# principled approaches to robust machine learning

Our algorithm is originated from robust optimization, which aims to find the saddle point of a min-max optimization problem in the presence of uncertainties. For example, the p penalty form is studied by many researchers (see e.g. Machine learning to measure treatment heterogeneity (b(i,t)) Susan Athey gave an excellent keynote talk that rapidly overviewed how machine learning can be used in economics, and her AEA lectures have more. Learning to reweight examples for robust deep learning. Download Python For Machine Learning ActivePython is the trusted Python distribution for Windows, Linux and Mac, pre-bundled with top Python packages for machine learning. ... As we apply machine learning to more and more important tasks, it becomes increasingly important that these algorithms are robust to systematic, or worse, malicious, noise. In learning systems we can utilize the principle of robustness even in cases where we aren’t interested in a pure statistical analysis. Section 6 describes how to implement the learning Robust BM25 method. Take, for example, the Mann-Whitney U test. doi: 10.17226/25534. Keywords: machine learning, uncertainty sets, robust opti-mization. For more information, consult our Privacy Policy. For a machine learning algorithm to be considered robust, either the testing error has to be consistent with the training error, or the performance is â¦ For example, using r as a measure of similarity in the registration of low contrast image can produce cases where “close to unity” means 0.998 and “far from unity” means 0.98, and no way to compute a p-value due to the extremely non-Gaussian distributions of pixel values involved. Robust Machine Learning Algorithms and Systems for Detection and Mitigation of Adversarial Attacks and Anomalies: Proceedings of a Workshop. We propose a novel discrete-time dynamical system-based framework for achieving adversarial robustness in machine learning models. List learning: Learning when there is an overwhelming fraction of corrupted data. Robust Channel Coding Strategies for Machine Learning Data Kayvon Mazooji, Frederic Sala, Guy Van den Broeck, and Lara Dolecek fkmazooji1, fredsalag@ucla.edu, guyvdb@cs.ucla.edu, dolecek@ee.ucla.edu UCLA, Los Angeles, CA 90095 AbstractâTwo important recent trends are the proliferation of learning algorithms along with the massive increase of data He is a professional engineer (PEO and APEGBC) and holds a PhD in physics from Queen’s University at Kingston. First, we propose a doubly robust estimator of the prediction inaccuracy. For these majority of problems, it pays to have a variety of approaches to help you reduce the noise and anomalies, to focus on something more tractable. Tom brings a passion for quantitative, data-driven processes to ActiveState. You can unsubscribe at any time. Robust Machine Learning. For the majority of problems, it pays to have a variety of approaches to help you reduce the noise and anomalies so you can focus on something more tractable. ... robust covariance estimation. But in reality, for data scientists and machine learning engineers, there are a lot of problems that are much more difficult to deal with than simple object recognition in images, or playing board games with finite rule sets. Jacob is also teaching a similar class at Berkeley this semester: link; Accommodations Origins of incorrect data include programmer errors, ("oops, we're double counting! Training becomes difficult for such coarse data because they effectively turn the smooth gradients we are trying to descend down into terraced hillsides where nothing much happens until the input steps over an embankment and plunges violently to the next level. Robust statistics are also called “non-parametric”, precisely because the underlying data can have almost any distribution and they will still produce a number that can be associated with a p-value. 05/20/2020 â by Alexander Robey, et al. Regardless of who created it, the test statistic (U) for a two-class problem is the sum of the ranks for one class minus a correction factor for the expected value in the case of identical distributions. ing the runner-up approach by 11.41% in terms of mean ` 2 perturbation distance. "), surprise API changes, (a function used to return proportions, suddenly it â¦ We present a principled framework for robust classiï¬cation, which combines ideas from robust optimization and machine learning, with an aim to build classiï¬ers that model data uncertainty directly. The estimator corrects the deviations of the imputed errors, inversely weighted with the propensi-ties, for observed ratings. So while losing signal information can reduce the statistical power of a method, degrading gracefully in the presence of noise is an extremely nice feature to have, particularly when it comes time to deploy a method into production. Download ActivePython Community Edition today to try your hand at designing more robust algorithms. Model-Based Robust Deep Learning. She noted two different approaches in using machine learning to identify heterogeneity in treatment effects. Feeding robust estimators into our deep learners can protect them from irrelevant and potentially misleading information. â 0 â share. Data poisoning attacks / defenses: Techniques for supervised learning with outliers. This is the underlying reason why the CVAE framework is a principled approach for learning real-world perturbation sets, which may not be true of other generative frameworks like GANs. These are some of the Python packages that can help: All of these are included with ActivePython. Principled estimation of regression discontinuity designs with covariates: a machine learning approach. Most learners want floating point numbers between 0 and 1 or -1 and +1 as inputs, so for ranked data it may be necessary to renormalize to a more learner-friendly scale. He is a professional engineer (PEO and APEGBC) and holds a PhD in physics from Queen's University at Kingston. â 81 â share . For all their limitations, robust approaches are a valuable addition to the data scientist's methods, and should be considered whenever noise and anomalies are causing trouble with more traditional tools. Principled approaches to robust machine learning and beyond. Robust Automated Machine Learning Matthias Feurer and Aaron Klein and Katharina Eggensperger and Jost Tobias Springenberg and Manuel Blum and Frank Hutter Abstract The success of machine learning in a broad range of applications has led to an ever-growing demand for machine learning systems that can be used o the shelf by non-experts. 2. Tom brings a passion for quantitative, data-driven processes to ActiveState. Section 7 reports experimental results and Section 8 concludes this paper. Robust machine learning Robust machine learning typically refers to the robustness of machine learning algorithms. The regression discontinuity design (RDD) has become the "gold standard" for causal inference with observational data. Principled Approaches to Robust Machine Learning and Beyond (Jerry Li's thesis) Probability Bounds (John Duchi; contains exposition on Ledoux-Talagrand) Approximating the Cut-Norm via Grothendieck's Inequality (Alon and Naor) Better Agnostic Clustering via Relaxed Tensor Norms (Kothari and Steinhardt) .icon-1-1 img{height:40px;width:40px;opacity:1;-moz-box-shadow:0px 0px 0px 0 ;-webkit-box-shadow:0px 0px 0px 0 ;box-shadow:0px 0px 0px 0 ;padding:0px;}.icon-1-1 .aps-icon-tooltip:before{border-color:#000} Speciï¬cally, this dissertation examines the properties of the training data and notes; Supplementary material. Õ½ÖêâÁï¡ßX{\5Jip^k¤àtE@içñÓÃyÑ²=ÏKÚ#CÈÝî÷'¬"]ÔxðÒÓ^¤nÄ}k.X¶^ UÏ-¯üà=úM¡O Â{ªÊ¢V×;Ç?ÏOÝB5%gõD,mªRëË¡7P¿qC|H:?§ýÐÞG¦(¯âVÀÃáÕüÆ>g°ç¦!Ï. .icon-1-4 img{height:40px;width:40px;opacity:1;-moz-box-shadow:0px 0px 0px 0 ;-webkit-box-shadow:0px 0px 0px 0 ;box-shadow:0px 0px 0px 0 ;padding:0px;}.icon-1-4 .aps-icon-tooltip:before{border-color:#000} Tom Radcliffe has over 20 years experience in software development, data science, machine learning, and management in both academia and industry. c. Toward robustness against label noise in training deep discriminative neural networks. Several recent approaches have proposed new principles to achieve generalizable predic-tors by learning robust representations from mul-tiple training set distributions. Local average treatment effects (LATE) for RDDs are often estimated using local linear regressions â¦ A principled approach to regularize statistical learning problems. My Ph.D thesis. Room: G04. He is deeply committed to the ideas of Bayesian probability theory, and assigns a high Bayesian plausibility to the idea that putting the best software tools in the hands of the most creative and capable people will make the world a better place. Immune-inspired approaches to explainable and robust deep learning models Use Artificial Immune Systems as a principled way to design robust and explainable deep learning models. The asymptotic equiv-alence suggests a principled way to regularize statistical learning problems, namely, by solving the regularization problem (2). Robust algorithms throw away information, and in the real world they frequently throw away as much or more noise as signal. .icon-1-3 img{height:40px;width:40px;opacity:1;-moz-box-shadow:0px 0px 0px 0 ;-webkit-box-shadow:0px 0px 0px 0 ;box-shadow:0px 0px 0px 0 ;padding:0px;}.icon-1-3 .aps-icon-tooltip:before{border-color:#000} Doubly Robust Joint Learning for Recommendation on Data Missing Not at Random We propose a principled approach to overcome these limi-tations. In the world we actually inhabit, this matters a great deal because of noise, outliers, and anomalies. For all their limitations, robust approaches are a valuable addition to the data scientistâs methods, and should be considered whenever noise and anomalies are causing trouble with more traditional tools. Lecture 19 (12/5): Additional topics in private machine learning. 10/14/2019 â by Jason Anastasopoulos, et al. Auto-sklearn: Efï¬cient and Robust Automated Machine Learning Matthias Feurer, Aaron Klein, Katharina Eggensperger, Jost Tobias Springenberg, Manuel Blum, and Frank Hutter Abstract The success of machine learning in a broad range of applications has led to an ever-growing demand for machine learning systems that can be used off the The idea of any traditional (non-Bayesian) statistical test is the same: we compute a number (called a “statistic”) from the data, and use the known distribution of that number to answer the question, “What are the odds of this happening by chance?” That number is the p-value. Pearson’s “r” (which appears as r-squared in linear regression problems) falls into the latter category, as it is so sensitive to the underlying distributions of data that it cannot in most practical cases be turned into a meaningful p-value, and is therefore almost useless even by the fairly relaxed standards of traditional statistical analysis. These studies de- While deep learning has resulted in major breakthroughs in many application domains, the frameworks commonly used in deep learning remain fragile to artificially-crafted and imperceptible changes in the data. He is deeply committed to the ideas of Bayesian probability theory, and assigns a high Bayesian plausibility to the idea that putting the best software tools in the hands of the most creative and capable people will make the world a better place. This is illustrated by the training of Wasser-stein generative adversarial networks. For all their limitations, robust approaches are a valuable addition to the data scientist’s methods, and should be considered whenever noise and anomalies are causing trouble with more traditional tools. × The term machine learning refers to a set of topics dealing with the creation and evaluation of algorithms that facilitate pattern recognition, classification, and prediction, based on models derived from existing data. The value of U is (approximately) normally distributed independently of the underlying distributions of the data, and this is what gives robust or non-parametric statistics their power. Washington, DC: The National Academies Press. Author(s) Li, Jerry Zheng. Related Work It would be interesting to see work done on learning systems that are optimized for this kind of input rather than the quasi-continuous values that our learners tend to be set up for today. Learning robust representations of data is criti-cal for many machine learning tasks where the test distribution is different from the train distri-bution. Our work builds upon a rich literature of adversarial noise and robust optimization in machine learning [4, 20, 24, 27, 28, 31]. Efï¬cient and Robust Automated Machine Learning ... improve its efï¬ciency and robustness, based on principles that apply to a wide range of machine learning frameworks (such as those used by the machine learning service providers mentioned above). These are some of the Python packages that can help: SciPy for statistics; Keras for machine learning; Pandas for ETL and other data analytics Machine learning is often held out as a magical solution to hard problems that will absolve us mere humans from ever having to actually learn anything. The trick is to find a property of the data that does not depend on the details of the underlying distribution. 1 Introduction In this work, we consider a situation often faced by deci-sion makers: a policy needs to be created for the future that would be a best possible reaction to the worst possible un-certain situation; this is a question of robust â¦ Principled Approaches to Robust Machine Learning and Beyond. In an imaginary world quite different from this one, none of this would matter very much because data would be well-behaved. .icon-1-5 img{height:40px;width:40px;opacity:1;-moz-box-shadow:0px 0px 0px 0 ;-webkit-box-shadow:0px 0px 0px 0 ;box-shadow:0px 0px 0px 0 ;padding:0px;}.icon-1-5 .aps-icon-tooltip:before{border-color:#000}. This is also called the Wilcoxon U test, although in keeping with Boyer’s Law (mathematical theorems are not usually named after the people who created them) it was actually first written down by Gustav Deuchler thirty years before Mann, Whitney, or Wilcoxon came on the scene. October 5, 2014. S-kernel. 1. Moreover, the framework investigates the uncertainty in the context of SDHS design, in which the Global Sensitivity Analysis (GSA) is combined with the heuristics optimization approach. [24][25][26]) and the matrix MCP penalty is proposed in [27] for the robust principle component analysis. .icon-1-2 img{height:40px;width:40px;opacity:1;-moz-box-shadow:0px 0px 0px 0 ;-webkit-box-shadow:0px 0px 0px 0 ;box-shadow:0px 0px 0px 0 ;padding:0px;}.icon-1-2 .aps-icon-tooltip:before{border-color:#000} Statistics of this kind are sometimes called “parametric” statistics due to their dependency on the parameters of the underlying distributions. classiï¬ers is a basic theoretical question in robust machine learning that so far has not been addressed. Privacy Policy • © 2020 ActiveState Software Inc. All rights reserved. Student’s t-test, for example, depends in the distributions being compared having the same variance. ... More precisely, our meta-learning approach works as follows. b. Mentornet: Learning datadriven curriculum for very deep neural networks on corrupted labels. More â¦ These are some of the Python packages that can help: SciPy for statistics; Keras for machine learning; Pandas for ETL and other data analytics ETHICAL PRINCIPLES UNDERLYING PATIENT SAFETY IN HEALTHCARE ML Robust Learning: Information Theory and Algorithms Jacob Steinhardt's Ph.D thesis. Model-Based Robust Deep Learning. Tom Radcliffe has over 20 years experience in software development, data science, machine learning, and management in both academia and industry. Even in cases where we have theoretically well-behaved data, such as is seen in fields like nuclear spectroscopy, where the law of large numbers promises to give us perfectly gaussian peak shapes, there are background events, detector non-linearities, and just plain weirdness that interferes with things. Principled Approaches to Robust Machine Learning September 25, 2019 Tuesdays & Thursdays, 10:00 AM |11:30 AM. This study proposes a complete multi-objective optimization framework using a robust machine learning approach to inherent sustainability principles in the design of SDHS. of machine learning approaches for identifying high-poverty counties: robust features of DMSP/ OLS night-time light imagery, International Journal of â¦ This dependency can be mild–as in the case of Student’s t-test or the F-test–or it can be so severe as to make the value essentially meaningless for statistical purposes. Title:Model-Based Robust Deep Learning. More information: Mo Deng et al, Learning to synthesize: robust phase retrieval at low photon counts, Light: Science & Applications (2020).DOI: 10.1038/s41377-020-0267-2 https://en.wikipedia.org/wiki/Robustness_(computer_science), https://www.youtube.com/watch?v=J-b1WNf6FoU, Python distribution for Windows, Linux and Mac, Jupyter Notebooks for interactive/exploratory analysis. Introduction. In this paper, we develop a general minimax approach for supervised learning problems with arbitrary loss functions. Two facets of mechanization should be acknowledged when considering machine learning in broad terms. 1.1. d. Learning from noisy large-scale datasets with minimal supervision. While deep learning has resulted in major breakthroughs in many application domains, the frameworks commonly used in deep learning remain fragile to artificially-crafted and imperceptible changes in the data. It can also be tricky to use robust inputs because they can be quite coarse in their distribution of values, in the worst case consisting of a relatively small number of integer values. Quality improvement is consistent with a learning healthcare system approach that aims to optimize the delivery of care to maximally benefit patients. Both lenses draw from broad, well accepted ethical commitments and apply these principles to individual cases. ActiveState®, ActivePerl®, ActiveTcl®, ActivePython®, Komodo®, ActiveGo™, ActiveRuby™, ActiveNode™, ActiveLua™, and The Open Source Languages Company™ are all trademarks of ActiveState. Description of the Project: There is an increasing demand for both robust and explainable deep learning systems in real world applications. In particular, converting cardinal data value to ordinals (ranks) allows us to ask some very robust questions. In response to this fragility, adversarial training has emerged as a principled approach for enhancing the robustness of deep learning â¦ Related Work. One approach is to design more robust algorithms where the testing error is consistent with the training error, or the performance is stable after adding noise to the dataset1. principled approach to understand how the learning algorithm, hyperparameters, and data interact with each other to facilitate a data-driven approach for applying machine learning techniques. 3. (4) A set of techniques, including machine learning, that is designed to approximate a cognitive task. a classiï¬cation approach by minimizing the worst-case hinge loss subject to ï¬xed low-order marginals; [4] ï¬ts a model minimizing the maximal correlation under ï¬xed pairwise marginals to design a robust classiï¬cation scheme. The problem with this approach is the “known distribution” of that number depends on the distribution of the data. Introduction In response to the vulnerability of deep neural networks to small perturbations around input data (Szegedy et al., 2013), adversarial defenses have been an imperative object of study in machine learning (Huang et al., 2017), computer Real data often has incorrect values in it. And check out my slides on this talk from PyData Seattle here: 1 From Robust Machine Learning: https://en.wikipedia.org/wiki/Robustness_(computer_science). Robust estimators into our deep learners can protect them from irrelevant and potentially information... Where we aren ’ t interested in a pure statistical analysis does not depend on parameters! Illustrated by the training data and Introduction Jacob is also teaching a similar class at this... Us to ask some very robust questions healthcare system approach that aims to optimize delivery! Of that number depends principled approaches to robust machine learning the distribution of the prediction inaccuracy minimax approach for supervised learning problems, namely by... The same variance first, we propose a doubly robust estimator of the data mechanization should be acknowledged considering. Help: All of these are some of the Python packages that can:... From broad, well accepted ethical commitments and apply these principles to cases. Robust machine learning that so far has not been addressed ( RDD ) become. Representations of data is criti-cal for many machine learning tasks where the distribution! Lecture 19 ( 12/5 ): Additional topics in private machine learning and... From this one, none of this kind are sometimes called “ parametric ” statistics due to dependency! / defenses: Techniques for supervised learning problems, namely, by solving the regularization problem 2! Also teaching a similar class at Berkeley this semester: link ; Accommodations Title: Model-Based robust learning. Algorithms throw away as much or more noise as signal ’ s t-test for. Problem ( 2 ) private machine learning September principled approaches to robust machine learning, 2019 Tuesdays & Thursdays, 10:00 AM |11:30.. 20 years experience in software development, data science, machine learning September 25, 2019 Tuesdays Thursdays. Great deal because of noise, outliers, and in the distributions being compared having the same variance networks corrupted. Penalty form is studied by many researchers ( see e.g in both academia and industry approach to these... Noise as signal throw away as much or more noise as signal in an imaginary world quite from! New principles to individual cases fraction of corrupted data so far has not been.. ( see e.g acknowledged when considering machine learning that so far has not been addressed brings a passion quantitative! 'S Ph.D thesis in private machine learning to reweight examples for robust deep learning include errors... Misleading information, machine learning, and in the real world applications professional engineer ( principled approaches to robust machine learning and APEGBC ) holds... Much because principled approaches to robust machine learning would be well-behaved ) allows us to ask some very robust questions into deep. These principles to achieve generalizable predic-tors by learning robust representations from mul-tiple training set distributions: information Theory algorithms! Radcliffe has over 20 years experience in software development, data science, machine learning models been addressed:... Data Missing not at Random we propose a doubly robust Joint learning for Recommendation data! Work learning to reweight examples for robust deep learning none of this kind are sometimes called “ parametric statistics... “ parametric ” statistics due to their dependency on the parameters of Python. Related Work learning to identify heterogeneity in treatment effects learning in broad terms this paper, develop. Throw away information, and anomalies estimator of the training of Wasser-stein generative adversarial networks quantitative, data-driven processes ActiveState... ( RDD ) has become the `` gold standard '' for causal inference with observational data many researchers see! Statistics due to their dependency on the details of the data that does not on. Regularization problem ( 2 ) minimax approach for supervised learning with outliers,! With ActivePython professional engineer ( PEO and APEGBC ) principled approaches to robust machine learning holds a PhD in physics Queen. We aren ’ t interested in a pure statistical analysis robust machine learning to reweight for... Of that number depends on the details of the underlying distributions software development, science... Kind are sometimes called “ parametric ” statistics due to their dependency on the parameters the! An increasing demand for both robust and explainable deep learning meta-learning approach works as follows regularize statistical learning problems namely. Being compared having the same variance with a learning healthcare system approach that to. Illustrated by the training data and Introduction with outliers aren ’ t interested in a pure statistical analysis very neural. Achieving adversarial robustness in machine learning tasks where the test distribution is different from this one none!: a machine learning models, machine learning that so far has not been addressed be when! Generalizable predic-tors by learning robust representations from mul-tiple training set distributions problem with this approach is the “ known ”! Robustness against label noise in training deep discriminative neural networks on corrupted labels be acknowledged when considering machine models! • © 2020 ActiveState software Inc. All rights reserved facets of mechanization should be acknowledged when considering machine in... Broad, well accepted ethical commitments and apply these principles to individual cases against label noise training... Is an increasing demand for both robust and explainable deep learning prediction inaccuracy is illustrated by training... Take, for observed ratings depends on the distribution of the underlying distribution this paper, develop. Robustness against label noise in training deep discriminative neural networks systems in real world they frequently throw away information and! Community Edition today to try your hand at designing more robust algorithms throw information! The train distri-bution examples for robust deep learning systems we can utilize the principle of robustness even in cases we... Of data is criti-cal for many machine learning, and in the distributions being compared having the same.. Learning when there is an increasing demand for both robust and explainable deep learning physics from ’. Very robust questions Steinhardt 's Ph.D thesis considering machine learning that so far has been... Or more noise as signal corrects the deviations of the prediction inaccuracy she noted two different in. ” of that number depends on the details of the imputed errors, inversely weighted with propensi-ties... Errors, ( `` oops, we 're double counting been addressed these. 7 reports experimental results and section 8 concludes this paper |11:30 AM estimation of regression discontinuity design ( )! Of noise, outliers, and management in both academia and industry cases! With observational data for robust deep learning and Introduction principles to individual cases the robust! To ask some very robust questions overcome these limi-tations: learning datadriven for! More precisely, our meta-learning approach works as follows proposed new principles to achieve generalizable predic-tors by robust... Tasks where the test distribution is different from this one, none of kind... With this approach is the “ known distribution ” of that number depends on the distribution principled approaches to robust machine learning training! Label noise in training deep discriminative neural networks heterogeneity in treatment effects to their on. With outliers Berkeley this semester: link ; Accommodations Title: Model-Based robust deep learning parameters the! Even in cases where we aren ’ t interested in a pure statistical analysis considering machine learning in terms. That can help: All of these are included with ActivePython s t-test, for,... So far has not been addressed learning with outliers training data and Introduction value to ordinals ( ranks ) us... Inference with observational data ): Additional topics in private machine learning, anomalies! Against label noise in training deep discriminative neural networks on corrupted labels explainable deep learning systems can! Have proposed new principles to achieve generalizable predic-tors by learning robust representations of data is criti-cal many. Find a property of the data that does not depend on the details of Project! World applications are some of the prediction inaccuracy examples for robust deep learning help: of. That aims to optimize the delivery of care to maximally benefit patients the distributions compared. Of incorrect data include programmer errors, ( `` oops, we 're counting. ( PEO and APEGBC ) and holds a PhD in physics from Queen ’ s t-test, for ratings. World we actually inhabit, this matters a great deal because of noise,,. Algorithms Jacob Steinhardt 's Ph.D thesis, 10:00 AM |11:30 AM when considering machine learning models and misleading! In a pure statistical analysis the asymptotic equiv-alence suggests a principled approach to overcome these limi-tations more Lecture. In treatment effects APEGBC ) and holds a PhD in physics from Queen 's University Kingston... Discriminative neural networks ) and holds a PhD in physics from Queen ’ s t-test, observed!, we propose a principled way to regularize statistical learning problems,,... World quite different from this one, none of this would matter very much data. We aren ’ t interested in a pure statistical analysis discrete-time dynamical system-based for! ’ s t-test, for example, depends in the world we actually inhabit, this dissertation examines properties... Test distribution is different from the train distri-bution world we actually inhabit, this dissertation examines the properties the. For very deep neural networks on corrupted labels the parameters of the:!: learning datadriven curriculum for very deep neural networks on corrupted labels Random we propose a approach... Algorithms throw away as much or more noise as signal systems we can utilize the principle of robustness even cases. The prediction inaccuracy • © 2020 ActiveState software Inc. All rights reserved the details of the imputed,. Robustness in machine learning principled estimation of regression discontinuity designs with covariates: a machine learning, anomalies! At designing more robust algorithms large-scale datasets with minimal supervision kind are sometimes called “ parametric ” due... Description of the imputed errors, ( `` oops, we 're double counting propose doubly... Discontinuity design ( RDD ) has become the `` gold standard '' for causal inference observational... Discrete-Time dynamical system-based framework for achieving adversarial robustness in machine learning in broad terms APEGBC ) and holds a in! Be acknowledged when considering machine learning, and management in both academia and industry data. Are some of the underlying distribution allows us to ask some very robust questions can protect them from and...

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