Machine Learning and Neural Networks - page 46

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CS480/680 Intro to Machine Learning - Spring 2019 - University of Waterloo


CS480/680 Lecture 1: Course Introduction

This lecture introduces the concept of machine learning, which is a new paradigm in computer science where computers can be taught to do complex tasks without having to write down instructions. This video provides a brief history of machine learning, and introduces the three key components of a machine learning algorithm - data, task, and performance.

  • 00:00:00 This lecture introduces the concept of machine learning, which is a new paradigm in computer science where computers can be taught to do complex tasks without having to write down instructions.

  • 00:05:00 This video provides a brief history of machine learning, and introduces the three key components of a machine learning algorithm - data, task, and performance.

  • 00:10:00 This lecture discusses the three main types of machine learning algorithms: supervised learning, unsupervised learning, and reinforcement learning. Supervised learning is when the computer is provided with a set of data that includes both the input and the output, while unsupervised learning is when the computer is provided with data but is not given any answers beforehand. Reinforcement learning is a middle ground, where the computer is provided with feedback indicating how
    well it is doing, but does not have a set answer for what the right answer is.

  • 00:15:00 The video discusses the problem of recognizing handwritten digits as part of a postal code, and presents a solution based on memorization. The approach suggested is to compare a query bitmap to those already in memory and find a match. This would be an instance of memorization, but would be susceptible to errors due to the number of possible bitmaps.

  • 00:20:00 Supervised learning is a technique used to find a function that approximates a known function. This is done by training a machine learning model on a set of examples and then trying to find a function that fits the data as closely as possible.

  • 00:25:00 This video discusses the different curves that can be used to represent data, and explains the "no free lunch theorem." It shows that there is no perfect curve that can be used to represent data, and that different curves can be justified based on a person's assumptions.

  • 00:30:00 Machine learning is difficult but powerful because it allows us to learn from data without needing to explicitly specify the rules governing that data. In supervised learning, we use data from a known set of examples to train a model which can then be used to make predictions for new data. In unsupervised learning, we use data without specifying a rule governing it. Generalization is a key criterion for judging the effectiveness of an algorithm, and is measured by how well it performs with respect to unseen examples.

  • 00:35:00 In this video, the author introduces the concept of machine learning, which is the process of training a computer to recognize patterns in data. Unsupervised learning is a more difficult form of machine learning, in which the computer is not provided with labels (the correct class for each image). Autoencoders are an example of a machine learning technique that can be used to compress data.

  • 00:40:00 This lecture introduces the concept of unsupervised machine learning, which refers to a type of machine learning where the training data is not labeled. It shows how a neural network can be designed to automatically detect features in images, and discusses how this can be used for face recognition and other tasks.

  • 00:45:00 This lecture covers the basics of machine learning, including a discussion of supervised and unsupervised learning, reinforcement learning, and the differences between these three forms of learning. It also covers the theory behind reinforcement learning, and how it can be implemented in computers.

  • 00:50:00 The video introduces the concept of reinforcement learning, which is a method of learning that relies on positive and negative feedback to modify behavior. DeepMind's AlphaGo program was able to defeat a top human player using this method, by learning to play at a level that humans could not.

  • 00:55:00 This lecture explains how reinforcement learning is used to achieve better results than a human could in some cases, such as in chess. AlphaGo achieved this through a combination of supervised and reinforcement learning. While the supervised learning part was necessary to provide a baseline, the reinforcement learning was necessary to find the best solution.

  • 01:00:00 This lecture provides a brief introduction to supervised and unsupervised machine learning, with a focus on the Alphago game. It explains that the move was seen as a good move by many at the time it was made, and points out that reinforcement learning could help us learn to make better decisions in the future.
 

CS480/680 Lecture 2: K-nearest neighbors


CS480/680 Lecture 2: K-nearest neighbours

This video covers the basics of supervised learning, including the differences between classification and regression. It also provides a brief introduction to machine learning and explains how the nearest neighbor algorithm works. Finally, it discusses how to evaluate an algorithm using cross-validation and how underfitting can affect machine learning. This lecture discusses how to use the k-nearest neighbors algorithm for regression and classification, as well as how to weight the neighbors based on their distance. Cross-validation is used to optimize the hyperparameter, and the entire data set is used to train the model.

  • 00:00:00 This lecture covers the basics of supervised learning, including induction and deduction, and the main difference between classification and regression.

  • 00:05:00 In this lecture, the author discusses the differences between classification and regression, and provides examples of both. He also provides a brief introduction to machine learning, highlighting the importance of the distinction between these two types of learning.

  • 00:10:00 The first two examples are classification problems and the next two are regression problems.

  • 00:15:00 The lecture discusses different types of speech recognition, and goes on to discuss digit recognition. It is noted that this is typically a classification problem, as there is no good way to order the discrete values that represent digital words.

  • 00:20:00 In this lecture, the four examples of problems that can be solved using K-nearest neighbors are discussed. The first example is a classification problem, where the input is a bitmap image and the output is a digit classification. The second example is a regression problem, where the input is a set of features related to a house and the output is a dollar value. The third example is a weather
    prediction problem, where the input is sensor data and satellite imagery and the output is a prediction of whether or not it will rain. The fourth example is a problem where the input is a question about a person's sleep habits, and the output is a prediction of whether or not the person will have a good sleep.

  • 00:25:00 In this lecture, the professor explains how machine learning works and how it differs from pure optimization. He goes on to discuss how machine learning can be used to solve problems such as classification and regression.

  • 00:30:00 This video discusses the goal of the lecture, which is to find a hypothesis that generalizes well. The example given is of trying to find a function that is not part of a space of polynomials of finite degrees.

  • 00:35:00 The speaker discusses the difficulties of trying to find a function that accurately predicts data when the data is noisy. This difficulty is compounded by the fact that most data is complex and expressionless. He suggests that, in practice, it is often necessary to compromise between the expressiveness and complexity of a hypothesis space.

  • 00:40:00 The nearest neighbor classifier divides a data space into regions according to a distance measure and returns the label of the closest point in each region. This allows us to understand what is happening with the nearest neighbor classifier more clearly. It is unstable, however, and can be fooled by noise in the data.

  • 00:45:00 In this lecture, the lecturer discusses the K nearest neighbor algorithm, which is a simple generalization of the nearest neighbor algorithm. He then shows how the algorithm partitions a data set into regions based on the most frequent class. Finally, he demonstrates how increasing the number of nearest neighbors affects the partitioning.

  • 00:50:00 This video discusses how to evaluate an algorithm in machine learning, using a standard procedure called "cross-validation." The procedure splits a data set into two parts, training and testing, and trains on the training set and tests on the test set. The accuracy of the algorithm is measured on the test set, and if the accuracy decreases as the number of neighbors increases, the algorithm is said to be "biased."

  • 00:55:00 This video discusses the phenomenon of underfitting and its effects on machine learning. It explains that underfitting occurs when an algorithm finds a hypothesis that is lower than the future accuracy of another hypothesis. This can be caused by the classifier not being expressive enough, which means that the hypothesis space is not expressive enough.

  • 01:00:00 In this video, the author explains how overfitting and underfitting can be determined mathematically. Overfitting occurs when an algorithm finds the highest power Eh values in the data, while underfitting occurs when the difference between the training accuracy and the future accuracy is smaller than the maximum possible value. Testing on the training set can be misleading, as it does not accurately reflect the amount of overfitting.

  • 01:05:00 In this lecture, the professor discusses how to choose a key for a machine learning algorithm, noting that it is important to obey the principle of least privilege. He also notes that it is possible to violate this principle by optimizing hyperparameters with respect to the test set, which can then no longer be trusted. To guard against this, he suggests splitting the data into three sets and training on each set in turn.

  • 01:10:00 In this lecture, the lecturer discusses the concept of "k-nearest neighbors" and how to select the best K for a given problem. He also discusses the use of cross-validation to ensure that the data used for training and validation is as representative as possible.

  • 01:15:00 In this video, the instructor demonstrates the use of fourfold cross-validation to validate and train a model.

  • 01:20:00 This lecture discusses the steps involved in optimizing a hyperparameter using K-nearest neighbor (KNN) with cross-validation. The hyperparameter is evaluated using a subset of the data, and a hypothesis is returned if the best KNN achieves the desired accuracy. Finally, the entire data set is used to train the hyperparameter.

  • 01:25:00 In this lecture, the instructor explains how to use K nearest neighbors for regression and classification. He also discusses how to weight nearest neighbors based on their distance.
 

CS480/680 Lecture 3: Linear Regression



CS480/680 Lecture 3: Linear Regression

The lecture on Linear Regression starts with an introduction to the problem of finding the best line that comes as close as possible to a given set of points. The lecturer explains that linear functions can be represented by a combination of weighted inputs. Linear regression can be solved via optimization, with the goal of minimizing the Euclidean loss by varying the weight vector, which can be done efficiently using convex optimization problems. The process of solving a linear regression equation involves finding the W variable, or weights, that will give the global minimum for the objective function, which can be done using techniques such as matrix inversion or iterative methods. The importance of regularization in preventing overfitting is also discussed, with a penalty term added to the objective function to constrain the magnitude of the weights and force them to be as small as possible. The lecture ends by discussing the importance of addressing the issue of overfitting in linear regression.

  • 00:00:00 In this section, the instructor introduces linear regression, which is a standard machine learning technique for regression, and explains the problem intuitively. The problem is to find the best line that comes as close as possible to a given set of points. The data consists of input features, X, and target output, T. The goal is to find a hypothesis H that maps X to T, assuming that H is linear. Linear functions can always be represented in the way of taking a weighted combination of the inputs where the weights are multiplied by the inputs and then added together.

  • 00:05:00 In this section, the speaker discusses the space of linear functions and the objective of finding the best linear functions to minimize a loss function. The Euclidean loss function is used, where the squared distance is taken by subtracting the prediction from the target. The speaker explains that Y is the output of the predictor, which is a linear function, and T1 is the price at which the house is sold, which is the ground truth. Multiple features, such as the number of bathrooms and bedrooms, are taken into account in the house valuation, resulting in a vector of size 25-30. The speaker also discusses the notation used in the slides and mentions that dividing by two is not necessarily needed in theory.

  • 00:10:00 In this section of the lecture, the professor discusses the notation he will be using throughout the course when referring to linear regression. He introduces the variables H for the hypothesis, X for data points, Y for the vector of outputs for all data points, and W for weight vector. He also mentions the use of X bar to represent a data point concatenated with a scalar one. The professor goes on to explain that linear regression can be solved via optimization, with the goal of minimizing the Euclidean loss by varying the W's. He notes that this optimization problem is easy because it is convex, which means there is one minimum and the global optimum can be found reliably.

  • 00:15:00 In this section of the lecture on linear regression, the speaker explains how convex optimization problems can be efficiently solved using gradient descent, which involves following the curvature of the function until arriving at the minimum. However, the speaker also notes that non-convex objectives can have multiple minima, making it difficult to reliably find the global optimum. The objective in linear regression is convex, and thus a more efficient solution is to compute the gradient, set it to zero, and solve for the single point that satisfies this equation, which is both necessary and sufficient for ensuring the minimum.

  • 00:20:00 In this section of the lecture, the professor explains the process of solving a linear regression equation to find the W variable, or weights, that will give the global minimum for the objective function. The system of linear equations can be rewritten into the form of W equals B by isolating W, and then the matrix A, which represents the input data, can be inverted to solve for W. However, there are other techniques such as Gaussian elimination, conjugate gradient, and iterative methods that can be faster and more efficient. The professor also draws a picture to demonstrate the concept of finding a line that will minimize the Euclidean distance with respect to the output, or Y-axis, by shrinking the vertical distances between the data points and the line.

  • 00:25:00 In this section, the lecturer explains the intuition behind minimizing the vertical distance in linear regression to obtain a single solution. The objective function is convex, and the ball-shaped function has a single minimum. However, the solution obtained by minimizing the least square objective is not stable, which can lead to overfitting. The lecturer illustrates this with two examples, one of which perturbs the input by epsilon. The lecture also discusses the important problem of not being able to invert the matrix A due to singularity or closeness to singularity.

  • 00:30:00 In this section of the lecture, the instructor gives two numerical examples of linear regression with the same matrix A, but different target values, B. The first example has a target value of exactly 1 for the first data point, while the second example has a target value of 1 plus epsilon for the same data point. The difference in the target values results in a significant change in the output, despite epsilon being a very small value. The instructor illustrates the problem with a graphical representation, highlighting the significance of changes in the input values and why it poses a challenge in linear regression.

  • 00:35:00 In this section, the lecturer explains linear regression with the help of two data points. X has two entries, but the second dimension is the one that varies, and the first entry is ignored. The lecturer draws two data points, one with X as 0 and the target as 1 + Epsilon, and the other with X as Epsilon and the target as 1. A line drawn through these points changes its slope from 0 to -1 when the target of the first data point is increased from 1 to 1 + Epsilon, showing overfitting due to insufficient data and noise. The solution is unstable, even if there is more data or higher dimensions.

  • 00:40:00 In this section, the concept of regularization in linear regression is introduced. Regularization adds a penalty term that constrains the magnitude of the weights, forcing them to be as small as possible. This penalty term is added to the original objective of minimizing the Euclidean distance between output and target. The use of regularization makes sense from both numerical and statistical perspectives, which will be explained in the following lecture. Depending on the problem, the hyper-parameter lambda, which determines the importance of the penalty term, will need to be tuned through cross-validation. Regularization in linear regression changes the system of linear equations to lambda I + A times W equals B. Through regularization, eigenvalues of the linear system are forced to be at least lambda, which bounds them away from 0, preventing numerical instability and errors.

  • 00:45:00 In this section, the lecturer discusses the application of regularization in linear regression to prevent overfitting. The regularization idea involves adding a penalty term to the objective function and introducing a parameter lambda to control the amount of weight assigned to the penalty term. The lecturer explains how this regularization technique works from the perspective of linear algebra. Additionally, an example is provided to illustrate how regularization can stabilize the solutions obtained in linear regression and prevent overfitting. The example shows that by minimizing the weights and adding a penalty term, solutions that are closer to each other can be obtained.

  • 00:50:00 In this section, the lecturer discusses the importance of regularization to mitigate the problem of overfitting in linear regression. Overfitting is a common issue in which a model performs well on the training data but poorly on the test data. Regularization is one way to address this problem, and the course will cover other approaches as well. In the next class, the topic will be approached from a statistical perspective.
 

CS480/680 Lecture 4: Statistical Learning



CS480/680 Lecture 4: Statistical Learning

In this lecture on statistical learning, the professor explains various concepts such as the marginalization rule, conditional probability, joint probability, Bayes Rule, and Bayesian learning. These concepts involve the use of probability distributions and updating them to reduce uncertainty when learning. The lecture emphasizes the importance of understanding these concepts for justifying and explaining various algorithms. The lecture also highlights the limitations of these concepts, particularly in dealing with large hypothesis spaces. Despite this limitation, Bayesian learning is considered optimal as long as the prior is correct, providing meaningful information to users.

In this lecture, the instructor explains the concept of approximate Bayesian learning as a solution for the tractability issue with Bayesian learning. Maximum likelihood and maximum a-posteriori are commonly used approximations in statistical learning, but they come with their own set of weaknesses, such as overfitting and less precise predictions than Bayesian learning. The lecture also covers the optimization problem arising from maximizing likelihood, the amount of data needed for different problems, and the importance of the next few slides for the course assignment. The instructor concludes by emphasizing that the algorithm will converge towards the best hypothesis within the given space, even if some ratios are not realizable.

  • 00:00:00 In this section of the lecture, the professor introduces the topic of statistical learning, which involves using statistics and probability theory to capture and reduce uncertainty when learning. The idea is to use probability distributions to quantify uncertainty and update them as learning progresses. The lecture also provides a review of probability distributions and the concept of joint probability distribution over multiple random variables. Ultimately, statistical learning helps explain and justify algorithms, including regularization, from a statistical perspective.

  • 00:05:00 In this section, the lecturer explains how to use the marginalization rule to extract a particular distribution from a joint distribution. He provides an example where a joint distribution over three variables of weather conditions, headache conditions, and a probability for each day is given. He demonstrates the computation of probabilities using marginal distributions, showing how it is possible to find a joint probability or the probabilities of specific weather or headache scenarios. By using this method, he arrives at the party of headache or sunny which comes to point twenty eight, thus showing how to extract a specific distribution from a joint distribution.

  • 00:10:00 In this section, the concept of conditional probability is discussed, which is denoted by the probability of one variable given another variable. The vertical bar represents the reference for the fraction and the numerator represents the worlds in which both variables are true. A graphical representation is used to explain this concept where the ratio of the number of people having both variables is taken into consideration. This concept is used to determine rare occurrences of events such as the probability of having a headache given the flu.

  • 00:15:00 In this section, the speaker explains how to compute conditional probabilities using counting and visualization methods. The general equation for conditional probability is a fraction of two areas representing the number of worlds with specific variables. The concept of joint probabilities and marginal probabilities is introduced, and the chain rule equation is explained, which allows us to factor a joint distribution into a conditional probability and a marginal probability. The speaker also warns about the common mistake of assuming that the probability of having the flu given a headache is the same as the probability of having a headache given the flu, and explains why this is incorrect.

  • 00:20:00 In this section, the speaker explores conditional probability in the context of diagnosing a disease based on symptoms. The order of the arguments in a conditional probability matters because the left-hand side is what is being estimated and the right-hand side is the context. The speaker illustrates this with the example of computing the probability of having the flu given a headache. The joint probability of having the flu and a headache is computed using the chain rule and then the conditional probability is obtained by dividing the joint probability by the marginal probability of having a headache. Another example is given with the three random variables of headache, sunny, and cold. The conditional probabilities of headache and cold given sunny are computed as well as the reverse conditional probability of sunny given headache and cold.

  • 00:25:00 In this section of the lecture, the instructor explains the calculation of joint probabilities for multiple events given a specific context and discusses why the probabilities may not add up to one in certain situations. The examples given involve the probability of having a headache and a cold given whether or not the day is sunny. The instructor then emphasizes the importance of considering all outcomes on the left-hand side of the vertical bar in order to determine if the probabilities should sum up to one, and cautions against the common mistake of assuming that changing the context of the events will result in probabilities that sum up to one.

  • 00:30:00 In this section, the instructor explains Bayes Rule, which is used for machine learning and inference. Bayes Rule allows for calculating the relationship between two conditional probabilities via interchanging arguments. It is used with a prior distribution that captures the initial uncertainty, followed by the evidence or data set that is used to revise the prior distribution to obtain the posterior distribution. This rule can also be used to measure the likelihood of obtaining certain data sets and can be an effective tool for learning by revising distributions that quantify uncertainty. The equation for Bayes Rule involves multiplying the prior by the likelihood and a constant instead of dividing it by the evidence.

  • 00:35:00 In this section of the lecture, the speaker explains that the property of evidence is a normalization constant from a learning perspective. It has the purpose of normalizing the numerator so that the resulting numbers are between 0 and 1. The process of Bayesian learning gives a posterior distribution, but in practice, what is desired is a hypothesis to use to make predictions. To do so, a weighted combination of hypotheses is used to make predictions by weighting them according to their corresponding posterior probability.

  • 00:40:00 In this section, the concept of using posterior distribution to define weights for different hypotheses for machine learning is discussed. An example of using Bayesian learning to estimate the ratio of flavors in a bag of candies is given, where the prior distribution is a guess made at the beginning, and the evidence corresponds to the data obtained by eating the candies. The posterior distribution is used to reduce uncertainty and learn about the ratio of flavors. The initial belief is subjective and can be based on an educated guess.

  • 00:45:00 In this section of the lecture, the speaker discusses Bayesian learning to estimate the ratio of flavors in a bag of candy. The likelihood distribution is calculated based on the assumption that candies are identically and independently distributed. Using Bayes' theorem and multiplying the prior with the likelihood, the posterior distribution is obtained, giving the posterior probabilities for each hypothesis. The speaker shows the posterior distributions graphically and explains how the probability of the hypothesis with everything lime dominates when all candies eaten so far are lime.

  • 00:50:00 In this section of the video on statistical learning, the presenter discusses the results of a candy bag experiment where candies are randomly drawn from a bag and their flavors noted. The hypothesis about the bag's flavor ratio is updated based on the observation and probability is calculated. It is observed that the probability of a hypothesis that the bag contains only cherries dips to zero when a lime is observed, while the probability of a hypothesis of 75% lime and 25% cherry increases with lime but dips back down after four candies. The presenter also explains that the initial probability chosen for each hypothesis represents the prior belief and selection is subjective depending on the expert's belief. Lastly, the presenter highlights the importance of making predictions using the posterior distribution in order to provide meaningful information to the users.

  • 00:55:00 In this section of the lecture, the speaker discusses Bayesian learning and its properties. Bayesian learning is considered optimal as long as the prior is correct and provides a principled way of making predictions. Additionally, it is generally immune to overfitting, which is an important problem in machine learning. However, the main drawback of Bayesian learning is that it is generally intractable, particularly when dealing with large hypothesis spaces. This makes computing the posterior distribution and prediction problematic.

  • 01:00:00 In this section, the concept of approximate Bayesian learning is introduced as a solution for the tractability issue with Bayesian learning. Maximum a-posteriori is one common approximation that involves selecting the hypothesis with the highest probability in the posterior and making predictions based on that. This approach can control but not eliminate overfitting and is less accurate than Bayesian prediction because it relies on a single hypothesis. Maximum likelihood is another approximation that involves selecting the hypothesis that fits the data best and does not use prior probabilities, making it simpler but less precise than Bayesian learning. Both approximations solve the intractability problem but replace it with optimization issues.

  • 01:05:00 In this section of the video, the instructor explains the concept of maximum likelihood, which is the hypothesis that fits the data best. However, this may include fitting everything, including the noise, which can lead to overfitting. While maximizing likelihood can simplify computations, it leads to less accurate predictions than Bayesian and MAP predictions. The optimization problem that arises from maximizing likelihood can still be intractable, but many algorithms in the course will be maximizing likelihood from a statistical perspective. Finally, the instructor discusses the question of how much data is needed for different problems, which belongs to the field of learning theory and is subjective to the size of the hypothesis space.

  • 01:10:00 In this section, the speaker concludes the lecture but mentions that he will cover a few more slides in the next lecture that will be important for the assignment. He also mentions that even if some of the ratios are not realizable, the algorithm will still converge towards the hypothesis that is best at making a prediction within the given space.
 

CS480/680 Lecture 5: Statistical Linear Regression



CS480/680 Lecture 5: Statistical Linear Regression

In this lecture on statistical linear regression, the professor covers numerous topics, starting with the concept of maximum likelihood and Gaussian likelihood distributions for noisy, corrupted data. They explain the use of maximum likelihood techniques in finding the weights that give the maximum probability for all the data points in the dataset. The lecture then delves into the idea of maximum a-posteriori (MAP), spherical Gaussian, and the covariance matrix. The speaker also discusses the use of a priori information and regularization. The expected error in linear regression is then broken down into two terms: one accounting for noise and another dependent on the weight vector, W, which can further be broken down into bias and variance. The lecture ends with a discussion on the use of Bayesian learning for computing the posterior distribution. Overall, the lecture covers a broad range of topics related to statistical linear regression and provides valuable insights into optimizing models to reduce prediction error.

The lecture focuses on Bayesian regression, which estimates a posterior distribution that converges towards the true set of weights as more data points are observed. The prior distribution is shown to be a distribution over pairs of W naught and W1 and is a distribution of lines. After observing a data point, the posterior distribution is calculated using prior and likelihood distributions, resulting in an updated belief over the line's position. To make predictions, a weighted combination of the hypotheses' predictions is taken based on the posterior distribution, leading to a Gaussian prediction with a mean and variance given by specific formulas. The trick to obtain an actual point prediction is to take the mean of the Gaussian prediction.

  • 00:00:00 In this section, the concept of maximum likelihood and maximum adversary envision learning in the context of linear regression is introduced. The data is assumed to come from measurements that are noisy and corrupted. The output observed is a corrupted version of the output of the underlying function with some noise added. Gaussian is assumed to denote the noise. A likelihood distribution is expressed to determine the likelihood of measuring a certain output for each input in the dataset. This understanding helps in making better choices for regularization.

  • 00:05:00 In this section of the lecture, the professor discusses the Gaussian distribution in the context of linear regression. They explain that when assuming that the underlying function is linear and deterministic, the resulting distribution is Gaussian with a mean equal to W transpose X and a variance equivalent to Sigma square. They then draw a graph of the Gaussian distribution to illustrate that the probability of measuring values around the mean is higher, with the width of the curve determined by Sigma square. The professor notes that this is the likelihood function, and we can use maximum likelihood techniques to find the W that gives the maximum probability for all the data points in our dataset.

  • 00:10:00 In this section, the lecturer explains how to select the best model for statistical linear regression, starting with optimizing the probability of observed Y's given specific input X's and a noise level with variance Sigma. The lecturer then shows a derivation of how to simplify and rescale this expression to a convex objective by taking the natural log and removing irrelevant factors. The result is the original least square problem, demonstrating the intuitive approach to minimize the distance between the points and the line in linear regression.

  • 00:15:00 In this section, the speaker discusses statistical perspective and how to find the W that would give the highest likelihood of observing the measurements by assuming a model with Gaussian noise. The optimization problem is equivalent mathematically, giving higher confidence in this approach. Removing Sigma from every term in the summation is mathematically equivalent to pulling it out of the summation, and it allows for the assumption that the same noise is present for every single measurement when W is selected. The speaker also mentions that it is important to have a model for the noise to find the best solution and to estimate Sigma based on repeated experiments to keep it fixed. The posterior distribution is computed by finding the W that has the highest probability in the posterior by calculating the posterior as the product of the prior by the likelihood and a normalization constant.

  • 00:20:00 In this section of the lecture, the instructor discusses the concept of maximum a-posteriori (MAP) and how it differs from maximum likelihood. MAP involves including the prior distribution in the calculation to refine the distribution of the hypothesis, which reduces uncertainty. The instructor explains how to define a Gaussian prior distribution for the vector of weights (W) and how to calculate the PDF of the multivariate Gaussian. The instructor also provides an example of drawing contour lines to illustrate the shape of the Gaussian distribution.

  • 00:25:00 In this section of the lecture, the instructor explains the concept of a spherical Gaussian and how it relates to the covariance matrix. The diagonal entries of the covariance matrix represent the variance of each weight, while the off-diagonal entries represent the covariance between the weights. The instructor then shows how to find the maximum of the posterior using a derivation, assuming that the inverse of the covariance matrix is equal to lambda times the identity matrix. In this way, the expression is equivalent to the regularized least square problem, with the penalty term being lambda times the squared norm of W. The regularization term can now be interpreted in a new way, making it clear that it comes from the prior distribution and that minimizing the norm of W is equivalent to making the weights closer to the mean of the distribution.

  • 00:30:00 In this section, the speaker discusses the use of a priori information to choose a covariance matrix in statistical linear regression. If there is information suggesting that solutions should be close to zero, then a prior of zero-mean is used with a covariance matrix defined by a bell-shaped distribution with a certain spread. Maximizing likelihood is equivalent to minimizing the regularized objective with the penalty term when using this prior. In situations where the Gaussian does not have a spherical shape, but a more general shape, the radius for each dimension is different, meaning that there are different values in the diagonal entries. It is reasonable to assume that a covariance matrix has a diagonal form, with the same width in every direction, which tends to work well in practice.

  • 00:35:00 In this section, the speaker discusses how the approaches of minimizing squared loss with an organizational term and maximizing the a posteriori hypothesis can lead to potentially different loss outcomes. The section analyzes the loss function and breaks down the expected loss into two different terms. The choice of lambda impacts the solution and thus the expected loss. The speaker then shows the mathematical derivation of how a given W can lead to an expected loss and how this loss can be decomposed into two different terms. The analysis is based on a sample dataset and the underlying distribution, and the results can be used to understand the expected loss of a given W and the impact of varying lambda.

  • 00:40:00 In this section of the lecture, the speaker explains the derivation of the expected error in a linear regression model. The expected error is broken down into two terms: one that accounts for the noise, and another that is dependent on the weight vector, W. This second term can be further expanded to show that it can be decomposed into the bias square and the variance. The bias measures the average difference between the output of the model and the true underlying function being approximated, while the variance measures the variability of the model's outputs around their mean. By understanding the contributions of bias and variance to the expected error, data scientists can better optimize their models to reduce prediction error.

  • 00:45:00 In this section of the lecture, the professor explains the decomposition of expected loss into three terms: noise, variance, and bias squared. This leads to a graph where the x-axis is lambda, the weight of the regularization term in the assignment. As lambda increases, the error decreases initially and then increases again. The expected loss is made up of the noise plus the variance plus the bias squared. The graph shows that the curve for variance plus bias squared is the sum of the individual curves for variance and bias squared. Cross-validation is used to find the best lambda value, which can control the error achieved, while the difference between expected loss and the actual loss is the noise that is present in all cases.

  • 00:50:00 In this section, the lecturer gives an example of nonlinear regression to illustrate how different curves obtained from applying maximum a-posteriori learning with different datasets relate to bias and variance. The lecturer explains that as lambda decreases, the bias decreases and the variance increases. The goal is to find a lambda that gives the best trade-off between bias and variance, as shown in the curve. The lecturer also mentions that the error is measured in terms of squared distance and that lambda is a parameter used in regularization.

  • 00:55:00 In this section, the lecturer discusses the idea of minimizing squared distances and adding a penalty term, where lambda is the weight for the penalty term. Varying lambda influences bias and variance, leading to different optimal W values, and the expected loss can be thought of as a function of lambda. Bayesian learning entails computing the posterior distribution by starting with a prior and reducing uncertainty through machine learning. The posterior distribution is computed by multiplying a Gaussian prior and a Gaussian likelihood, resulting in a Gaussian posterior.

  • 01:00:00 In this section, the concept of Bayesian regression is explained with the help of a Gaussian prior distribution in the space of w's, which can represent a line. The prior distribution is shown to be a distribution over pairs of w naught and w1 and is a distribution of lines. Then, after observing a single data point, a posterior distribution is calculated by multiplying prior and likelihood distributions. The resulting posterior distribution is elongated along the ridge and somewhat round, and thus, becomes the updated belief over the line's position.

  • 01:05:00 this section, the lecturer explains how Bayesian learning estimates a posterior distribution that converges towards the true set of weights as more data points are observed. The red lines represent samples from the corresponding posterior distribution, which is a distribution with respect to weights that define a corresponding line in the data space. However, there is still a question of how to make predictions based on the final posterior distribution.

  • 01:10:00 In this section, the speaker explains how to make predictions using Bayesian learning, which involves taking a weighted combination of the predictions made by each hypothesis. The prediction is made for a new input, and the weights are determined by the posterior distribution. The speaker uses a Gaussian posterior and likelihood to arrive at a Gaussian prediction, with a mean and variance given by specific formulas. Finally, a common trick to obtain an actual point prediction is to take the mean of the Gaussian prediction.
 

CS480/680 Lecture 6: Tools for surveys (Paulo Pacheco)



CS480/680 Lecture 6: Tools for surveys (Paulo Pacheco)

In this video, Paulo Pacheco introduces two academic tools for surveys: Google Scholar and RefWorks. He explains how to search for academic papers and sort them by citations using Google Scholar, and suggests filtering out older papers for more recent ones. Pacheco emphasizes the importance of exporting and managing citations, and introduces RefWorks as a tool for this task. He also provides tips for accessing academic publications, including using creative keyword searches and potentially requiring university network access or a VPN.

  • 00:00:00 In this section, Paulo Pacheco introduces two tools for conducting surveys: Google Scholar and the library's RefWorks. He explains how Google Scholar can be used to search for academic papers and order them approximately by citations. He also suggests how to filter out older papers and focus on more recent ones. Pacheco highlights the importance of exporting and managing citations for academic work, and mentions RefWorks as a tool that can assist in that process.

  • 00:05:00 In this section, the speaker discusses various tools and tips for accessing academic publications, specifically through Google Scholar and the University of Waterloo library. He explains how Google Scholar can be used to find relevant papers and sort them by year or number of citations, and also notes that accessing full texts may require university network access or the use of a VPN. Additionally, he suggests using a creative keyword search like "awesome datasets for NLP" or "awesome links for computer vision" to find inspiration and high-quality resources.
 

CS480/680 Lecture 6: Kaggle datasets and competitions



CS480/680 Lecture 6: Kaggle datasets and competitions

The lecture discusses Kaggle, a community for data science practitioners to compete in sponsored competitions using provided datasets for a cash prize, offering kernels for machine learning model training and data feature extraction, and a vast selection of almost 17,000 datasets for use in designing algorithms. The lecturer also notes that company GitHub repositories can provide valuable datasets, codes, and published papers for competitions.

  • 00:00:00 In this section, the lecturer talks about Kaggle, a data science community where data science practitioners can compete in sponsored competitions by private companies where they provide a dataset and a cash prize. Participants can download the data, train machine learning algorithms and submit predictions to the competition to win if their predictions are the best for the data set. Kaggle also provides kernels, snippets of code submitted by different users that are helpful for feature extraction or training a particular type of model on some data. In addition to competitions and kernels, Kaggle provides almost 17,000 datasets that cover any discipline that you can think of. Users can shop around a bit to find a dataset that may meet the assumptions they need for designing an algorithm.

  • 00:05:00 In this section, the speaker discusses some sources from where one can find datasets for various competitions. He mentions Kaggle as a great source of datasets. He also suggests looking into company GitHub repositories where paid codes and published papers are available along with data that can be used to run the code on. This can be a valuable resource for obtaining high-quality datasets.
 

CS480/680 Lecture 6: Normalizing flows (Priyank Jaini)



CS480/680 Lecture 6: Normalizing flows (Priyank Jaini)

The video provides an introduction to normalizing flows in deep generative models, a technique that learns a function to transform one distribution to another, with the goal of transforming a known distribution to an unknown distribution of interest. The video also discusses possible research projects related to normalizing flows, including conducting a survey of different papers and advancements related to normalizing flows and analyzing the transformation of a single Gaussian into a mixture of Gaussians. The lecturer encourages exploration of the many different applications of normalizing flows.

  • 00:00:00 In this section, the speaker provides an introduction to normalizing flows in deep generative models. Learning a distribution is a key aspect of machine learning, and the speaker explains that normalizing flows is a technique that learns a function to transform one distribution to another. The goal is to transform a known distribution, such as a Gaussian distribution, to an unknown distribution of interest. In practice, a neural network is used for this transformation and the research focus has been on designing neural networks to obtain the desired distribution.

  • 00:05:00 In this section, the lecturer discusses possible research projects related to normalizing flows, which is a hot topic in machine learning that has gained a lot of attention in recent years. One project idea is to conduct a survey on the different papers and advancements related to normalizing flows, which could potentially be publishable. Another idea is to analyze the transformation of a single Gaussian into a mixture of Gaussians using certain functions and how this can be extended to other distributions such as exponential and student T distributions. The lecturer also highlights theoretically open questions in capturing heavy-tailed behavior in financial capital markets. Overall, the lecturer encourages exploring the many different applications of normalizing flows and welcomes interested students to contact them for more knowledge on the t
 

CS480/680 Lecture 6: Unsupervised word translation (Kira Selby)



CS480/680 Lecture 6: Unsupervised word translation (Kira Selby)

The video discusses unsupervised word translation, which involves training a machine learning model to translate to and from a language without any cross-lingual information or dictionary matching. The Muse model is introduced as an approach that can achieve state-of-the-art accuracy on hundreds of languages without any cross-lingual information and comes close to supervised models in performance. The process of unsupervised word translation employs a matrix that translates the embedding spaces of different language words, using GAN or generative adversarial networks. By training these two models against each other, a way to map two distributions to one space is created, providing better translation results. The models can achieve 82.3% accuracy in word-to-word translations.

  • 00:00:00 In this section, the lecturer discusses the topic of unsupervised word translation, which involves training a machine learning model to translate to and from a language without any cross-lingual information or dictionary matching. The lecturer explains the concept of word embeddings, where words are turned into vectors that can become part of a model. The lecturer introduces the Muse model, which uses a simple hypothesis that a linear transformation can connect vector spaces of different languages. Muse can achieve state-of-the-art accuracy on hundreds of languages without any cross-lingual information and comes close to supervised models in performance.

  • 00:05:00 In this section, Kira Selby explains the process of unsupervised word translation using a matrix that translates the embedding spaces of different language words. The matrix can compare a whole bunch of vectors from one language space transformed into another language space. The goal is to achieve coincident language spaces to achieve translations. This process employs GAN or generative adversarial networks in which the generator is the matrix u that takes in a source space vector and provides a target space vector. Meanwhile, the discriminator learns to tell whether a set of vectors is from real French data or approximated French data generated by the model. By training these two models against each other, a way to map two distributions to one space is created, providing better translation results. The models can achieve 82.3% accuracy in word-to-word translations, although it is yet to converge on several languages such as English to Farsi, Hindi, Japanese, and Vietnamese.
 

CS480/680 Lecture 6: Fact checking and reinforcement learning (Vik Goel)



CS480/680 Lecture 6: Fact checking and reinforcement learning (Vik Goel)

Computer scientist Vik Goel discusses the application of reinforcement learning in fact-checking online news and proposes using a recommendation system to insert supporting evidence in real-time. He suggests using a large corpus of academic papers as a data source to train a classifier to predict where a citation is needed. Additionally, Goel explains how researchers have begun encoding human priors into reinforcement learning models to accelerate the process and recognize different objects in video games. This presents a promising research area where additional priors can improve the learning process.

  • 00:00:00 In this section of the lecture, Vik Goel discusses the idea of using reinforcement learning to fact check online news. He explains that Google has compiled a dataset of fact-checking websites that could be used to train classification models to determine the veracity of news articles. However, as most news articles lack in-text citations, Goel suggests developing a recommendation system to insert supporting evidence in real-time. He proposes using a large corpus of academic papers as a data source and training a classifier to predict where in each article a citation is needed. The application of a recommendation system can then suggest what sources should be cited, helping to prevent the spread of misinformation online.

  • 00:05:00 In this section, computer scientist Vik Goel explains the concept of reinforcement learning, where an agent attempts to achieve a goal by maximizing rewards in an environment. Current models take millions of interactions with the environment, making it challenging to learn to play video games. To accelerate the process, researchers have begun exploring encoding human priors into models, allowing agents to understand and recognize different objects in the game. This approach presents a wide-open research area where scientists can add more priors to improve the learning process dramatically.
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