowers the barrier of entry and therefore mitigates the risk of excluding interested parties from participating. The challenge: enabling wide participation With the goal to run a challenge that mobilises the largest possible pool of participants from IBM (global), we designed a use case around previous work in epileptic seizure prediction [3]. In this “Deep Learning Epilepsy Detection Challenge”, participants were asked to develop an automatic labelling system to reduce the time a clinician would need to diagnose patients with epilepsy. Labelled training and blind validation data for the challenge were generously provided by Temple University Hospital (TUH) [4]. TUH also devised a novel scoring metric for the detection of seizures that was used as basis for algorithm evaluation [5]. In order to provide an experience with a low barrier of entry, we designed a generalisable challenge platform under the following principles: 1. No participant should need to have in-depth knowledge of the specific domain. (i.e. no participant should need to be a neuroscientist or epileptologist.) 2. No participant should need to be an expert data scientist. 3. No participant should need more than basic programming knowledge. (i.e. no participant should need to learn how to process fringe data formats and stream data efficiently.) 4. No participant should need to provide their own computing resources. In addition to the above, our platform should further • guide participants through the entire process from sign-up to model submission, • facilitate collaboration, and • provide instant feedback to the participants through data visualisation and intermediate online leaderboards. The platform The architecture of the platform that was designed and developed is shown in Figure 1. The entire system consists of a number of interacting components. (1) A web portal serves as the entry point to challenge participation, providing challenge information, such as timelines and challenge rules, and scientific background. The portal also facilitated the formation of teams and provided participants with an intermediate leaderboard of submitted results and a final leaderboard at the end of the challenge. (2) IBM Watson Studio [6] is the umbrella term for a number of services offered by IBM. Upon creation of a user account through the web portal, an IBM Watson Studio account was automatically created for each participant that allowed users access to IBM's Data Science Experience (DSX), the analytics engine Watson Machine Learning (WML), and IBM's Cloud Object Storage (COS) [7], all of which will be described in more detail in further sections. (3) The user interface and starter kit were hosted on IBM's Data Science Experience platform (DSX) and formed the main component for designing and testing models during the challenge. DSX allows for real-time collaboration on shared notebooks between team members. A starter kit in the form of a Python notebook, supporting the popular deep learning libraries TensorFLow [8] and PyTorch [9], was provided to all teams to guide them through the challenge process. Upon instantiation, the starter kit loaded necessary python libraries and custom functions for the invisible integration with COS and WML. In dedicated spots in the notebook, participants could write custom pre-processing code, machine learning models, and post-processing algorithms. The starter kit provided instant feedback about participants' custom routines through data visualisations. Using the notebook only, teams were able to run the code on WML, making use of a compute cluster of IBM's resources. The starter kit also enabled submission of the final code to a data storage to which only the challenge team had access. (4) Watson Machine Learning provided access to shared compute resources (GPUs). Code was bundled up automatically in the starter kit and deployed to and run on WML. WML in turn had access to shared storage from which it requested recorded data and to which it stored the participant's code and trained models. (5) IBM's Cloud Object Storage held the data for this challenge. Using the starter kit, participants could investigate their results as well as data samples in order to better design custom algorithms. (6) Utility Functions were loaded into the starter kit at instantiation. This set of functions included code to pre-process data into a more common format, to optimise streaming through the use of the NutsFlow and NutsML libraries [10], and to provide seamless access to the all IBM services used. Not captured in the diagram is the final code evaluation, which was conducted in an automated way as soon as code was submitted though the starter kit, minimising the burden on the challenge organising team. Figure 1: High-level architecture of the challenge platform Measuring success The competitive phase of the "Deep Learning Epilepsy Detection Challenge" ran for 6 months. Twenty-five teams, with a total number of 87 scientists and software engineers from 14 global locations participated. All participants made use of the starter kit we provided and ran algorithms on IBM's infrastructure WML. Seven teams persisted until the end of the challenge and submitted final solutions. The best performing solutions reached seizure detection performances which allow to reduce hundred-fold the time eliptologists need to annotate continuous EEG recordings. Thus, we expect the developed algorithms to aid in the diagnosis of epilepsy by significantly shortening manual labelling time. Detailed results are currently in preparation for publication. Equally important to solving the scientific challenge, however, was to understand whether we managed to encourage participation from non-expert data scientists. Figure 2: Primary occupation as reported by challenge participants Out of the 40 participants for whom we have occupational information, 23 reported Data Science or AI as their main job description, 11 reported being a Software Engineer, and 2 people had expertise in Neuroscience. Figure 2 shows that participants had a variety of specialisations, including some that are in no way related to data science, software engineering, or neuroscience. No participant had deep knowledge and experience in data science, software engineering and neuroscience. Conclusion Given the growing complexity of data science problems and increasing dataset sizes, in order to solve these problems, it is imperative to enable collaboration between people with differences in expertise with a focus on inclusiveness and having a low barrier of entry. We designed, implemented, and tested a challenge platform to address exactly this. Using our platform, we ran a deep-learning challenge for epileptic seizure detection. 87 IBM employees from several business units including but not limited to IBM Research with a variety of skills, including sales and design, participated in this highly technical challenge.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S0962492921000027
