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Caltech's Machine Learning Course - CS 156. Lecture 08 - Bias-Variance Tradeoff
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:16
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 08 - Bias-Variance Tradeoff
The professor discusses the bias-variance tradeoff in machine learning, explaining how the complexity of the hypothesis set affects the tradeoff between generalization and approximation. The lecturer introduces the concept of bias and variance, which measure the deviation between the average of hypotheses a machine learning algorithm produces and the actual target function and how much a given model's distribution of hypotheses varies based on different datasets, respectively. The tradeoff results in a larger hypothesis set having a smaller bias but a larger variance, while a smaller hypothesis set will have a larger bias but a smaller variance. The lecturer emphasizes the importance of having enough data resources to effectively navigate the hypothesis set and highlights the difference in scale between the bias-variance analysis and the VC analysis.
Also he discusses the tradeoff between simple and complex models in terms of their ability to approximate and generalize, with fewer examples requiring simple models and larger resources of examples requiring more complex models. The bias-variance analysis is specific to linear regression and assumes knowledge of the target function, with validation being the gold standard for choosing a model. Ensemble learning is discussed through Bagging, which uses bootstrapping to average multiple data sets, reducing variance. The balance between variance and covariance in ensemble learning is also explained, and linear regression is classified as a learning technique with fitting as the first part of learning, while the theory emphasizes good out-of-sample performance.
Caltech's Machine Learning Course - CS 156. Lecture 09 - The Linear Model II
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:18
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 09 - The Linear Model II
This lecture covers various aspects of the linear model, including the bias-variance decomposition, learning curves, and techniques for linear models such as perceptrons, linear regression, and logistic regression. The speaker emphasizes the tradeoff between complexity and generalization performance, cautioning against overfitting and emphasizing the importance of properly charging the VC dimension of the hypothesis space for valid warranties. The use of nonlinear transforms and their impact on generalization behavior is also discussed. The lecture further covers the logistic function and its applications in estimating probabilities, and introduces the concepts of likelihood and cross-entropy error measures in the context of logistic regression. Finally, iterative methods for optimizing the error function, such as gradient descent, are explained.
Also the lecture covers a range of topics related to linear models and optimization algorithms in machine learning. The professor explains the compromise between learning rate and speed in gradient descent optimization, introducing the logistic regression algorithm and discussing its error measures and learning algorithm. The challenges of termination in gradient descent and multi-class classification are also addressed. The role of derivation and selection of features in machine learning is emphasized and discussed as an art in application domains, charged in terms of VC dimension. Overall, this lecture provides a comprehensive overview of linear models and optimization algorithms for machine learning.
Caltech's Machine Learning Course - CS 156. Lecture 10 - Neural Networks
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:19
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 10 - Neural Networks
Yaser Abu-Mostafa, the professor at the California Institute of Technology, discusses logistic regression and neural networks in this lecture. Logistic regression is a linear model that calculates a probability interpretation of a bounded real-valued function. It is unable to optimize its error measure directly, so the method of gradient descent is introduced to minimize an arbitrary nonlinear function that is smooth enough and twice differentiable. Although there is no closed-form solution, the error measure is a convex function, making it relatively easy to optimize using gradient descent.
Stochastic gradient descent is an extension of gradient descent that is used in neural networks. Neural networks are a model that implements a hypothesis motivated by a biological viewpoint and related to perceptrons. The backpropagation algorithm is an efficient algorithm that goes with neural networks and makes the model particularly practical. The model has a biological link that got people excited and was easy to implement using the algorithm. Although it is not the model of choice nowadays, neural networks were successful in practical applications and are still used as a standard in many industries, such as banking and credit approval.
Brief summary:
Caltech's Machine Learning Course - CS 156. Lecture 11 - Overfitting
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:21
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 11 - Overfitting
This lecture introduces the concept and importance of overfitting in machine learning. Overfitting occurs when a model is trained on noise instead of the signal, resulting in poor out-of-sample fit. The lecture includes various experiments to illustrate the effects of different parameters, such as noise level and target complexity, on overfitting. The lecturer stresses the importance of detecting overfitting early on and the use of regularization and validation techniques to prevent it. The impact of deterministic and stochastic noise on overfitting is also discussed, and the lecture concludes by introducing the next two lectures on avoiding overfitting through regularization and validation.
The concept of overfitting is discussed, and the importance of regularization in preventing it is emphasized. The professor highlights the trade-off between overfitting and underfitting and explains the VC dimension's role in overfitting, where the discrepancy in VC dimension given the same number of examples results in discrepancies in out-of-sample and in-sample error. The practical issue of validating a model and how it can impact overfitting and model selection is also covered. Furthermore, the professor emphasizes the role of piecewise linear functions in preventing overfitting and highlights the importance of considering the number of degrees of freedom in the model and restricting it through regularization.
Forum on trading, automated trading systems and testing trading strategies
Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:24
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 12 - Regularization
This lecture on regularization begins with an explanation of overfitting and its negative impact on the generalization of machine learning models. Two approaches to regularization are discussed: mathematical and heuristic. The lecture then delves into the impact of regularization on bias and variance in linear models, using the example of Legendre polynomials as expanding components. The relationship between C and lambda in regularization is also covered, with an introduction to augmented error and its role in justifying regularization for generalization. Weight decay/growth techniques and the importance of choosing the right regularizer to avoid overfitting are also discussed. The lecture ends with a focus on choosing a good omega as a heuristic exercise and hopes that lambda will serve as a saving grace for regularization.
The second part discusses the weight decay as a way of balancing simplicity of the network with its functionality. The lecturer cautions against over-regularization and non-optimal performance, emphasizing the use of validation to determine optimal regularization parameters for different levels of noise. Regularization is discussed as experimental with a basis in theory and practice. Common types of regularization such as L1/L2, early stopping, and dropout are introduced, along with how to determine the appropriate regularization method for different problems. Common hyperparameters associated with implementing regularization are also discussed.
Caltech's Machine Learning Course - CS 156. Lecture 13 - Validation
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:26
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 13 - Validation
In lecture 13, the focus is on validation as an important technique in machine learning for model selection. The lecture goes into the specifics of validation, including why it's called validation and why it's important for model selection. Cross-validation is also discussed as a type of validation that allows for the use of all available examples for training and validation. The lecturer explains how to estimate the out-of-sample error using the random variable that takes an out-of-sample point and calculates the difference between the hypothesis and the target value. The lecture also discusses the bias introduced when using the estimate to choose a particular model, as it is no longer reliable since it was selected based on the validation set. The concept of cross-validation is introduced as a method for evaluating the out-of-sample error for different hypotheses.
Also he covers the use of cross-validation for model selection and validation to prevent overfitting, with a focus on "leave one out" and 10-fold cross-validation. The professor demonstrates the importance of accounting for out-of-sample discrepancy and data snooping, and suggests including randomizing methods to avoid sampling bias. He explains that although cross-validation can add complexity, combining it with regularization can select the best model, and because validation doesn't require assumptions, it's unique. The professor further explains how cross-validation can help make principled choices even when comparing across different scenarios and models, and how total validation points determine the error bar and bias.
Caltech's Machine Learning Course - CS 156. Lecture 14 - Support Vector Machines
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:27
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 14 - Support Vector Machines
The lecture covers the importance of validation and its use in machine learning, as well as the advantages of cross-validation over validation. The focus of the lecture is on support vector machines (SVMs) as the most effective learning model for classification, with a detailed outline of the section that involves maximization of the margin, formulation, and analytical solutions through constrained optimization presented. The lecture covers a range of technicalities, including how to calculate the distance between a point and a hyperplane in SVMs, how to solve the optimization problem for SVMs, and how to formulate the SVM optimization problem in its dual formulation. The lecturer also discusses the practical aspects of using quadratic programming to solve the optimization problem and the importance of identifying support vectors. The lecture concludes with a brief discussion of the use of nonlinear transformations in SVMs.
The second part of this lecture on support vector machines (SVM), the lecturer explains how the number of support vectors divided by the number of examples gives an upper bound on the probability of error in classifying an out-of-sample point, making the use of support vectors with nonlinear transformation feasible. The professor also discusses the normalization of w transposed x plus b to be 1 and its necessity for optimization, as well as the soft-margin version of SVM, which allows for errors and penalizes them. In addition, the relationship between the number of support vectors and the VC dimension is explained, and the method's resistance to noise is mentioned, with the soft version of the method used in cases of noisy data.
Caltech's Machine Learning Course - CS 156. Lecture 15 - Kernel Methods
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:29
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 15 - Kernel Methods
This lecture on kernel methods introduces support vector machines (SVMs) as a linear model that is more performance-driven than traditional linear regression models because of the concept of maximizing the margin. If the data is not linearly separable, nonlinear transforms can be used to create wiggly surfaces that still enable complex hypotheses without paying a high price in complexity. The video explains kernel methods that go to high-dimensional Z space, explaining how to compute the inner product without computing the individual vectors. The video also outlines the different approaches to obtaining a valid kernel for classification problems and explains how to apply SVM to non-separable data. Finally, the video explains the concept of slack and quantifying the margin violation in SVM, introducing a variable xi to penalize margin violation and reviewing the Lagrangian formulation to solve for alpha.
The second part covers practical aspects of using support vector machines (SVMs) and kernel methods. He explains the concept of soft margin support vector machines and how they allow for some misclassification while maintaining a wide margin. He talks about the importance of the parameter C, which determines how much violation can occur, and suggests using cross-validation to determine its value. He also addresses concerns about the constant coordinate in transformed data and assures users that it plays the same role as the bias term. Additionally, he discusses the possibility of combining kernels to produce new kernels and suggests heuristic methods that can be used when quadratic programming fails in solving SVMs with too many data points.
Caltech's Machine Learning Course - CS 156. Lecture 16 - Radial Basis Functions
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:31
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 16 - Radial Basis Functions
In this lecture on radial basis functions, the professor Yaser Abu-Mostafa covers a range of topics from SVMs to clustering, unsupervised learning, and function approximation using RBFs. The lecture discusses the parameter learning process for RBFs, the effect of gamma on the outcome of a Gaussian in RBF models, and using RBFs for classification. The concept of clustering is introduced for unsupervised learning, with Lloyd's algorithm and K-means clustering discussed in detail. He also describes a modification to RBFs where certain representative centers are chosen for the data to influence the neighborhood around them, and the K-means algorithm is used to select these centers. The importance of selecting an appropriate value for the gamma parameter when implementing RBFs for function approximation is also discussed, along with the use of multiple gammas for different data sets and the relation of RBFs to regularization.
In the second part Yaser Abu-Mostafa discusses radial basis functions (RBF) and how they can be derived based on regularization. The professor introduces a smoothness constraint approach using derivatives to achieve a smooth function and presents the challenges of choosing the number of clusters and gamma when dealing with high-dimensional spaces. Additionally, the professor explains that using RBF assumes the target function is smooth and takes into account input noise in the data set. The limitations of clustering are also discussed, but it can be useful to obtain representative points for supervised learning. Finally, the professor mentions that in certain cases, RBFs can outperform support vector machines (SVMs) if the data is clustered in a particular way and the clusters have a common value.
the solution is simply w equals the inverse of phi times y. By using the Gaussian kernel, the interpolation between points is exact, and the effect of fixing the parameter gamma is analyzed.
Caltech's Machine Learning Course - CS 156. Lecture 17 - Three Learning Principles
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Machine Learning and Neural Networks
MetaQuotes, 2023.04.07 12:34
Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa
Caltech's Machine Learning Course - CS 156. Lecture 17 - Three Learning Principles
This lecture on Three Learning Principles covers Occam's razor, sampling bias, and data snooping in machine learning. The principle of Occam's razor is discussed in detail, along with the complexity of an object and a set of objects, which can be measured in different ways. The lecture explains how simpler models are often better, as they reduce complexity and improve out-of-sample performance. The concepts of falsifiability and non-falsifiability are also introduced. Sampling bias is another key concept discussed, along with methods to deal with it, such as matching distributions of input and test data. Data snooping is also covered, with examples of how it can affect the validity of a model, including through normalization and reusing the same data set for multiple models.
The second part covers the topic of data snooping and its dangers in machine learning, specifically in financial applications where overfitting due to data snooping can be especially risky. The professor suggests two remedies for data snooping: avoiding it or accounting for it. The lecture also touches on the importance of scaling and normalization of input data, as well as the principle of Occam's razor in machine learning. Additionally, the video discusses how to properly correct sampling bias in computer vision applications and concludes with a summary of all the topics covered.