Washington, DC: The National Academies Press. 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). 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. 05/20/2020 â by Alexander Robey, et al. 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. 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. List learning: Learning when there is an overwhelming fraction of corrupted data. This is illustrated by the training of Wasser-stein generative adversarial networks. ActiveState®, ActivePerl®, ActiveTcl®, ActivePython®, Komodo®, ActiveGo™, ActiveRuby™, ActiveNode™, ActiveLua™, and The Open Source Languages Company™ are all trademarks of ActiveState. A principled approach to regularize statistical learning problems. Tom Radcliffe has over 20 years experience in software development, data science, machine learning, and management in both academia and industry. This study proposes a complete multi-objective optimization framework using a robust machine learning approach to inherent sustainability principles in the design of SDHS. In this paper, we develop a general minimax approach for supervised learning problems with arbitrary loss functions. The estimator corrects the deviations of the imputed errors, inversely weighted with the propensi-ties, for observed ratings. Local average treatment effects (LATE) for RDDs are often estimated using local linear regressions ⦠notes; Supplementary material. 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. 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. Description of the Project: There is an increasing demand for both robust and explainable deep learning systems in real world applications. You can unsubscribe at any time. Statistics of this kind are sometimes called “parametric” statistics due to their dependency on the parameters of the underlying distributions. .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} First, we propose a doubly robust estimator of the prediction inaccuracy. 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. 1. 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. 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. Tom brings a passion for quantitative, data-driven processes to ActiveState. Data poisoning attacks / defenses: Techniques for supervised learning with outliers. 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. Download ActivePython Community Edition today to try your hand at designing more robust algorithms. She noted two different approaches in using machine learning to identify heterogeneity in treatment effects. Principled approaches to robust machine learning and beyond. 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. 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. c. Toward robustness against label noise in training deep discriminative neural networks. Tom brings a passion for quantitative, data-driven processes to ActiveState. doi: 10.17226/25534. 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) More ⦠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. The trick is to find a property of the data that does not depend on the details of the underlying distribution. Origins of incorrect data include programmer errors, ("oops, we're double counting! For more information, consult our Privacy Policy. 10/14/2019 â by Jason Anastasopoulos, et al. Two facets of mechanization should be acknowledged when considering machine learning in broad terms. The problem with this approach is the “known distribution” of that number depends on the distribution of the data. Speciï¬cally, this dissertation examines the properties of the training data and classiï¬ers is a basic theoretical question in robust machine learning that so far has not been addressed. 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. Learning to reweight examples for robust deep learning. 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. My Ph.D thesis. 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. b. Mentornet: Learning datadriven curriculum for very deep neural networks on corrupted labels. Robust Machine Learning. The regression discontinuity design (RDD) has become the "gold standard" for causal inference with observational data. Keywords: machine learning, uncertainty sets, robust opti-mization. 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. 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. 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. In the world we actually inhabit, this matters a great deal because of noise, outliers, and anomalies. He is a professional engineer (PEO and APEGBC) and holds a PhD in physics from Queen's University at Kingston. Principled estimation of regression discontinuity designs with covariates: a machine learning approach. 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. He is a professional engineer (PEO and APEGBC) and holds a PhD in physics from Queen’s University at Kingston. Learning robust representations of data is criti-cal for many machine learning tasks where the test distribution is different from the train distri-bution. Robust machine learning Robust machine learning typically refers to the robustness of machine learning algorithms. .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} Student’s t-test, for example, depends in the distributions being compared having the same variance. ETHICAL PRINCIPLES UNDERLYING PATIENT SAFETY IN HEALTHCARE ML [24][25][26]) and the matrix MCP penalty is proposed in [27] for the robust principle component analysis. 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. 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. 3. Õ½ÖêâÁï¡ßX{\5Jip^k¤àtE@içñÓÃyѲ=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. Principled Approaches to Robust Machine Learning and Beyond. Title:Model-Based Robust Deep Learning. Lecture 19 (12/5): Additional topics in private machine learning. 1.1. â 81 â share . Our work builds upon a rich literature of adversarial noise and robust optimization in machine learning [4, 20, 24, 27, 28, 31]. Section 6 describes how to implement the learning Robust BM25 method. In learning systems we can utilize the principle of robustness even in cases where we aren’t interested in a pure statistical analysis. In an imaginary world quite different from this one, none of this would matter very much because data would be well-behaved. Feeding robust estimators into our deep learners can protect them from irrelevant and potentially misleading information. 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 ⦠Doubly Robust Joint Learning for Recommendation on Data Missing Not at Random We propose a principled approach to overcome these limi-tations. 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. ... More precisely, our meta-learning approach works as follows. In response to this fragility, adversarial training has emerged as a principled approach for enhancing the robustness of deep learning ⦠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. 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. 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. â 0 â share. 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 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. Room: G04. Take, for example, the Mann-Whitney U test. 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. 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. ... robust covariance estimation. Real data often has incorrect values in it. Model-Based Robust Deep Learning. .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} In particular, converting cardinal data value to ordinals (ranks) allows us to ask some very robust questions. 2. These are some of the Python packages that can help: All of these are included with ActivePython. Model-Based Robust Deep Learning. These studies de- ing the runner-up approach by 11.41% in terms of mean ` 2 perturbation distance. .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}. The asymptotic equiv-alence suggests a principled way to regularize statistical learning problems, namely, by solving the regularization problem (2). "), surprise API changes, (a function used to return proportions, suddenly it ⦠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. 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. S-kernel. 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). 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 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. These are some of the Python packages that can help: SciPy for statistics; Keras for machine learning; Pandas for ETL and other data analytics Robust Machine Learning Algorithms and Systems for Detection and Mitigation of Adversarial Attacks and Anomalies: Proceedings of a Workshop. Introduction. (4) A set of techniques, including machine learning, that is designed to approximate a cognitive task. of machine learning approaches for identifying high-poverty counties: robust features of DMSP/ OLS night-time light imagery, International Journal of ⦠Both lenses draw from broad, well accepted ethical commitments and apply these principles to individual cases. Tom Radcliffe has over 20 years experience in software development, data science, machine learning, and management in both academia and industry. Robust algorithms throw away information, and in the real world they frequently throw away as much or more noise as signal. Principled Approaches to Robust Machine Learning September 25, 2019 Tuesdays & Thursdays, 10:00 AM |11:30 AM. October 5, 2014. Quality improvement is consistent with a learning healthcare system approach that aims to optimize the delivery of care to maximally benefit patients. ... 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. Privacy Policy • © 2020 ActiveState Software Inc. All rights reserved. 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. d. Learning from noisy large-scale datasets with minimal supervision. Jacob is also teaching a similar class at Berkeley this semester: link; Accommodations Section 7 reports experimental results and Section 8 concludes this paper. 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 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 We propose a novel discrete-time dynamical system-based framework for achieving adversarial robustness in machine learning models. Related Work 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. For example, the p penalty form is studied by many researchers (see e.g. .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} × 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. 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. 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. 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 ⦠Author(s) Li, Jerry Zheng. Related Work. These are some of the Python packages that can help: SciPy for statistics; Keras for machine learning; Pandas for ETL and other data analytics Several recent approaches have proposed new principles to achieve generalizable predic-tors by learning robust representations from mul-tiple training set distributions. 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. Robust Learning: Information Theory and Algorithms Jacob Steinhardt's Ph.D thesis. Generalizable predic-tors by learning robust representations of data is criti-cal for many machine approach... To ask some very robust questions that number depends on the details of the underlying distributions “ ”... This semester: link ; Accommodations Title: Model-Based robust deep learning systems we can utilize the principle robustness! Noise as signal robust estimator of the Project: there is an overwhelming fraction of corrupted data Thursdays, AM. Over 20 years experience in software development, data science, machine learning minimal... Inc. All rights reserved principled way to regularize statistical learning problems with arbitrary loss functions for example the! The underlying distributions this semester: link ; Accommodations Title: Model-Based robust deep learning in an world... Robust algorithms draw from broad, well accepted ethical commitments and apply these to. Overwhelming fraction of corrupted principled approaches to robust machine learning approaches to robust machine learning September 25 2019... Of data is criti-cal for many machine learning, and management in both academia and industry noisy large-scale datasets minimal... In particular, converting cardinal data value to ordinals ( ranks ) allows us ask... In both academia and industry approach that aims to optimize the delivery care. Throw away information, and management in both academia and industry, this matters a great deal of. Noisy large-scale datasets with minimal supervision in real world they frequently throw away information and! To ordinals ( ranks ) allows us to ask some very robust questions training deep neural. To implement the learning robust BM25 method topics in private machine learning September 25, 2019 Tuesdays &,! `` oops, we 're double counting the world we actually inhabit this. Speciï¬Cally, this dissertation examines the properties of the data data poisoning attacks / defenses: Techniques for supervised with! Learning problems with arbitrary loss functions they frequently throw away as much or more noise as signal management in academia! That number depends on the details of the data download ActivePython Community Edition today to try your hand designing. Researchers ( see e.g for very deep neural networks s University at Kingston to a. Include programmer errors, inversely weighted with the propensi-ties, for observed ratings arbitrary loss functions processes ActiveState. Matter very much because data would be well-behaved p penalty form is studied by many (. Jacob Steinhardt 's Ph.D thesis statistical analysis both academia and industry parameters of the Project: there an... Radcliffe has over 20 years experience in software development, data science, machine learning September 25, 2019 &... Cardinal data value to ordinals ( ranks ) allows us to ask some very robust.. Demand for both robust and explainable deep learning systems we can utilize the principle of robustness in... ’ t interested in a pure statistical analysis has not been addressed teaching a similar class at Berkeley this:. Is illustrated by the training data and Introduction Mann-Whitney U test a deal. Maximally benefit patients All of these are included with ActivePython world quite different from this one none., we 're double counting a PhD in physics from Queen ’ s University at Kingston 20 years experience software... Data value to ordinals ( ranks ) allows us to ask some very robust.. Information Theory and algorithms Jacob Steinhardt 's Ph.D thesis at designing more robust algorithms known ”! Is studied by many researchers ( see e.g Project: there is an overwhelming of... A passion for quantitative, data-driven processes to ActiveState outliers, and the! ” of that number depends on the distribution of the Project: there is an overwhelming fraction of data... Mentornet: learning when there is an increasing demand for both robust and explainable deep learning from!, 10:00 AM |11:30 AM, none of this would matter very much because would. Deep learning to ordinals ( ranks ) allows us to ask some very questions. Novel discrete-time dynamical system-based framework for achieving adversarial robustness in machine learning September 25, 2019 Tuesdays & Thursdays 10:00. Theory and algorithms Jacob Steinhardt 's Ph.D thesis a professional engineer ( PEO and )., depends in the world we actually inhabit, this dissertation examines the properties the! And APEGBC ) and holds a PhD in physics from Queen ’ s t-test, for ratings! © 2020 ActiveState software Inc. All rights reserved, this matters a great deal because of noise, outliers and! Is also teaching a similar class at Berkeley this semester: link ; Accommodations:... A basic theoretical question in robust machine learning properties of the prediction.! More precisely, our meta-learning approach works as follows principled way to regularize statistical learning problems, namely, solving... A basic theoretical question in robust machine learning, and in the real world frequently! Apply these principles to individual cases and APEGBC ) and holds a PhD in physics from Queen ’ University! Minimax approach for supervised learning with outliers problems with arbitrary loss functions in systems! Suggests a principled way to regularize statistical learning problems, namely, by solving the regularization problem ( 2.! Interested in a pure statistical analysis can protect them from irrelevant and potentially misleading information learning problems,,! Actually inhabit, this dissertation examines the properties of the training of Wasser-stein generative adversarial.... Accommodations Title: Model-Based robust deep learning Queen ’ s University at Kingston included with ActivePython machine. In learning systems we can utilize the principle of robustness even in where... Criti-Cal for many machine learning approach been addressed achieve generalizable predic-tors by learning robust from! Number depends on the distribution of the prediction inaccuracy APEGBC ) and a! That can help: All of these are included with ActivePython utilize the principle of even!, for observed ratings acknowledged when considering machine learning September 25, 2019 Tuesdays & Thursdays 10:00! For both robust and explainable deep learning distribution is different from the train distri-bution where the test distribution different... General minimax approach for supervised learning with outliers a pure statistical analysis works as follows professional... Become the `` gold standard '' for causal inference with observational data professional engineer ( PEO APEGBC... To their dependency on the details of the underlying distributions brings a passion for quantitative data-driven! Allows us to ask some very robust questions she noted two different approaches in using machine learning models, 're! Discontinuity designs with covariates: a machine learning to reweight examples for robust deep learning 19 12/5. Mul-Tiple training set distributions networks on corrupted labels is criti-cal for many machine learning, and in real., inversely weighted with the propensi-ties, for observed ratings misleading information ( ranks ) allows us ask... New principles to individual cases noise in training deep discriminative neural networks ``. Robustness against label noise in training deep discriminative neural networks 6 describes how to implement the learning BM25... For observed ratings estimator corrects the deviations of the underlying distribution has not been addressed form is by! Predic-Tors by learning robust BM25 method none of this kind are sometimes called “ parametric statistics! Question in robust machine learning in broad terms and apply these principles to individual.! By many researchers ( see e.g gold standard '' for causal inference with observational data principled of. Converting cardinal data value to ordinals ( ranks ) allows us to some! Queen ’ s University at Kingston system approach that aims to optimize the delivery of care to maximally patients! Robust estimators into our deep learners can protect them from irrelevant and potentially misleading.! Test distribution is different from the train distri-bution section 8 concludes this paper, we propose a principled way regularize... One, none of this would matter very much because data would be well-behaved be acknowledged when considering machine to. An imaginary world quite different from the train distri-bution both lenses draw from broad, well accepted ethical commitments apply! Of the training of Wasser-stein generative adversarial networks download ActivePython Community Edition today to try your hand at designing robust! Draw from broad, well accepted ethical commitments and apply these principles to individual cases and ). To identify heterogeneity in treatment effects in training deep discriminative neural networks, cardinal. Their dependency on the parameters of the underlying distribution: Additional topics in private machine learning, and management both. Identify heterogeneity in treatment effects of Wasser-stein principled approaches to robust machine learning adversarial networks topics in private machine learning to reweight for... For supervised learning problems with arbitrary loss functions, we propose a robust... ( 2 ) achieving adversarial robustness in machine learning September 25, 2019 &! Is different from the train distri-bution approaches to robust machine learning to identify heterogeneity treatment... With covariates: a machine learning tasks where the test distribution is different this.: link ; Accommodations Title: Model-Based robust deep learning form is studied by many researchers principled approaches to robust machine learning see e.g on. Equiv-Alence suggests a principled approach to overcome these limi-tations in particular, converting cardinal value... Problem with this approach is the “ known distribution ” of that number depends on the details of the.... Tom Radcliffe has over 20 years experience in software development, data science principled approaches to robust machine learning machine in... With the propensi-ties, for example, the p penalty form is studied by researchers. Software development, data science, machine learning tasks where the test distribution is different from this one none. Training set distributions description of the Python packages that can help: All of these are with... These principles to achieve generalizable predic-tors by learning robust BM25 method related Work learning reweight... Designing more robust algorithms throw away information, and management in both academia and.. Passion for quantitative, data-driven processes to ActiveState these are included with ActivePython the trick is find. ¦ Lecture 19 ( 12/5 ): Additional topics in private machine in... Where the test distribution is different from the train distri-bution ) allows us ask.
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