DOCSLIB.ORG

Machine Learning Lecture 1: Overview of Class, LFD 1.1, 1.2

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Machine Learning Lecture 1: Overview of Class, LFD 1.1, 1.2 ECS171: Machine Learning Lecture 1: Overview of class, LFD 1.1, 1.2 Cho-Jui Hsieh UC Davis Jan 8, 2018 Course Information Website: http://www.stat.ucdavis.edu/~chohsieh/teaching/ ECS171_Winter2018/main.html and canvas My office: Mathematical Sciences Building (MSB) 4232 Office hours: Tuesday 1pm-2pm, MSB 4232 (starting next week) TAs: Patrick Chen ([email protected]) Xuanqing Liu ([email protected]) Office hour: Thursday 10AM{11AM Kemper 55 (starting next week) My email: [email protected] Course Information Course Material: Part I (before midterm exam): Use the book \Learning from data" (LFD) by Abu-Mostafa, Magdon-Ismail and Hsuan-Tian Lin Foundation of machine learning: why can we learn from data? overfitting, underfitting, training vs testing, regularization ∼11 lectures Most slides are based on Yaser Abu-Mostafa (Caltech): http://work.caltech.edu/lectures.html#lectures Hsuan-Tian Lin (NTU): https://www.csie.ntu.edu.tw/~htlin/course/mlfound17fall/ Part II: Introduce some practical machine learning models. Deep learning, kernel methods, boosting, tree-based approach, clustering, dimension reduction Grading Policy Midterm (30%) Written exam for Part I Homework (30%) 2 or 3 homeworks Final project (40%) Competition? Final project Group of ≤ 4 students. We will announce the dataset and task Kaggle-styled competition Upload your model/prediction online Our website will report the accuracy Final report: Report the algorithms you have tested and the implementation details Discuss your findings The Learning Problem From learning to machine learning What is learning? observations ! Learning ! Skill Machine learning: data ! Machine Learning ! Skill Automatic the learning process! Skill: how to make decision (action) Classify an image Predict bitcoin price ::: Example: movie recommendation Data: user-movie ratings Skill: predict how a user rate an unrated movie Known as the “Netflix problem" A competition held by Netflix in 2006 1 million ratings, 480K users, 17K movies 10% improvement over baseline ) 1 million dollar price Movie rating - a solution Each viewer/movie is associated with a \latent factor" Prediction: Rating viewer/movie factors Learning: Known ratings ! viewer/movie factors Credit Approval Problem Customer record: To be learned: \Is Approving credit card good for bank?" Formalize the Learning Problem Input: x 2 X (customer application) e.g., x = [23; 1; 1000000; 1; 0:5; 200000] Output: y 2 Y (good/bad after approving credit card) Target function to be learned: f : X!Y (ideal credit approval formula) Data (historical records in bank): D = f(x1; y1); (x2; y2); ··· ; (xN ; yN )g Hypothesis (function) g : X!Y (learned formula to be used) Basic Setup of Learning Problem Learning Model A learning model has two components: The hypothesis set H: Set of candidate hypothesis (functions) The learning algorithm: To pick a hypothesis (function) from the H Usually optimization algorithm (choose the best function to minimize the training error) Perceptron Our first ML model: perceptron (1957) Learning a linear function Single layer neural network Next, we introduce two components of perceptron: What's the hypothesis space? What's the learning algorithm? Perceptron Hypothesis Space Define the hypothesis set H For input x = (x1;:::; xd ) \attributes of a customer" d X Approve credit if wi xi > threshold; i=1 d X Deny credit if wi xi < threshold i=1 Define Y = f+1(good); −1(bad)g Linear hypothesis space H: all the h with the following form d X h(x) = sign( wi xi − threshold) i=1 (perceptron hypothesis) Perceptron Hypothesis Space (cont'd) Introduce an artificial coordinate x0 = −1 and set w0 = threshold d d X X T h(x) = sign( wi xi − threshold) = sign( wi xi ) = sign(w x) i=1 i=0 (vector form) Customer features x: points on Rd (d dimensional space) Labels y: +1 or −1 Hypothesis h: linear hyperplanes Select g from H H: all possible linear hyperplanes How to select the best one? g(xn) ≈ f (xn) = yn for most of the n = 1; ··· ; N Naive approach: Test all h 2 H and choose the best one minimizing the \training error" N 1 X train error = I (h(x ) 6= y ) N n n n=1 (I (·): indicator) Difficult: H is of infinite size Perceptron Learning Algorithm Perceptron Learning Algorithm (PLA) Initial from some w (e.g., w = 0) For t = 1; 2; ··· Find a misclassified point n(t): T sign(w xn(t)) 6= yn(t) Update the weight vector: w w + yn(t)xn(t) PLA Iteratively Find a misclassified point Rotate the hyperplane according to the misclassified point Perceptron Learning Algorithm Converge for \linearly separable" case: Linearly separable: there exists a perceptron (linear) hypothesis f with 0 training error PLA is guaranteed to obtain f (Stop when no more misclassified point) Binary classification Data: N d Features for each training example: fxngn=1, each xn 2 R Labels for each training example: yn 2 f+1; −1g d Goal: learn a function f : R ! f+1; −1g Examples: Credit approve/disapprove Email spam/not-spam patient sick/not sick ::: Other types of labels - Multi-class Multi-class classification: yn 2 f1; ··· ; Cg (C-way classification) Example: Coin recognition 2 Classify coins by two features (size; mass) (xn 2 R ) yn 2 Y = f1c; 5c; 10c; 25cg (Y = f1; 2; 3; 4g) Other examples: hand-written digits, ··· Other types of labels - Regression Regression: yn 2 R (output is a real number) Example: Stock price prediction Movie rating prediction ··· Other types of labels - structure prediction I love ML |{z} |{z} |{z} pronoun verb noun Multiclass classification for each word (word ) word class) (not using information of the whole sentence) Structure prediction problem: sentence ) structure (class of each word) Other examples: speech recognition, image captioning, ::: Machine Learning Problems Machine learning problems can usually be categorized into Supervised learning: every xn comes with yn (label) (semi-supervised learning) Unsupervised learning: only xn, no yn Reinforcement learning: Examples contain (input, some output, grade for this output) Unsupervised Learning (no yn) Clustering: given examples x1;:::; xN , classify them into K classes Other unsupervised learning: Outlier detection: fxng ) unusual(x) Dimensional reduction ::: Semi-supervised learning Only some (few) xn has yn Labeled data is much more expensive than unlabeled data Reinforcement Learning Used a lot in game AI, robotic controls Agent observe state St Agent conduct action At (ML model, based on input St ) Environment gives agent reward Rt Environment gives agent next state St+1 Only observe \grade" for a certain action (best action is not revealed) Ads system: (customer, ad choice, click or not) Conclusions Two components in ML: Set up a hypothesis space (potential functions) Develop an algorithm to choose a good hypothesis based on training examples A perceptron algorithm (linear classification) Supervised vs unsupervised learning Next class: LFD 1.3, 1.4 Questions?.
Load more

Recommended publications
  • Self-Discriminative Learning for Unsupervised Document Embedding
    Self-Discriminative Learning for Unsupervised Document Embedding Hong-You Chen∗1, Chin-Hua Hu∗1, Leila Wehbe2, Shou-De Lin1 1Department of Computer Science and Information Engineering, National Taiwan University 2Machine Learning Department, Carnegie Mellon University fb03902128, [email protected], [email protected], [email protected] Abstract ingful a document embedding as they do not con- sider inter-document relationships. Unsupervised document representation learn- Traditional document representation models ing is an important task providing pre-trained such as Bag-of-words (BoW) and TF-IDF show features for NLP applications. Unlike most competitive performance in some tasks (Wang and previous work which learn the embedding based on self-prediction of the surface of text, Manning, 2012). However, these models treat we explicitly exploit the inter-document infor- words as flat tokens which may neglect other use- mation and directly model the relations of doc- ful information such as word order and semantic uments in embedding space with a discrimi- distance. This in turn can limit the models effec- native network and a novel objective. Exten- tiveness on more complex tasks that require deeper sive experiments on both small and large pub- level of understanding. Further, BoW models suf- lic datasets show the competitiveness of the fer from high dimensionality and sparsity. This is proposed method. In evaluations on standard document classification, our model has errors likely to prevent them from being used as input that are relatively 5 to 13% lower than state-of- features for downstream NLP tasks. the-art unsupervised embedding models. The Continuous vector representations for docu- reduction in error is even more pronounced in ments are being developed.
    [Show full text]
  • Q-Learning in Continuous State and Action Spaces
    -Learning in Continuous Q State and Action Spaces Chris Gaskett, David Wettergreen, and Alexander Zelinsky Robotic Systems Laboratory Department of Systems Engineering Research School of Information Sciences and Engineering The Australian National University Canberra, ACT 0200 Australia [cg dsw alex]@syseng.anu.edu.au j j Abstract. -learning can be used to learn a control policy that max- imises a scalarQ reward through interaction with the environment. - learning is commonly applied to problems with discrete states and ac-Q tions. We describe a method suitable for control tasks which require con- tinuous actions, in response to continuous states. The system consists of a neural network coupled with a novel interpolator. Simulation results are presented for a non-holonomic control task. Advantage Learning, a variation of -learning, is shown enhance learning speed and reliability for this task.Q 1 Introduction Reinforcement learning systems learn by trial-and-error which actions are most valuable in which situations (states) [1]. Feedback is provided in the form of a scalar reward signal which may be delayed. The reward signal is defined in relation to the task to be achieved; reward is given when the system is successfully achieving the task. The value is updated incrementally with experience and is defined as a discounted sum of expected future reward. The learning systems choice of actions in response to states is called its policy. Reinforcement learning lies between the extremes of supervised learning, where the policy is taught by an expert, and unsupervised learning, where no feedback is given and the task is to find structure in data.
    [Show full text]
  • A Survey on Data Collection for Machine Learning a Big Data - AI Integration Perspective
    1 A Survey on Data Collection for Machine Learning A Big Data - AI Integration Perspective Yuji Roh, Geon Heo, Steven Euijong Whang, Senior Member, IEEE Abstract—Data collection is a major bottleneck in machine learning and an active research topic in multiple communities. There are largely two reasons data collection has recently become a critical issue. First, as machine learning is becoming more widely-used, we are seeing new applications that do not necessarily have enough labeled data. Second, unlike traditional machine learning, deep learning techniques automatically generate features, which saves feature engineering costs, but in return may require larger amounts of labeled data. Interestingly, recent research in data collection comes not only from the machine learning, natural language, and computer vision communities, but also from the data management community due to the importance of handling large amounts of data. In this survey, we perform a comprehensive study of data collection from a data management point of view. Data collection largely consists of data acquisition, data labeling, and improvement of existing data or models. We provide a research landscape of these operations, provide guidelines on which technique to use when, and identify interesting research challenges. The integration of machine learning and data management for data collection is part of a larger trend of Big data and Artificial Intelligence (AI) integration and opens many opportunities for new research. Index Terms—data collection, data acquisition, data labeling, machine learning F 1 INTRODUCTION E are living in exciting times where machine learning expertise. This problem applies to any novel application that W is having a profound influence on a wide range of benefits from machine learning.
    [Show full text]
  • Survey on Reinforcement Learning for Language Processing
    Survey on reinforcement learning for language processing V´ıctorUc-Cetina1, Nicol´asNavarro-Guerrero2, Anabel Martin-Gonzalez1, Cornelius Weber3, Stefan Wermter3 1 Universidad Aut´onomade Yucat´an- fuccetina, [email protected] 2 Aarhus University - [email protected] 3 Universit¨atHamburg - fweber, [email protected] February 2021 Abstract In recent years some researchers have explored the use of reinforcement learning (RL) algorithms as key components in the solution of various natural language process- ing tasks. For instance, some of these algorithms leveraging deep neural learning have found their way into conversational systems. This paper reviews the state of the art of RL methods for their possible use for different problems of natural language processing, focusing primarily on conversational systems, mainly due to their growing relevance. We provide detailed descriptions of the problems as well as discussions of why RL is well-suited to solve them. Also, we analyze the advantages and limitations of these methods. Finally, we elaborate on promising research directions in natural language processing that might benefit from reinforcement learning. Keywords| reinforcement learning, natural language processing, conversational systems, pars- ing, translation, text generation 1 Introduction Machine learning algorithms have been very successful to solve problems in the natural language pro- arXiv:2104.05565v1 [cs.CL] 12 Apr 2021 cessing (NLP) domain for many years, especially supervised and unsupervised methods. However, this is not the case with reinforcement learning (RL), which is somewhat surprising since in other domains, reinforcement learning methods have experienced an increased level of success with some impressive results, for instance in board games such as AlphaGo Zero [106].
    [Show full text]
  • Reinforcement Learning Data Science Africa 2018 Abuja, Nigeria (12 Nov - 16 Nov 2018)
    Reinforcement Learning Data Science Africa 2018 Abuja, Nigeria (12 Nov - 16 Nov 2018) Chika Yinka-Banjo, PhD Ayorkor Korsah, PhD University of Lagos Ashesi University Nigeria Ghana Outline • Introduction to Machine learning • Reinforcement learning definitions • Example reinforcement learning problems • The Markov decision process • The optimal policy • Value function & Q-value function • Bellman Equation • Q-learning • Building a simple Q-learning agent (coding) • Recap • Where to go from here? Introduction to Machine learning • Artificial Intelligence (AI) is the study and design of Intelligent agents. • An Intelligent agent can perceive its environment through sensors and it can act on its environment through actuators. • E.g. Agent: Humanoid robot • Environment: Earth? • Sensors: Camera, tactile sensor etc. • Actuators: Motors, grippers etc. • Machine learning is a subfield of Artificial Intelligence Branches of AI Introduction to Machine learning • Machine learning techniques learn from data without being explicitly programmed to do so. • Machine learning models enable the agent to learn from its own experience by extracting useful information from feedback from its environment. • Three types of learning feedback: • Supervised learning • Unsupervised learning • Reinforcement learning Branches of Machine learning Supervised learning • Supervised learning: the machine learning model is trained on many labelled examples of input-output pairs. • Such that when presented with a novel input, the model can estimate accurately what the correct output should be. • Data(x, y): x is input data, y is label Supervised learning task in the form of classification • Goal: learn a function to map x -> y • Examples include; Classification, regression object detection, image captioning etc. Unsupervised learning • Unsupervised learning: here the model extract useful information from unlabeled and unstructured data.
    [Show full text]
  • A Review of Unsupervised Artificial Neural Networks with Applications
    A REVIEW OF UNSUPERVISED ARTIFICIAL NEURAL NETWORKS WITH APPLICATIONS Samson Damilola Fabiyi Department of Electronic and Electrical Engineering, University of Strathclyde 204 George Street, G1 1XW, Glasgow, United Kingdom [email protected] ABSTRACT designer) who uses his or her knowledge of the environment to Artificial Neural Networks (ANNs) are models formulated to train the network with labelled data sets [7]. Hence, the mimic the learning capability of human brains. Learning in artificial neural networks learn by receiving input and target ANNs can be categorized into supervised, reinforcement and pairs of several observations from the labelled data sets, unsupervised learning. Application of supervised ANNs is processing the input, comparing the output with the target, limited to when the supervisor’s knowledge of the environment computing the error between the output and target, and using is sufficient to supply the networks with labelled datasets. the error signal and the concept of backward propagation to Application of unsupervised ANNs becomes imperative in adjust the weights interconnecting the network’s neurons with situations where it is very difficult to get labelled datasets. This the aim of minimising the error and optimising performance [6, paper presents the various methods, and applications of 7]. Fine-tuning of the network continues until the set of weights unsupervised ANNs. In order to achieve this, several secondary that minimise the discrepancy between the output and the sources of information, including academic journals and desired output is obtained. Figure 1 shows the block diagram conference proceedings, were selected. Autoencoders, self- which conceptualizes supervised learning in ANNs.
    [Show full text]
  • A Deep Reinforcement Learning Neural Network Folding Proteins
    DeepFoldit - A Deep Reinforcement Learning Neural Network Folding Proteins Dimitra Panou1, Martin Reczko2 1University of Athens, Department of Informatics and Telecommunications 2Biomedical Sciences Research Center “Alexander Fleming” ABSTRACT Despite considerable progress, ab initio protein structure prediction remains suboptimal. A crowdsourcing approach is the online puzzle video game Foldit [1], that provided several useful results that matched or even outperformed algorithmically computed solutions [2]. Using Foldit, the WeFold [3] crowd had several successful participations in the Critical Assessment of Techniques for Protein Structure Prediction. Based on the recent Foldit standalone version [4], we trained a deep reinforcement neural network called DeepFoldit to improve the score assigned to an unfolded protein, using the Q-learning method [5] with experience replay. This paper is focused on model improvement through hyperparameter tuning. We examined various implementations by examining different model architectures and changing hyperparameter values to improve the accuracy of the model. The new model’s hyper-parameters also improved its ability to generalize. Initial results, from the latest implementation, show that given a set of small unfolded training proteins, DeepFoldit learns action sequences that improve the score both on the training set and on novel test proteins. Our approach combines the intuitive user interface of Foldit with the efficiency of deep reinforcement learning. KEYWORDS: ab initio protein structure prediction, Reinforcement Learning, Deep Learning, Convolution Neural Networks, Q-learning 1. ALGORITHMIC BACKGROUND Machine learning (ML) is the study of algorithms and statistical models used by computer systems to accomplish a given task without using explicit guidelines, relying on inferences derived from patterns. ML is a field of artificial intelligence.
    [Show full text]
  • An Introduction to Deep Reinforcement Learning
    An Introduction to Deep Reinforcement Learning Ehsan Abbasnejad Remember: Supervised Learning We have a set of sample observations, with labels learn to predict the labels, given a new sample cat Learn the function that associates a picture of a dog/cat with the label dog Remember: supervised learning We need thousands of samples Samples have to be provided by experts There are applications where • We can’t provide expert samples • Expert examples are not what we mimic • There is an interaction with the world Deep Reinforcement Learning AlphaGo Scenario of Reinforcement Learning Observation Action State Change the environment Agent Don’t do that Reward Environment Agent learns to take actions maximizing expected Scenario of Reinforcement Learningreward. Observation Action State Change the environment Agent Thank you. Reward https://yoast.com/how-t Environment o-clean-site-structure/ Machine Learning Actor/Policy ≈ Looking for a Function Action = π( Observation ) Observation Action Function Function input output Used to pick the Reward best function Environment Reinforcement Learning in a nutshell RL is a general-purpose framework for decision-making • RL is for an agent with the capacity to act • Each action influences the agent’s future state • Success is measured by a scalar reward signal Goal: select actions to maximise future reward Deep Learning in a nutshell DL is a general-purpose framework for representation learning • Given an objective • Learning representation that is required to achieve objective • Directly from raw inputs
    [Show full text]
  • A Hybrid Model Consisting of Supervised and Unsupervised Learning for Landslide Susceptibility Mapping
    remote sensing Article A Hybrid Model Consisting of Supervised and Unsupervised Learning for Landslide Susceptibility Mapping Zhu Liang 1, Changming Wang 1,* , Zhijie Duan 2, Hailiang Liu 1, Xiaoyang Liu 1 and Kaleem Ullah Jan Khan 1 1 College of Construction Engineering, Jilin University, Changchun 130012, China; [email protected] (Z.L.); [email protected] (H.L.); [email protected] (X.L.); [email protected] (K.U.J.K.) 2 State Key Laboratory of Hydroscience and Engineering Tsinghua University, Beijing 100084, China; [email protected] * Correspondence: [email protected]; Tel.: +86-135-0441-8751 Abstract: Landslides cause huge damage to social economy and human beings every year. Landslide susceptibility mapping (LSM) occupies an important position in land use and risk management. This study is to investigate a hybrid model which makes full use of the advantage of supervised learning model (SLM) and unsupervised learning model (ULM). Firstly, ten continuous variables were used to develop a ULM which consisted of factor analysis (FA) and k-means cluster for a preliminary landslide susceptibility map. Secondly, 351 landslides with “1” label were collected and the same number of non-landslide samples with “0” label were selected from the very low susceptibility area in the preliminary map, constituting a new priori condition for a SLM, and thirteen factors were used for the modeling of gradient boosting decision tree (GBDT) which represented for SLM. Finally, the performance of different models was verified using related indexes. The results showed that the performance of the pretreated GBDT model was improved with sensitivity, specificity, accuracy Citation: Liang, Z.; Wang, C.; Duan, and the area under the curve (AUC) values of 88.60%, 92.59%, 90.60% and 0.976, respectively.
    [Show full text]
  • Modelling Working Memory Using Deep Recurrent Reinforcement Learning
    Modelling Working Memory using Deep Recurrent Reinforcement Learning Pravish Sainath1;2;3 Pierre Bellec1;3 Guillaume Lajoie 2;3 1Centre de Recherche, Institut Universitaire de Gériatrie de Montréal 2Mila - Quebec AI Institute 3Université de Montréal Abstract 1 In cognitive systems, the role of a working memory is crucial for visual reasoning 2 and decision making. Tremendous progress has been made in understanding the 3 mechanisms of the human/animal working memory, as well as in formulating 4 different frameworks of artificial neural networks. In the case of humans, the [1] 5 visual working memory (VWM) task is a standard one in which the subjects are 6 presented with a sequence of images, each of which needs to be identified as to 7 whether it was already seen or not. Our work is a study of multiple ways to learn a 8 working memory model using recurrent neural networks that learn to remember 9 input images across timesteps in supervised and reinforcement learning settings. 10 The reinforcement learning setting is inspired by the popular view in Neuroscience 11 that the working memory in the prefrontal cortex is modulated by a dopaminergic 12 mechanism. We consider the VWM task as an environment that rewards the 13 agent when it remembers past information and penalizes it for forgetting. We 14 quantitatively estimate the performance of these models on sequences of images [2] 15 from a standard image dataset (CIFAR-100 ) and their ability to remember 16 and recall. Based on our analysis, we establish that a gated recurrent neural 17 network model with long short-term memory units trained using reinforcement 18 learning is powerful and more efficient in temporally consolidating the input spatial 19 information.
    [Show full text]
  • Reinforcement Learning: a Survey
    Journal of Articial Intelligence Research Submitted published Reinforcement Learning A Survey Leslie Pack Kaelbling lpkcsbrownedu Michael L Littman mlittmancsbrownedu Computer Science Department Box Brown University Providence RI USA Andrew W Mo ore awmcscmuedu Smith Hal l Carnegie Mel lon University Forbes Avenue Pittsburgh PA USA Abstract This pap er surveys the eld of reinforcement learning from a computerscience p er sp ective It is written to b e accessible to researchers familiar with machine learning Both the historical basis of the eld and a broad selection of current work are summarized Reinforcement learning is the problem faced by an agent that learns b ehavior through trialanderror interactions with a dynamic environment The work describ ed here has a resemblance to work in psychology but diers considerably in the details and in the use of the word reinforcement The pap er discusses central issues of reinforcement learning including trading o exploration and exploitation establishing the foundations of the eld via Markov decision theory learning from delayed reinforcement constructing empirical mo dels to accelerate learning making use of generalization and hierarchy and coping with hidden state It concludes with a survey of some implemented systems and an assessment of the practical utility of current metho ds for reinforcement learning Intro duction Reinforcement learning dates back to the early days of cyb ernetics and work in statistics psychology neuroscience and computer science In the last ve to ten years
    [Show full text]
  • Learning from Noisy Labels with Deep Neural Networks: a Survey Hwanjun Song, Minseok Kim, Dongmin Park, Yooju Shin, Jae-Gil Lee
    UNDER REVIEW 1 Learning from Noisy Labels with Deep Neural Networks: A Survey Hwanjun Song, Minseok Kim, Dongmin Park, Yooju Shin, Jae-Gil Lee Abstract—Deep learning has achieved remarkable success in 100% 100% numerous domains with help from large amounts of big data. Noisy w/o. Reg. Noisy w. Reg. 75% However, the quality of data labels is a concern because of the 75% Clean w. Reg Gap lack of high-quality labels in many real-world scenarios. As noisy 50% 50% labels severely degrade the generalization performance of deep Noisy w/o. Reg. neural networks, learning from noisy labels (robust training) is 25% Accuracy Test 25% Training Accuracy Training Noisy w. Reg. becoming an important task in modern deep learning applica- Clean w. Reg tions. In this survey, we first describe the problem of learning with 0% 0% 1 30 60 90 120 1 30 60 90 120 label noise from a supervised learning perspective. Next, we pro- Epochs Epochs vide a comprehensive review of 57 state-of-the-art robust training Fig. 1. Convergence curves of training and test accuracy when training methods, all of which are categorized into five groups according WideResNet-16-8 using a standard training method on the CIFAR-100 dataset to their methodological difference, followed by a systematic com- with the symmetric noise of 40%: “Noisy w/o. Reg.” and “Noisy w. Reg.” are parison of six properties used to evaluate their superiority. Sub- the models trained on noisy data without and with regularization, respectively, sequently, we perform an in-depth analysis of noise rate estima- and “Clean w.
    [Show full text]