The document discusses experiments performed using the Weka machine learning tool to evaluate the performance of a multi-layer perceptron classifier on a soybean dataset. The experiments varied hyperparameters like the number of epochs, learning rate, and number of hidden layers. Increasing the epochs improved accuracy up to 100 epochs. Increasing the learning rate from 0.1 to 0.3 also improved accuracy, but higher rates did not. Increasing the hidden layers from 1 to 20 significantly improved accuracy, but more layers did not help as much. Using multiple hidden layers together worked best, achieving over 94% accuracy with 10 hidden layers.
The document discusses three exercises related to data mining and machine learning algorithms:
1. Drawing a decision tree corresponding to a logical formula in disjunctive normal form about loan eligibility.
2. Calculating the information gain of attributes to determine the best attribute to use for the first branch in a decision tree.
3. Providing an example of when a decision tree would overfit the training data by perfectly modeling unique observations but being unable to generalize to new data.
The document discusses various concepts in data mining and decision trees including:
1) Pruning trees to address overfitting and improve generalization,
2) Separating data into training, development and test sets to evaluate model performance,
3) Information gain favoring attributes with many values by having less entropy,
4) Strategies for dealing with missing attribute values such as predicting values or focusing on other attributes/classes,
5) Changing stopping conditions for regression trees to use standard deviation thresholds rather than discrete classes.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
Lazy learning differs from other machine learning approaches in that it stores all training data and uses it directly to make predictions on new data, rather than developing a predictive model or function from the training data. k-nearest neighbor classification can overfit if too small a value for k is used, but this can be addressed by increasing k to consider more neighboring points. Given sample data, instances 7 and 8 are classified as positive using k=1,3 and the prototype classifier, which determines class prototypes as the average values for each class.
This document provides examples and explanations for statistical concepts covered on a final exam, including the normal distribution, hypothesis testing, and probability distributions. It includes sample problems calculating probabilities and critical values for hypothesis tests on means and proportions. Excel templates are referenced for finding probabilities based on the standard normal and Poisson distributions. Step-by-step workings are shown for several problems to illustrate statistical calculations and interpretations.
Chapter 04 random variables and probabilityJuncar Tome
This chapter discusses discrete random variables and their probability distributions. It introduces the concept of a random variable and defines discrete and continuous random variables. It then covers the probability distributions for discrete random variables including the binomial, Poisson, and hypergeometric distributions. It defines key terms like expected value and variance and provides examples of calculating probabilities using these distributions.
The document summarizes key points from a lecture on combinations of events. It discusses intersections of events, unions of events, and examples involving quality checks of television sets and games of chance. Intersections refer to outcomes that are contained within both events A and B. Unions refer to outcomes contained within at least one of events A or B. Examples calculate probabilities of intersections and unions for events like appliances passing quality checks or dice rolls resulting in certain scores. The document also introduces combinations of three or more events using unions and partitions of a sample space.
The document discusses three exercises related to data mining and machine learning algorithms:
1. Drawing a decision tree corresponding to a logical formula in disjunctive normal form about loan eligibility.
2. Calculating the information gain of attributes to determine the best attribute to use for the first branch in a decision tree.
3. Providing an example of when a decision tree would overfit the training data by perfectly modeling unique observations but being unable to generalize to new data.
The document discusses various concepts in data mining and decision trees including:
1) Pruning trees to address overfitting and improve generalization,
2) Separating data into training, development and test sets to evaluate model performance,
3) Information gain favoring attributes with many values by having less entropy,
4) Strategies for dealing with missing attribute values such as predicting values or focusing on other attributes/classes,
5) Changing stopping conditions for regression trees to use standard deviation thresholds rather than discrete classes.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
Lazy learning differs from other machine learning approaches in that it stores all training data and uses it directly to make predictions on new data, rather than developing a predictive model or function from the training data. k-nearest neighbor classification can overfit if too small a value for k is used, but this can be addressed by increasing k to consider more neighboring points. Given sample data, instances 7 and 8 are classified as positive using k=1,3 and the prototype classifier, which determines class prototypes as the average values for each class.
This document provides examples and explanations for statistical concepts covered on a final exam, including the normal distribution, hypothesis testing, and probability distributions. It includes sample problems calculating probabilities and critical values for hypothesis tests on means and proportions. Excel templates are referenced for finding probabilities based on the standard normal and Poisson distributions. Step-by-step workings are shown for several problems to illustrate statistical calculations and interpretations.
Chapter 04 random variables and probabilityJuncar Tome
This chapter discusses discrete random variables and their probability distributions. It introduces the concept of a random variable and defines discrete and continuous random variables. It then covers the probability distributions for discrete random variables including the binomial, Poisson, and hypergeometric distributions. It defines key terms like expected value and variance and provides examples of calculating probabilities using these distributions.
The document summarizes key points from a lecture on combinations of events. It discusses intersections of events, unions of events, and examples involving quality checks of television sets and games of chance. Intersections refer to outcomes that are contained within both events A and B. Unions refer to outcomes contained within at least one of events A or B. Examples calculate probabilities of intersections and unions for events like appliances passing quality checks or dice rolls resulting in certain scores. The document also introduces combinations of three or more events using unions and partitions of a sample space.
No machine learning algorithm dominates in every domain, but random forests are usually tough to beat by much. And they have some advantages compared to other models. No much input preparation needed, implicit feature selection, fast to train, and ability to visualize the model. While it is easy to get started with random forests, a good understanding of the model is key to get the most of them.
This talk will cover decision trees from theory, to their implementation in scikit-learn. An overview of ensemble methods and bagging will follow, to end up explaining and implementing random forests and see how they compare to other state-of-the-art models.
The talk will have a very practical approach, using examples and real cases to illustrate how to use both decision trees and random forests.
We will see how the simplicity of decision trees, is a key advantage compared to other methods. Unlike black-box methods, or methods tough to represent in multivariate cases, decision trees can easily be visualized, analyzed, and debugged, until we see that our model is behaving as expected. This exercise can increase our understanding of the data and the problem, while making our model perform in the best possible way.
Random Forests can randomize and ensemble decision trees to increase its predictive power, while keeping most of their properties.
The main topics covered will include:
* What are decision trees?
* How decision trees are trained?
* Understanding and debugging decision trees
* Ensemble methods
* Bagging
* Random Forests
* When decision trees and random forests should be used?
* Python implementation with scikit-learn
* Analysis of performance
Decision tree, softmax regression and ensemble methods in machine learningAbhishek Vijayvargia
This document discusses decision trees, softmax regression, and ensemble methods in machine learning. It provides details on how decision trees use information gain to split nodes based on attributes. Softmax regression is described as a generalization of logistic regression for multi-class classification problems. Ensemble methods like bagging, random forests, and boosting are covered as techniques that improve performance by combining multiple models.
2013-1 Machine Learning Lecture 06 - Artur Ferreira - A Survey on Boosting…Dongseo University
This document summarizes a survey on boosting algorithms for supervised learning. It begins with an introduction to ensembles of classifiers and boosting, describing how boosting builds ensembles by combining simple classifiers with associated contributions. The AdaBoost algorithm and its variants are then explained in detail. Experimental results on synthetic and standard datasets are presented, comparing boosting with generative and RBF weak learners. The results show that boosting algorithms can achieve low error rates, with AdaBoost performing well when weak learners are only slightly better than random.
1. The document discusses categorical data analysis and goodness-of-fit tests. It introduces concepts such as univariate categorical data, expected counts, the chi-square test statistic, and assumptions of the chi-square test.
2. An example analyzes faculty status data from a university using a goodness-of-fit test to determine if the proportions are equal across categories. The test fails to reject the null hypothesis that the proportions are equal.
3. Tests for homogeneity and independence in two-way tables are described. Examples calculate expected counts and perform chi-square tests to compare populations' category proportions.
Here are the calculations for the summary statistics:
Mean = (100 + 95 + 120 + 190 + 200 + 200 + 280) / 7 = 169.3
Median = 190
Mode = 200 (occurs 3 times)
Variance = (100-169.3)^2 + (95-169.3)^2 + ... + (280-169.3)^2 / 7 = 4553.6
Range = 280 - 100 = 185
This sample is unlikely to have come from a normal population. The mean, median and mode are all different values, which would not occur in a normal distribution. The variance is also quite high relative to the mean. So in summary, the differences between the
The document contains data on lab report scores of 8 students and the number of hours they spent preparing. It shows the highest possible score was 40. It then provides the regression equation to predict scores based on hours and defines the correlation coefficient. It predicts a score of 28 for someone who spent 1 hour preparing. It also defines the correlation coefficient and what it indicates about the relationship between variables.
This document discusses sample size and power calculations for clinical studies. It provides formulas for calculating the required sample size to detect a desired effect size with a specified power and significance level. Formulas are presented for comparing means between two independent groups, comparing proportions between two independent groups, and comparing means within a paired or dependent groups design. Key factors that affect statistical power, and thus required sample size, are described as the size of the effect, standard deviation, sample size, and desired significance level. Examples are provided to demonstrate how to apply the formulas and calculate sample size for different study designs and scenarios.
Quantitative Methods for Lawyers - Class #22 - Regression Analysis - Part 1Daniel Katz
This document discusses regression analysis techniques for predicting lawyer hourly rates. It provides an example regression model that estimates rate based on city, firm size, years of experience, practice area, and other independent variables. Graphs and equations are shown to illustrate how regression can be used to model the relationship between a dependent variable (rate) and multiple independent predictors. The document also discusses key regression concepts like the regression coefficient, standard error, and interpreting statistical significance.
This document provides an overview of the Student's t-test, which is used to test the significance of differences between two means. It describes unpaired t-tests which compare two independent groups, and paired t-tests which compare two related groups or repeated measures on the same individuals. Two examples of each type of t-test are shown, with step-by-step calculations to test the null hypothesis that the means are not significantly different between groups. The examples conclude whether the differences are statistically significant or could have occurred by chance.
This document discusses various numerical methods for describing data, including measures of central tendency (mean, median), variability (range, variance, standard deviation), and graphical representations (boxplots). It provides examples and formulas for calculating the mean, median, quartiles, interquartile range, variance, standard deviation, and constructing boxplots. Outliers are defined as observations more than 1.5 times the interquartile range from the quartiles.
This document summarizes exponent properties for adding, subtracting, multiplying, and dividing terms with exponents. It provides examples for each property:
1) When adding or subtracting terms with the same base and exponent, only the coefficient changes.
2) When multiplying terms, you add the exponents and multiply the coefficients.
3) When dividing terms, you subtract the bottom exponent from the top and divide the coefficients.
4) When simplifying powers of powers, you distribute the exponent and multiply the exponents.
This document provides a summary of key concepts and examples for a statistics quiz on normal distributions, the central limit theorem, confidence intervals, and hypothesis testing. It reviews formulas and how to apply them to calculate probabilities, z-scores, confidence levels, sample sizes, and margins of error. Examples of problems cover finding areas under the normal curve, interpreting confidence intervals, and constructing confidence intervals for means, proportions, and more.
This document discusses algorithm-independent machine learning techniques. It introduces concepts like bias and variance, which can quantify how well a learning algorithm matches a problem without depending on a specific algorithm. Methods like cross-validation, bootstrapping, and resampling can be used with different algorithms. While no algorithm is inherently superior, such techniques provide guidance on algorithm use and help integrate multiple classifiers.
This document discusses systems of inequalities in two variables and linear programming. It begins with an overview of graphing inequalities and systems of inequalities. Examples are provided of graphing linear inequalities and solving systems of inequalities graphically. Linear programming is then introduced as a method for finding maximum and minimum values of an objective function subject to constraints. An example linear programming problem is worked through to find the maximum and minimum values.
This document provides an overview of functions and function notation that will be used in Calculus. It defines a function as an equation where each input yields a single output. Examples demonstrate determining if equations are functions and evaluating functions using function notation. The key concepts of domain and range of a function are explained. The document concludes by finding the domains of various functions involving fractions, radicals, and inequalities.
- A function is a rule that maps each input to a unique output. Not every rule defines a valid function.
- For a rule to be a valid function, it must map each input to only one output. The domain is the set of valid inputs, and the range is the set of corresponding outputs.
- Functions can be represented graphically by plotting the input-output pairs. The graph of a valid function should only intersect the vertical line above each input once.
Discrete Random Variable (Probability Distribution)LeslyAlingay
This presentation the statistics teachers to discuss discrete random variable since it includes examples and solutions.
Content:
-definition of random variable
-creating a frequency distribution table
- creating a histogram
-solving for the mean, variance and standard deviation.
References:
http://www.elcamino.edu/faculty/klaureano/documents/math%20150/chapternotes/chapter6.sullivan.pdf
https://www.mathsisfun.com/data/random-variables-mean-variance.html
https://www.youtube.com/watch?v=OvTEhNL96v0
https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch12/5214891-eng.htm
Quantitative Methods for Lawyers - Class #19 - Regression Analysis - Part 2Daniel Katz
This document summarizes key concepts from a lecture on regression analysis:
1) Regression analysis estimates the relationship between variables and the effect of changing one variable over another, assuming a linear relationship and additive effects.
2) Bivariate regression on SAT scores and education expenditures in U.S. states found a negative relationship, unlike initial assumptions.
3) Multivariate regression controls for multiple predictor variables simultaneously to better estimate relationships between variables like SAT scores and expenditures.
AdaBoost is an adaptive boosting algorithm that aggregates multiple weak learners, giving higher weight to misclassified examples. It reduces bias and models for low variance and high bias. The algorithm resamples the training data and runs multiple iterations, adjusting the weights each time to focus on problematic examples. As an example, it is used to classify 10 points into two classes by generating weak classifiers at each step that focus on the misclassified points from the previous step. AdaBoost achieves high precision but is sensitive to outliers.
This document discusses determining sample size for statistical analysis. It provides formulas for calculating the minimum sample size needed when estimating a population mean or proportion. For a population mean, the formula is: n = (za/2σ/E)2, where z is the confidence level, σ is the population standard deviation, and E is the desired level of accuracy or margin of error. For a population proportion, the formula is: n = pq(za/2/E)2, where p is the population proportion and q is 1-p. The document provides examples of using these formulas to determine the required sample size for different studies based on the confidence level, population characteristics, and margin of error. It also discusses rounding
The J48 decision tree classifier was used to classify instances in the zoo.test.arff dataset into animal types. It correctly classified 17 of 20 instances (85%). The decision tree examines attributes like feathers, milk, legs, fins to determine if an animal is a mammal, bird, reptile, fish, etc. New instances are classified by traversing the tree and seeing which leaf node they reach based on their attribute values.
The document discusses experimental data and uncertainty. It explains that all data has some uncertainty due to limitations of instruments and humans. It also discusses accuracy, precision, and significant figures when reporting results. The mean, uncertainty in the mean, and fractional and percentage uncertainties are also covered.
No machine learning algorithm dominates in every domain, but random forests are usually tough to beat by much. And they have some advantages compared to other models. No much input preparation needed, implicit feature selection, fast to train, and ability to visualize the model. While it is easy to get started with random forests, a good understanding of the model is key to get the most of them.
This talk will cover decision trees from theory, to their implementation in scikit-learn. An overview of ensemble methods and bagging will follow, to end up explaining and implementing random forests and see how they compare to other state-of-the-art models.
The talk will have a very practical approach, using examples and real cases to illustrate how to use both decision trees and random forests.
We will see how the simplicity of decision trees, is a key advantage compared to other methods. Unlike black-box methods, or methods tough to represent in multivariate cases, decision trees can easily be visualized, analyzed, and debugged, until we see that our model is behaving as expected. This exercise can increase our understanding of the data and the problem, while making our model perform in the best possible way.
Random Forests can randomize and ensemble decision trees to increase its predictive power, while keeping most of their properties.
The main topics covered will include:
* What are decision trees?
* How decision trees are trained?
* Understanding and debugging decision trees
* Ensemble methods
* Bagging
* Random Forests
* When decision trees and random forests should be used?
* Python implementation with scikit-learn
* Analysis of performance
Decision tree, softmax regression and ensemble methods in machine learningAbhishek Vijayvargia
This document discusses decision trees, softmax regression, and ensemble methods in machine learning. It provides details on how decision trees use information gain to split nodes based on attributes. Softmax regression is described as a generalization of logistic regression for multi-class classification problems. Ensemble methods like bagging, random forests, and boosting are covered as techniques that improve performance by combining multiple models.
2013-1 Machine Learning Lecture 06 - Artur Ferreira - A Survey on Boosting…Dongseo University
This document summarizes a survey on boosting algorithms for supervised learning. It begins with an introduction to ensembles of classifiers and boosting, describing how boosting builds ensembles by combining simple classifiers with associated contributions. The AdaBoost algorithm and its variants are then explained in detail. Experimental results on synthetic and standard datasets are presented, comparing boosting with generative and RBF weak learners. The results show that boosting algorithms can achieve low error rates, with AdaBoost performing well when weak learners are only slightly better than random.
1. The document discusses categorical data analysis and goodness-of-fit tests. It introduces concepts such as univariate categorical data, expected counts, the chi-square test statistic, and assumptions of the chi-square test.
2. An example analyzes faculty status data from a university using a goodness-of-fit test to determine if the proportions are equal across categories. The test fails to reject the null hypothesis that the proportions are equal.
3. Tests for homogeneity and independence in two-way tables are described. Examples calculate expected counts and perform chi-square tests to compare populations' category proportions.
Here are the calculations for the summary statistics:
Mean = (100 + 95 + 120 + 190 + 200 + 200 + 280) / 7 = 169.3
Median = 190
Mode = 200 (occurs 3 times)
Variance = (100-169.3)^2 + (95-169.3)^2 + ... + (280-169.3)^2 / 7 = 4553.6
Range = 280 - 100 = 185
This sample is unlikely to have come from a normal population. The mean, median and mode are all different values, which would not occur in a normal distribution. The variance is also quite high relative to the mean. So in summary, the differences between the
The document contains data on lab report scores of 8 students and the number of hours they spent preparing. It shows the highest possible score was 40. It then provides the regression equation to predict scores based on hours and defines the correlation coefficient. It predicts a score of 28 for someone who spent 1 hour preparing. It also defines the correlation coefficient and what it indicates about the relationship between variables.
This document discusses sample size and power calculations for clinical studies. It provides formulas for calculating the required sample size to detect a desired effect size with a specified power and significance level. Formulas are presented for comparing means between two independent groups, comparing proportions between two independent groups, and comparing means within a paired or dependent groups design. Key factors that affect statistical power, and thus required sample size, are described as the size of the effect, standard deviation, sample size, and desired significance level. Examples are provided to demonstrate how to apply the formulas and calculate sample size for different study designs and scenarios.
Quantitative Methods for Lawyers - Class #22 - Regression Analysis - Part 1Daniel Katz
This document discusses regression analysis techniques for predicting lawyer hourly rates. It provides an example regression model that estimates rate based on city, firm size, years of experience, practice area, and other independent variables. Graphs and equations are shown to illustrate how regression can be used to model the relationship between a dependent variable (rate) and multiple independent predictors. The document also discusses key regression concepts like the regression coefficient, standard error, and interpreting statistical significance.
This document provides an overview of the Student's t-test, which is used to test the significance of differences between two means. It describes unpaired t-tests which compare two independent groups, and paired t-tests which compare two related groups or repeated measures on the same individuals. Two examples of each type of t-test are shown, with step-by-step calculations to test the null hypothesis that the means are not significantly different between groups. The examples conclude whether the differences are statistically significant or could have occurred by chance.
This document discusses various numerical methods for describing data, including measures of central tendency (mean, median), variability (range, variance, standard deviation), and graphical representations (boxplots). It provides examples and formulas for calculating the mean, median, quartiles, interquartile range, variance, standard deviation, and constructing boxplots. Outliers are defined as observations more than 1.5 times the interquartile range from the quartiles.
This document summarizes exponent properties for adding, subtracting, multiplying, and dividing terms with exponents. It provides examples for each property:
1) When adding or subtracting terms with the same base and exponent, only the coefficient changes.
2) When multiplying terms, you add the exponents and multiply the coefficients.
3) When dividing terms, you subtract the bottom exponent from the top and divide the coefficients.
4) When simplifying powers of powers, you distribute the exponent and multiply the exponents.
This document provides a summary of key concepts and examples for a statistics quiz on normal distributions, the central limit theorem, confidence intervals, and hypothesis testing. It reviews formulas and how to apply them to calculate probabilities, z-scores, confidence levels, sample sizes, and margins of error. Examples of problems cover finding areas under the normal curve, interpreting confidence intervals, and constructing confidence intervals for means, proportions, and more.
This document discusses algorithm-independent machine learning techniques. It introduces concepts like bias and variance, which can quantify how well a learning algorithm matches a problem without depending on a specific algorithm. Methods like cross-validation, bootstrapping, and resampling can be used with different algorithms. While no algorithm is inherently superior, such techniques provide guidance on algorithm use and help integrate multiple classifiers.
This document discusses systems of inequalities in two variables and linear programming. It begins with an overview of graphing inequalities and systems of inequalities. Examples are provided of graphing linear inequalities and solving systems of inequalities graphically. Linear programming is then introduced as a method for finding maximum and minimum values of an objective function subject to constraints. An example linear programming problem is worked through to find the maximum and minimum values.
This document provides an overview of functions and function notation that will be used in Calculus. It defines a function as an equation where each input yields a single output. Examples demonstrate determining if equations are functions and evaluating functions using function notation. The key concepts of domain and range of a function are explained. The document concludes by finding the domains of various functions involving fractions, radicals, and inequalities.
- A function is a rule that maps each input to a unique output. Not every rule defines a valid function.
- For a rule to be a valid function, it must map each input to only one output. The domain is the set of valid inputs, and the range is the set of corresponding outputs.
- Functions can be represented graphically by plotting the input-output pairs. The graph of a valid function should only intersect the vertical line above each input once.
Discrete Random Variable (Probability Distribution)LeslyAlingay
This presentation the statistics teachers to discuss discrete random variable since it includes examples and solutions.
Content:
-definition of random variable
-creating a frequency distribution table
- creating a histogram
-solving for the mean, variance and standard deviation.
References:
http://www.elcamino.edu/faculty/klaureano/documents/math%20150/chapternotes/chapter6.sullivan.pdf
https://www.mathsisfun.com/data/random-variables-mean-variance.html
https://www.youtube.com/watch?v=OvTEhNL96v0
https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch12/5214891-eng.htm
Quantitative Methods for Lawyers - Class #19 - Regression Analysis - Part 2Daniel Katz
This document summarizes key concepts from a lecture on regression analysis:
1) Regression analysis estimates the relationship between variables and the effect of changing one variable over another, assuming a linear relationship and additive effects.
2) Bivariate regression on SAT scores and education expenditures in U.S. states found a negative relationship, unlike initial assumptions.
3) Multivariate regression controls for multiple predictor variables simultaneously to better estimate relationships between variables like SAT scores and expenditures.
AdaBoost is an adaptive boosting algorithm that aggregates multiple weak learners, giving higher weight to misclassified examples. It reduces bias and models for low variance and high bias. The algorithm resamples the training data and runs multiple iterations, adjusting the weights each time to focus on problematic examples. As an example, it is used to classify 10 points into two classes by generating weak classifiers at each step that focus on the misclassified points from the previous step. AdaBoost achieves high precision but is sensitive to outliers.
This document discusses determining sample size for statistical analysis. It provides formulas for calculating the minimum sample size needed when estimating a population mean or proportion. For a population mean, the formula is: n = (za/2σ/E)2, where z is the confidence level, σ is the population standard deviation, and E is the desired level of accuracy or margin of error. For a population proportion, the formula is: n = pq(za/2/E)2, where p is the population proportion and q is 1-p. The document provides examples of using these formulas to determine the required sample size for different studies based on the confidence level, population characteristics, and margin of error. It also discusses rounding
The J48 decision tree classifier was used to classify instances in the zoo.test.arff dataset into animal types. It correctly classified 17 of 20 instances (85%). The decision tree examines attributes like feathers, milk, legs, fins to determine if an animal is a mammal, bird, reptile, fish, etc. New instances are classified by traversing the tree and seeing which leaf node they reach based on their attribute values.
The document discusses experimental data and uncertainty. It explains that all data has some uncertainty due to limitations of instruments and humans. It also discusses accuracy, precision, and significant figures when reporting results. The mean, uncertainty in the mean, and fractional and percentage uncertainties are also covered.
This document outlines the key topics in Analytical Chemistry I including significant figures, types of errors, propagation of uncertainty, and systematic vs random errors. It discusses how measurements have uncertainty and errors. There are two main types of errors - systematic errors which affect accuracy and can be discovered and corrected, and random errors which cannot be eliminated and have equal chances of being positive or negative. The document also describes how to calculate the propagation of uncertainty through calculations using addition, subtraction, multiplication, division and other operations. It emphasizes keeping extra digits in calculations to properly account for uncertainty.
Solution manual for design and analysis of experiments 9th edition douglas ...Salehkhanovic
Solution Manual for Design and Analysis of Experiments - 9th Edition
Author(s): Douglas C Montgomery
Solution manual for 9th edition include chapters 1 to 15. There is one PDF file for each of chapters.
DATA MINING - EVALUATING CLUSTERING ALGORITHMTochukwu Udeh
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). It is a main task of exploratory data mining, and a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics.
According to Vladimir Estivill-Castro, the notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms.[4] There is a common denominator: a group of data objects. However, different researchers employ different cluster models, and for each of these cluster models again different algorithms can be given. The notion of a cluster, as found by different algorithms, varies significantly in its properties. Understanding these "cluster models" is key to understanding the differences between the various algorithms. Typical cluster models include:
Connectivity models: for example hierarchical clustering builds models based on distance connectivity.
Centroid models: for example the k-means algorithm represents each cluster by a single mean vector.
Distribution models: clusters are modeled using statistical distributions, such as multivariate normal distributions used by the Expectation-maximization algorithm.
Density models: for example DBSCAN and OPTICS defines clusters as connected dense regions in the data space.
Subspace models: in Biclustering (also known as Co-clustering or two-mode-clustering), clusters are modeled with both cluster members and relevant attributes.
Group models: some algorithms do not provide a refined model for their results and just provide the grouping information.
Graph-based models: a clique, i.e., a subset of nodes in a graph such that every two nodes in the subset are connected by an edge can be considered as a prototypical form of cluster. Relaxations of the complete connectivity requirement (a fraction of the edges can be missing) are known as quasi-cliques.
A "clustering" is essentially a set of such clusters, usually containing all objects in the data set. Additionally, it may specify the relationship of the clusters to each other, for example a hierarchy of clusters embedded in each other. Clusterings can be roughly distinguished as:
hard clustering: each object belongs to a cluster or not
soft clustering (also: fuzzy clustering): each object belongs to each cluster to a certain degree (e.g. a likelihood of belonging to the cluster)
There are also finer distinctions possible, for example:
strict partitioning clustering: here each object belongs to exactly one cluster
strict partitioning clustering with outliers: objects can also belong to no cluster, and are considered outliers.
overlapping clustering (also: alternative clustering, multi-view clustering): while usually a hard cluste
This document discusses estimating uncertainties in experimental measurements. It explains that all measured values must include an estimated error or uncertainty. For a tennis ball measured to have a diameter of 6.4 cm, the estimated error is ±0.1 cm, meaning the actual diameter lies between 6.3-6.5 cm. There are two main types of errors: systematic errors associated with measurement devices or procedures, and random errors from fluctuating conditions. When adding or subtracting measured values, the numerical uncertainties are added. When multiplying or dividing, the percentage errors are added. Formulas are provided for calculating percentage error from numerical error. Examples demonstrate applying these rules to operations with measured values.
1. Cross-validation is commonly used to evaluate machine learning algorithms and estimate their performance on new data. It involves partitioning the dataset into training and test sets and measuring the accuracy on the held-out test sets.
2. Tuning sets are often used to select hyperparameters like the number of hidden units. Performance on the tuning set is used to estimate future performance on new examples.
3. Statistical tests like paired t-tests are used to determine if differences in performance between algorithms on test sets are statistically significant.
1. Cross-validation is commonly used to evaluate machine learning algorithms and estimate their performance on new data. It involves partitioning the dataset into training and test sets and measuring the accuracy on the held-out test sets.
2. Tuning sets are often used to select hyperparameters like the number of hidden units. Performance on the tuning set is used to estimate future performance on new examples.
3. Statistical tests like paired t-tests are used to determine if differences in performance between algorithms on test sets are statistically significant.
The document discusses how to build an effective incident detection system using statistics. It explains that a baseline is needed to determine what normal behavior looks like and how to define abnormal behavior that requires an alert. Key metrics like errors, response times, and percentiles are identified. The document provides examples of how to use statistical distributions like the binomial distribution to calculate the likelihood of an observed value and determine if it warrants an alert or is still within the expected range of normal behavior.
I split the presentation for the unit into two, as I added so many slides to help with student questions and misconceptions. This one focuses on mathematical aspects of the unit.
This document discusses evaluating machine learning model performance. It covers classification evaluation metrics like accuracy, precision, recall, F1 score, and confusion matrices. It also discusses regression metrics like MAE, MSE, and RMSE. The document discusses techniques for dealing with class imbalance like oversampling and undersampling. It provides examples of evaluating models and interpreting results based on these various performance metrics.
Reinforcement learning Research experiments OpenAIRaouf KESKES
The document summarizes the results of several reinforcement learning experiments. It discusses using UCB-V, Linear UCB, Q-learning, Sarsa, and Dyna-Q on multi-armed bandit and gridworld problems. It also covers implementing Deep Q-Network on CartPole and LunarLander tasks. Finally, it explains Actor-Critic methods and shows results applying A2C to CartPole, achieving the maximum reward of 500 actions after several episodes of training.
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1. Data mining
‘Epochs & Accuracy’
~ Using the MultiLayerPerceptron function on a deliverd database ~
COMPUTER ASSIGNMENT 3
BARRY KOLLEE
10349863
2. Computerassignment 3
Exercise 1a): In the GUI screen you need to adjust the epochs (500 is too much). Start by
choosing 5. Select Start. Select Accept. The output screen gives you the accuracy of the
learned model.
I’ve loaded up the soybean.arff file into weka and did the following:
• Used the MultiLayerPerceptron classifier
• Set training set under test options
Set GUI on true
I performed the MultiLayerPerceptron with an Epoch of 5. The accuracy of an epoch of 5 (5 iterations) is
given in red.
Epoch of 5
Correctly Classified Instances 534 78.1845 %
Incorrectly Classified Instances 149 21.8155 %
Info about this evaluation
Epoch = 5
Error per Epoch = 0.0164204
Learning Rate = 0.3
Momentum = 0.2
Exercise 1b): Repeat the training with different settings (epochs 5, 10, 50 and 100) and see
what happens to the performance.
Epoch set to 10
Correctly Classified Instances 638 93.4114 %
Incorrectly Classified Instances 45 6.5886 %
Info about this evaluation
Epoch = 10
Error per Epoch = 0.0068437
Learning Rate = 0.3
Momentum = 0.2
Epoch set to 50
Correctly Classified Instances 674 98.6823 %
Incorrectly Classified Instances 9 1.3177 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.0004657
Learning Rate = 0.3
Momentum = 0.2
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3. Computerassignment 3
Epoch set to 100
Correctly Classified Instances 679 99.4143 %
Incorrectly Classified Instances 4 0.5857 %
Info about this evaluation
Epoch = 100
Error per Epoch = 0.0002785
Learning Rate = 0.3
Momentum = 0.2
Now we place all our findings of the different epochs into one table. Then it becomes clear which epoch
gives us the highest accuracy. The learning rate within the underneath table has been set to 0.3.
Number of Epochs/iterations Accuracy (number of correct classified instances)
5 78.1845 %
10 93.4114 %
50 98.6823 %
100 99.4143 %
It becomes clear that, when we increase the number of epochs (iterations), the accuracy climbs up also.
The increasing of the accuracy is mostly occurring when the epoch (number of iterations) is between 1
and 10. When we increase the number epochs to a value which is higher then 10, then there’s a
significant lower increase of the accuracy. The percentage of incorrect classified instances, when using
100 as the input value of Epoch, has been decreased to 0.5657 %. So that might be ‘negligbible’. In
conclusion we can state that using higher values for epoch wouldn’t be necessary with this learning rate.
If we also check the tables with ‘info about this evaluation’ we can also see that the error per epoch has
been decreased significantly when we increased the number of epoch(s).
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4. Computerassignment 3
Exercise 2: Pick one epoch value, and start playing with the "learning rate" parameter, e.g. try
0.1, 0.3, and 0.6. Again, look for each value what happens to the accuracy.
I’ve chosen for using an epoch value of 10 within the three outputs listed below. The accuracy (number
of correct and incorrect instances) is given in red.
Learning rate set to 0.1
Correctly Classified Instances 494 72.328 %
Incorrectly Classified Instances 189 27.672 %
Info about this evaluation
Epoch = 10
Error per Epoch = 0.0196909
Learning Rate = 0.1
Momentum = 0.2
Learning rate set to 0.3
Epoch set to 10
Correctly Classified Instances 638 93.4114 %
Incorrectly Classified Instances 45 6.5886 %
Info about this evaluation
Epoch = 10
Error per Epoch = 0.0068437
Learning Rate = 0.3
Momentum = 0.2
Learning rate set to 0.6
Correctly Classified Instances 638 93.4114 %
Incorrectly Classified Instances 45 6.5886 %
Info about this evaluation
Epoch = 10
Error per Epoch = 0.0050657
Learning Rate = 0.6
Momentum = 0.2
Now we place our findings in a table where we put the learning rate
Learning rate Accuracy (number of correct classified instances)
0.1 72.328 %
0.3 93.4114 %
0.6 93.4114 %
We see that increasing the learning rate from 0.1 to 0.3 has affected the accuracy in a good way.
However we see that if we would increase the learning rate it’s value even more that we won’t have a
higher accuracy. It might be interesting to take a look at a learning rate of 0.2 and check if the accuracy,
when using a learning rate of 0.2, has been affected if we compare it to a learning rate of 0.1.
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5. Computerassignment 3
The result of a learning set which has been set to 0.2 is listed below. The accuracy is given in red.
Correctly Classified Instances 612 89.6047 %
Incorrectly Classified Instances 71 10.3953 %
Info about this evaluation
Epoch = 10
Error per Epoch = 0.0112326
Learning Rate = 0.2
Momentum = 0.2
We see that the accuracy has climbed up significantly if we compare the learning rates of 0.1, 0.2 and
0.3.
learning rate 0.1 = 72.328 %
learning rate 0.2 = 89.6047 %
89.6047 / 72.3280 ≈ 1.24 increase factor
learning rate 0.2 = 89.6047 %
learning rate 0.3 = 93.4114 %
93.4114 / 89.6047 ≈ 1.04 increase factor
learning rate 0.1 = 72.328 %
learning rate 0.3 = 93.4114 %
93.4114 / 89.6047 ≈ 1.29 increase factor
Another conclusion we can make is that the highest increasing factor is between a learning rate of 0.1
and 0.2. When increasing the learning rate any further is has a small effect on the accuracy of our model.
Another thing we can conclude is that the highest accuracy within this test has occurred when using a
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learning rate of 0.3. We did observed a decrease of the error per epoch of 0.001 between the learning
rates 0.3 and 0.6, but that hasn’t affected the accuracy (number of correctly classified instances).
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See ‘info about this evaluation’ of learing rate 0.3 & 0.6. Difference between these values.
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Unfortunately Weka was not able to set the learning rate to a higher value then 1.0. There was a fixed maximum set
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6. Computerassignment 3
Exercise 3. As a final experiment, pick one value for both epoch and learning rate, and play
with the hiddenLayers (in the same window as where you set GUI to true). The default value
is 'a', try setting it differently (e.g. 5 or 10) and try multiple values at the same time (e.g. 10,10).
Again, look at performance of the model for various settings.
For the final experiment I’ve chosen to an epoch of 50 and a learning rate of 0.2.
These are the results when the hiddenLayers feature is set to it’s default value ‘a’. The accuracy is given
in red.
Correctly Classified Instances 673 98.5359 %
Incorrectly Classified Instances 10 1.4641 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.0008995
Learning Rate = 0.2
Momentum = 0.2
hiddenLayers = ‘a’
Now we set the value of hiddenLayers to 1. The output is listed below (and the accuracy in red).
Correctly Classified Instances 91 13.3236 %
Incorrectly Classified Instances 592 86.6764 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.0481054
Learning Rate = 0.2
Momentum = 0.2
hiddenLayers = ‘1’
Now we set the hiddenLayer option to 3. The accuracy is given in red again
Correctly Classified Instances 408 59.7365 %
Incorrectly Classified Instances 275 40.2635 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.0269675
Learning Rate = 0.2
Momentum = 0.2
hiddenLayers = ‘3’
Now we set the hiddenLayer option to 5. The accuracy is given in red again.
Correctly Classified Instances 478 69.9854 %
Incorrectly Classified Instances 205 30.0146 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.0173471
Learning Rate = 0.2
Momentum = 0.2
hiddenLayers = ‘5’
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7. Computerassignment 3
Now we set the hiddenLayer value to 10. The accuracy is given in red (again):
Correctly Classified Instances 615 90.0439 %
Incorrectly Classified Instances 68 9.9561 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.0062486
Learning Rate = 0.2
Momentum = 0.2
hiddenLayers = ‘10’
Now we set the hiddenLayers option to 20. The accuracy is given in red again.
Correctly Classified Instances 667 97.6574 %
Incorrectly Classified Instances 16 2.3426 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.001507
Learning Rate = 0.2
Momentum = 0.2
hiddenLayers = ‘20’
Now we do a final test to see if there’s still a significant increase within the accuracy. We set the
hiddenLayers option to 30. The results are listed below with the accuracy in red.
Correctly Classified Instances 672 98.3895 %
Incorrectly Classified Instances 11 1.6105 %
Info about this evaluation
Epoch = 50
Error per Epoch = 0.0014833
Learning Rate = 0.2
Momentum = 0.2
hiddenLayers = ‘30’
We can now make a clear table where we note all accuracy’s weighted to the hiddenLayers it’s input
value. The underneath table shows us that the most significant increase of the accuracy is within 1 to 10
layers. After 20-30 hiddenLayers we have an almost perfect accuracy.
hiddenLayers value Accuracy (number of correct classified instances)
‘a’ (default) 98.5359 %
1 13.3236 %
3 59.7365 %
5 69.9854 %
10 90.0439 %
20 97.6574 %
30 98.3895 %
I’ve also visualized the outputs. It’s becoming clear that the more hiddenLayers we put in the more
connections can me made between the input attributes and the output attributes. We see that the red
dots represents the number of hiddenLayers which we have put in.
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8. Computerassignment 3
Epoch of 1 Epoch of 3 Epoch of 10 Epoch of 20 Epoch of 30
Now we test the same number of hiddenLayers but then with a learning rate of 0.3 and we leave the
epoch as it was (50 iterations). The accuracy of these output are listed below. If we compare these
numbers to the previous table we can state that they’re pretty similar and that it’s hard to say how they
differ.
hiddenLayers value Accuracy (number of correct classified instances)
‘a’ (default) 98.6823 %
1 24.0117 %
3 55.7833 %
5 68.6676 %
10 91.8009 %
20 98.0966 %
30 98.6823 %
Now we try different settings for the hiddenLayer feature. Instead of adding one integer we add two. This
will result in 2 layers of hiddenLayers. We leave the learning rate as 0.3 and use an epoch of 50 (50
iterations) as we have used in the previous examples also. We see that we get a ‘multi layer perceptron’.
Epoch set to 5,1 Epoch set to 1,5 Epoch set to 5,5
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9. Computerassignment 3
hiddenLayer value Accuracy (number of correct classified instances)
1,1 26.2079 %
5,1 32.0644 %
10,1 26.2079 %
1,5 30.7467 %
5,5 62.0791 %
10,5 64.1288 %
1,10 32.7965 %
5,10 65.593 %
10,10 71.5959 %
Now we do the same thing but we only adjust the learning rate to 0.6
hiddenLayer value Accuracy (number of correct classified instances)
1,1 26.2079 %
5,1 32.7965 %
10,1 39.6779 %
1,5 26.2079 %
5,5 74.0849 %
10,5 79.063 %
1,10 23.1332 %
5,10 77.5988 %
10,10 94.2899 %
Now we do the same thing but we only adjust the learning rate to 1.0. Unfortunately weka was unable to
set a higher learning rate then 1.0. So 1.0 is the heighest value which we could pick.
hiddenLayer value Accuracy (number of correct classified instances)
1,1 26.2079 %
5,1 38.9458 %
10,1 49.3411 %
1,5 28.1113 %
5,5 69.5461 %
10,5 80.9663 %
1,10 23.1332 %
5,10 76.2811 %
10,10 89.019 %
As a final test we want to know what the accuracy is we have a maximum value but below 1.0. So for
this final test we set the learning rate to a value of 0.9.
hiddenLayer value Accuracy (number of correct classified instances)
1,1 26.2079 %
5,1 27.0864 %
10,1 48.3163 %
1,5 28.5505 %
5,5 67.4963 %
10,5 82.4305 %
1,10 28.1113 %
5,10 73.3529 %
10,10 94.8755 %
If we observe the tables which are listed above it’s hard to say where our increase of accuracy is. What
we do see is that our maximum hiddenLayer gives us the highest accuracy. This counts for using both
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the learning rates 0.6 and 0.9 (94,8755 %).
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Unfortunately Weka was not able to set the learning rate to a higher value then 1.0. There was a fixed maximum set
of 1.0 withing the program
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