In this session we will discuss about various methods to optimise a machine learning model and, how we can adjust the hyper-parameters to minimise the cost function.
The document discusses gradient descent methods for unconstrained convex optimization problems. It introduces gradient descent as an iterative method to find the minimum of a differentiable function by taking steps proportional to the negative gradient. It describes the basic gradient descent update rule and discusses convergence conditions such as Lipschitz continuity, strong convexity, and condition number. It also covers techniques like exact line search, backtracking line search, coordinate descent, and steepest descent methods.
This document summarizes various optimization techniques for deep learning models, including gradient descent, stochastic gradient descent, and variants like momentum, Nesterov's accelerated gradient, AdaGrad, RMSProp, and Adam. It provides an overview of how each technique works and comparisons of their performance on image classification tasks using MNIST and CIFAR-10 datasets. The document concludes by encouraging attendees to try out the different optimization methods in Keras and provides resources for further deep learning topics.
The document discusses hyperparameters and hyperparameter tuning in deep learning models. It defines hyperparameters as parameters that govern how the model parameters (weights and biases) are determined during training, in contrast to model parameters which are learned from the training data. Important hyperparameters include the learning rate, number of layers and units, and activation functions. The goal of training is for the model to perform optimally on unseen test data. Model selection, such as through cross-validation, is used to select the optimal hyperparameters. Training, validation, and test sets are also discussed, with the validation set used for model selection and the test set providing an unbiased evaluation of the fully trained model.
Hands-On Machine Learning with Scikit-Learn and TensorFlow - Chapter8Hakky St
This is the documentation of the study-meeting in lab.
Tha book title is "Hands-On Machine Learning with Scikit-Learn and TensorFlow" and this is the chapter 8.
This document provides an overview of activation functions in deep learning. It discusses the purpose of activation functions, common types of activation functions like sigmoid, tanh, and ReLU, and issues like vanishing gradients that can occur with some activation functions. It explains that activation functions introduce non-linearity, allowing neural networks to learn complex patterns from data. The document also covers concepts like monotonicity, continuity, and differentiation properties that activation functions should have, as well as popular methods for updating weights during training like SGD, Adam, etc.
Talk on Optimization for Deep Learning, which gives an overview of gradient descent optimization algorithms and highlights some current research directions.
Lecture 18: Gaussian Mixture Models and Expectation Maximizationbutest
This document discusses Gaussian mixture models (GMMs) and the expectation-maximization (EM) algorithm. GMMs model data as coming from a mixture of Gaussian distributions, with each data point assigned soft responsibilities to the different components. EM is used to estimate the parameters of GMMs and other latent variable models. It iterates between an E-step, where responsibilities are computed based on current parameters, and an M-step, where new parameters are estimated to maximize the expected complete-data log-likelihood given the responsibilities. EM converges to a local optimum for fitting GMMs to data.
The document discusses gradient descent methods for unconstrained convex optimization problems. It introduces gradient descent as an iterative method to find the minimum of a differentiable function by taking steps proportional to the negative gradient. It describes the basic gradient descent update rule and discusses convergence conditions such as Lipschitz continuity, strong convexity, and condition number. It also covers techniques like exact line search, backtracking line search, coordinate descent, and steepest descent methods.
This document summarizes various optimization techniques for deep learning models, including gradient descent, stochastic gradient descent, and variants like momentum, Nesterov's accelerated gradient, AdaGrad, RMSProp, and Adam. It provides an overview of how each technique works and comparisons of their performance on image classification tasks using MNIST and CIFAR-10 datasets. The document concludes by encouraging attendees to try out the different optimization methods in Keras and provides resources for further deep learning topics.
The document discusses hyperparameters and hyperparameter tuning in deep learning models. It defines hyperparameters as parameters that govern how the model parameters (weights and biases) are determined during training, in contrast to model parameters which are learned from the training data. Important hyperparameters include the learning rate, number of layers and units, and activation functions. The goal of training is for the model to perform optimally on unseen test data. Model selection, such as through cross-validation, is used to select the optimal hyperparameters. Training, validation, and test sets are also discussed, with the validation set used for model selection and the test set providing an unbiased evaluation of the fully trained model.
Hands-On Machine Learning with Scikit-Learn and TensorFlow - Chapter8Hakky St
This is the documentation of the study-meeting in lab.
Tha book title is "Hands-On Machine Learning with Scikit-Learn and TensorFlow" and this is the chapter 8.
This document provides an overview of activation functions in deep learning. It discusses the purpose of activation functions, common types of activation functions like sigmoid, tanh, and ReLU, and issues like vanishing gradients that can occur with some activation functions. It explains that activation functions introduce non-linearity, allowing neural networks to learn complex patterns from data. The document also covers concepts like monotonicity, continuity, and differentiation properties that activation functions should have, as well as popular methods for updating weights during training like SGD, Adam, etc.
Talk on Optimization for Deep Learning, which gives an overview of gradient descent optimization algorithms and highlights some current research directions.
Lecture 18: Gaussian Mixture Models and Expectation Maximizationbutest
This document discusses Gaussian mixture models (GMMs) and the expectation-maximization (EM) algorithm. GMMs model data as coming from a mixture of Gaussian distributions, with each data point assigned soft responsibilities to the different components. EM is used to estimate the parameters of GMMs and other latent variable models. It iterates between an E-step, where responsibilities are computed based on current parameters, and an M-step, where new parameters are estimated to maximize the expected complete-data log-likelihood given the responsibilities. EM converges to a local optimum for fitting GMMs to data.
This document discusses dimensionality reduction techniques for data mining. It begins with an introduction to dimensionality reduction and reasons for using it. These include dealing with high-dimensional data issues like the curse of dimensionality. It then covers major dimensionality reduction techniques of feature selection and feature extraction. Feature selection techniques discussed include search strategies, feature ranking, and evaluation measures. Feature extraction maps data to a lower-dimensional space. The document outlines applications of dimensionality reduction like text mining and gene expression analysis. It concludes with trends in the field.
This document provides an overview of different techniques for hyperparameter tuning in machine learning models. It begins with introductions to grid search and random search, then discusses sequential model-based optimization techniques like Bayesian optimization and Tree-of-Parzen Estimators. Evolutionary algorithms like CMA-ES and particle-based methods like particle swarm optimization are also covered. Multi-fidelity methods like successive halving and Hyperband are described, along with recommendations on when to use different techniques. The document concludes by listing several popular libraries for hyperparameter tuning.
Fuzzy inference systems use fuzzy logic to map inputs to outputs. There are two main types:
Mamdani systems use fuzzy outputs and are well-suited for problems involving human expert knowledge. Sugeno systems have faster computation using linear or constant outputs.
The fuzzy inference process involves fuzzifying inputs, applying fuzzy logic operators, and using if-then rules. Outputs are determined through implication, aggregation, and defuzzification. Mamdani systems find the centroid of fuzzy outputs while Sugeno uses weighted averages, making it more efficient.
The document discusses artificial neural networks and backpropagation. It provides an overview of backpropagation algorithms, including how they were developed over time, the basic methodology of propagating errors backwards, and typical network architectures. It also gives examples of applying backpropagation to problems like robotics, space robots, handwritten digit recognition, and face recognition.
Overview on Optimization algorithms in Deep LearningKhang Pham
Overview on function optimization in general and in deep learning. The slides cover from basic algorithms like batch gradient descent, stochastic gradient descent to the state of art algorithm like Momentum, Adagrad, RMSprop, Adam.
Artificial neural networks mimic the human brain by using interconnected layers of neurons that fire electrical signals between each other. Activation functions are important for neural networks to learn complex patterns by introducing non-linearity. Without activation functions, neural networks would be limited to linear regression. Common activation functions include sigmoid, tanh, ReLU, and LeakyReLU, with ReLU and LeakyReLU helping to address issues like vanishing gradients that can occur with sigmoid and tanh functions.
Tabu search is a metaheuristic technique that guides a local search procedure to explore the solution space beyond local optimality. It uses flexible memory-based processes to escape the trap of cycling. Particle swarm optimization is a swarm intelligence technique inspired by bird flocking where potential solutions fly through hyperspace to find optimal regions. Ant colony optimization is another swarm intelligence technique inspired by how ants find food, where artificial ants cooperate to find good solutions.
1. Autoencoders are unsupervised neural networks that are useful for dimensionality reduction and clustering. They compress the input into a latent-space representation then reconstruct the output from this representation.
2. Deep autoencoders stack multiple autoencoder layers to learn hierarchical representations of the data. Each layer is trained sequentially.
3. Variational autoencoders use probabilistic encoders and decoders to learn a Gaussian latent space. They can generate new samples from the learned data distribution.
Transfer Learning and Fine-tuning Deep Neural NetworksPyData
This document outlines Anusua Trivedi's talk on transfer learning and fine-tuning deep neural networks. The talk covers traditional machine learning versus deep learning, using deep convolutional neural networks (DCNNs) for image analysis, transfer learning and fine-tuning DCNNs, recurrent neural networks (RNNs), and case studies applying these techniques to diabetic retinopathy prediction and fashion image caption generation.
Support Vector Machine ppt presentationAyanaRukasar
Support vector machines (SVM) is a supervised machine learning algorithm used for both classification and regression problems. However, it is primarily used for classification. The goal of SVM is to create the best decision boundary, known as a hyperplane, that separates clusters of data points. It chooses extreme data points as support vectors to define the hyperplane. SVM is effective for problems that are not linearly separable by transforming them into higher dimensional spaces. It works well when there is a clear margin of separation between classes and is effective for high dimensional data. An example use case in Python is presented.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, and then a quick dive into CNNs. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session.
Part 2 of the Deep Learning Fundamentals Series, this session discusses Tuning Training (including hyperparameters, overfitting/underfitting), Training Algorithms (including different learning rates, backpropagation), Optimization (including stochastic gradient descent, momentum, Nesterov Accelerated Gradient, RMSprop, Adaptive algorithms - Adam, Adadelta, etc.), and a primer on Convolutional Neural Networks. The demos included in these slides are running on Keras with TensorFlow backend on Databricks.
Introduction to linear regression and the maths behind it like line of best fit, regression matrics. Other concepts include cost function, gradient descent, overfitting and underfitting, r squared.
Data preprocessing is the process of preparing raw data for analysis by cleaning it, transforming it, and reducing it. The key steps in data preprocessing include data cleaning to handle missing values, outliers, and noise; data transformation techniques like normalization, discretization, and feature extraction; and data reduction methods like dimensionality reduction and sampling. Preprocessing ensures the data is consistent, accurate and suitable for building machine learning models.
Reinforcement learning is a machine learning technique where an agent learns how to behave in an environment by receiving rewards or punishments for its actions. The goal of the agent is to learn an optimal policy that maximizes long-term rewards. Reinforcement learning can be applied to problems like game playing, robot control, scheduling, and economic modeling. The reinforcement learning process involves an agent interacting with an environment to learn through trial-and-error using state, action, reward, and policy. Common algorithms include Q-learning which uses a Q-table to learn the optimal action-selection policy.
A Support Vector Machine (SVM) is a discriminative classifier formally defined by a separating hyperplane. In other words, given labeled training data (supervised learning), the algorithm outputs an optimal hyperplane which categorizes new examples. In two dimentional space this hyperplane is a line dividing a plane in two parts where in each class lay in either side.
The document summarizes statistical pattern recognition techniques. It is divided into 9 sections that cover topics like dimensionality reduction, classifiers, classifier combination, and unsupervised classification. The goal of pattern recognition is supervised or unsupervised classification of patterns based on features. Dimensionality reduction aims to reduce the number of features to address the curse of dimensionality when samples are limited. Multiple classifiers can be combined through techniques like stacking, bagging, and boosting. Unsupervised classification uses clustering algorithms to construct decision boundaries without labeled training data.
Neural networks can be used for tasks like time-series forecasting, algorithmic trading, and credit risk modeling. They contain layers of interconnected nodes called perceptrons that are similar to multiple linear regression models. Optimization algorithms like gradient descent are used to minimize losses during neural network training by adjusting weights. Stochastic gradient descent makes updates using small random samples rather than the whole dataset, helping address issues with gradient descent like becoming stuck in local minima. Momentum can be added to gradient descent to help it build inertia and overcome flat spots during optimization. Adaptive learning methods like AdaGrad dynamically adjust the learning rate for each parameter. Fuzzy logic systems use degrees of membership rather than binary values, allowing approximate reasoning. They have components
https://github.com/telecombcn-dl/dlmm-2017-dcu
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of big annotated data and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which had been addressed until now with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks and Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles and applications of deep learning to computer vision problems, such as image classification, object detection or text captioning.
This document discusses dimensionality reduction techniques for data mining. It begins with an introduction to dimensionality reduction and reasons for using it. These include dealing with high-dimensional data issues like the curse of dimensionality. It then covers major dimensionality reduction techniques of feature selection and feature extraction. Feature selection techniques discussed include search strategies, feature ranking, and evaluation measures. Feature extraction maps data to a lower-dimensional space. The document outlines applications of dimensionality reduction like text mining and gene expression analysis. It concludes with trends in the field.
This document provides an overview of different techniques for hyperparameter tuning in machine learning models. It begins with introductions to grid search and random search, then discusses sequential model-based optimization techniques like Bayesian optimization and Tree-of-Parzen Estimators. Evolutionary algorithms like CMA-ES and particle-based methods like particle swarm optimization are also covered. Multi-fidelity methods like successive halving and Hyperband are described, along with recommendations on when to use different techniques. The document concludes by listing several popular libraries for hyperparameter tuning.
Fuzzy inference systems use fuzzy logic to map inputs to outputs. There are two main types:
Mamdani systems use fuzzy outputs and are well-suited for problems involving human expert knowledge. Sugeno systems have faster computation using linear or constant outputs.
The fuzzy inference process involves fuzzifying inputs, applying fuzzy logic operators, and using if-then rules. Outputs are determined through implication, aggregation, and defuzzification. Mamdani systems find the centroid of fuzzy outputs while Sugeno uses weighted averages, making it more efficient.
The document discusses artificial neural networks and backpropagation. It provides an overview of backpropagation algorithms, including how they were developed over time, the basic methodology of propagating errors backwards, and typical network architectures. It also gives examples of applying backpropagation to problems like robotics, space robots, handwritten digit recognition, and face recognition.
Overview on Optimization algorithms in Deep LearningKhang Pham
Overview on function optimization in general and in deep learning. The slides cover from basic algorithms like batch gradient descent, stochastic gradient descent to the state of art algorithm like Momentum, Adagrad, RMSprop, Adam.
Artificial neural networks mimic the human brain by using interconnected layers of neurons that fire electrical signals between each other. Activation functions are important for neural networks to learn complex patterns by introducing non-linearity. Without activation functions, neural networks would be limited to linear regression. Common activation functions include sigmoid, tanh, ReLU, and LeakyReLU, with ReLU and LeakyReLU helping to address issues like vanishing gradients that can occur with sigmoid and tanh functions.
Tabu search is a metaheuristic technique that guides a local search procedure to explore the solution space beyond local optimality. It uses flexible memory-based processes to escape the trap of cycling. Particle swarm optimization is a swarm intelligence technique inspired by bird flocking where potential solutions fly through hyperspace to find optimal regions. Ant colony optimization is another swarm intelligence technique inspired by how ants find food, where artificial ants cooperate to find good solutions.
1. Autoencoders are unsupervised neural networks that are useful for dimensionality reduction and clustering. They compress the input into a latent-space representation then reconstruct the output from this representation.
2. Deep autoencoders stack multiple autoencoder layers to learn hierarchical representations of the data. Each layer is trained sequentially.
3. Variational autoencoders use probabilistic encoders and decoders to learn a Gaussian latent space. They can generate new samples from the learned data distribution.
Transfer Learning and Fine-tuning Deep Neural NetworksPyData
This document outlines Anusua Trivedi's talk on transfer learning and fine-tuning deep neural networks. The talk covers traditional machine learning versus deep learning, using deep convolutional neural networks (DCNNs) for image analysis, transfer learning and fine-tuning DCNNs, recurrent neural networks (RNNs), and case studies applying these techniques to diabetic retinopathy prediction and fashion image caption generation.
Support Vector Machine ppt presentationAyanaRukasar
Support vector machines (SVM) is a supervised machine learning algorithm used for both classification and regression problems. However, it is primarily used for classification. The goal of SVM is to create the best decision boundary, known as a hyperplane, that separates clusters of data points. It chooses extreme data points as support vectors to define the hyperplane. SVM is effective for problems that are not linearly separable by transforming them into higher dimensional spaces. It works well when there is a clear margin of separation between classes and is effective for high dimensional data. An example use case in Python is presented.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, and then a quick dive into CNNs. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session.
Part 2 of the Deep Learning Fundamentals Series, this session discusses Tuning Training (including hyperparameters, overfitting/underfitting), Training Algorithms (including different learning rates, backpropagation), Optimization (including stochastic gradient descent, momentum, Nesterov Accelerated Gradient, RMSprop, Adaptive algorithms - Adam, Adadelta, etc.), and a primer on Convolutional Neural Networks. The demos included in these slides are running on Keras with TensorFlow backend on Databricks.
Introduction to linear regression and the maths behind it like line of best fit, regression matrics. Other concepts include cost function, gradient descent, overfitting and underfitting, r squared.
Data preprocessing is the process of preparing raw data for analysis by cleaning it, transforming it, and reducing it. The key steps in data preprocessing include data cleaning to handle missing values, outliers, and noise; data transformation techniques like normalization, discretization, and feature extraction; and data reduction methods like dimensionality reduction and sampling. Preprocessing ensures the data is consistent, accurate and suitable for building machine learning models.
Reinforcement learning is a machine learning technique where an agent learns how to behave in an environment by receiving rewards or punishments for its actions. The goal of the agent is to learn an optimal policy that maximizes long-term rewards. Reinforcement learning can be applied to problems like game playing, robot control, scheduling, and economic modeling. The reinforcement learning process involves an agent interacting with an environment to learn through trial-and-error using state, action, reward, and policy. Common algorithms include Q-learning which uses a Q-table to learn the optimal action-selection policy.
A Support Vector Machine (SVM) is a discriminative classifier formally defined by a separating hyperplane. In other words, given labeled training data (supervised learning), the algorithm outputs an optimal hyperplane which categorizes new examples. In two dimentional space this hyperplane is a line dividing a plane in two parts where in each class lay in either side.
The document summarizes statistical pattern recognition techniques. It is divided into 9 sections that cover topics like dimensionality reduction, classifiers, classifier combination, and unsupervised classification. The goal of pattern recognition is supervised or unsupervised classification of patterns based on features. Dimensionality reduction aims to reduce the number of features to address the curse of dimensionality when samples are limited. Multiple classifiers can be combined through techniques like stacking, bagging, and boosting. Unsupervised classification uses clustering algorithms to construct decision boundaries without labeled training data.
Neural networks can be used for tasks like time-series forecasting, algorithmic trading, and credit risk modeling. They contain layers of interconnected nodes called perceptrons that are similar to multiple linear regression models. Optimization algorithms like gradient descent are used to minimize losses during neural network training by adjusting weights. Stochastic gradient descent makes updates using small random samples rather than the whole dataset, helping address issues with gradient descent like becoming stuck in local minima. Momentum can be added to gradient descent to help it build inertia and overcome flat spots during optimization. Adaptive learning methods like AdaGrad dynamically adjust the learning rate for each parameter. Fuzzy logic systems use degrees of membership rather than binary values, allowing approximate reasoning. They have components
https://github.com/telecombcn-dl/dlmm-2017-dcu
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of big annotated data and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which had been addressed until now with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks and Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles and applications of deep learning to computer vision problems, such as image classification, object detection or text captioning.
The document provides an overview of regression problems in machine learning. It discusses the different types of regression including simple linear regression, multiple linear regression, and polynomial regression. It explains concepts like error, metrics like R-squared, MAE, and MSE. It also covers model performance issues like underfitting and overfitting, and techniques to address them such as regularization, early stopping, gradient descent, and cross-validation. The goal is to help learners understand regression problems and how to develop and evaluate regression models.
Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.
A presentation about NGBoost (Natural Gradient Boosting) which I presented in the Information Theory and Probabilistic Programming course at the University of Oklahoma.
This document provides an overview of deep learning concepts including neural networks, supervised and unsupervised learning, and key terms. It explains that deep learning uses neural networks with many hidden layers to learn features directly from raw data. Supervised learning algorithms learn from labeled examples to perform classification or regression on unseen data. Unsupervised learning finds patterns in unlabeled data. Key terms defined include neurons, activation functions, loss functions, optimizers, epochs, batches, and hyperparameters.
Optimization is considered to be one of the pillars of statistical learning and also plays a major role in the design and development of intelligent systems such as search engines, recommender systems, and speech and image recognition software. Machine Learning is the study that gives the computers the ability to learn and also the ability to think without being explicitly programmed. A computer is said to learn from an experience with respect to a specified task and its performance related to that task. The machine learning algorithms are applied to the problems to reduce efforts. Machine learning algorithms are used for manipulating the data and predict the output for the new data with high precision and low uncertainty. The optimization algorithms are used to make rational decisions in an environment of uncertainty and imprecision. In this paper a methodology is presented to use the efficient optimization algorithm as an alternative for the gradient descent machine learning algorithm as an optimization algorithm.
The document provides guidelines for training deep neural networks (DNNs). It discusses obtaining large, clean training datasets and using data augmentation. It recommends tanh or ReLU activation functions to avoid problems with sigmoid functions. The number of hidden units and layers should be optimized, and weights initialized randomly. Learning rates can use adaptive methods like Adam. Hyperparameter tuning is best done with random search instead of grid search. Mini-batch training provides faster learning than stochastic methods. Dropout helps prevent overfitting.
The document discusses key concepts in neural networks including units, layers, batch normalization, cost/loss functions, regularization techniques, activation functions, backpropagation, learning rates, and optimization methods. It provides definitions and explanations of these concepts at a high level. For example, it defines units as the activation function that transforms inputs via a nonlinear function, and hidden layers as layers other than the input and output layers that receive weighted input and pass transformed values to the next layer. It also summarizes common cost functions, regularization approaches like dropout, and optimization methods like gradient descent and stochastic gradient descent.
Lecture 7 - Bias, Variance and Regularization, a lecture in subject module St...Maninda Edirisooriya
Bias and Variance are the deepest concepts in ML which drives the decision making of a ML project. Regularization is a solution for the high variance problem. This was one of the lectures of a full course I taught in University of Moratuwa, Sri Lanka on 2023 second half of the year.
Copy of CRICKET MATCH WIN PREDICTOR USING LOGISTIC ...PATHALAMRAJESH
This project uses logistic regression to build a cricket match win predictor. It analyzes match and ball-by-ball data to extract important features, performs exploratory data analysis to derive additional predictive features, and fits a logistic regression model to predict the winning probability of teams based on the game situation. The model achieves an accuracy of 86% on the test data. Future work includes predicting the winner based only on the first innings and adding a user interface to allow custom predictions.
L1 and L2 regularization are techniques to prevent overfitting in machine learning models. L1 regularization adds a penalty term to the loss function based on the absolute values of the model's parameters, encouraging sparsity. L2 regularization uses the squared values instead, which does not induce sparsity but helps prevent overfitting by keeping parameter values small. The degree of regularization is controlled by the hyperparameter lambda. L1 regularization is useful for feature selection with high-dimensional data, while L2 regularization produces simpler, more robust models.
The document provides an introduction to supervised learning. It discusses how supervised learning models are trained on labelled datasets containing both input data and corresponding results or labels. The model learns from these examples to predict accurate results for new, unseen data. Common applications of supervised learning mentioned include sentiment analysis, recommendations, and spam filtration. Decision trees and K-nearest neighbors are discussed as examples of supervised learning algorithms. Decision trees use a top-down approach to split the dataset into more homogeneous subsets. K-nearest neighbors classifies new data based on similarity to labelled examples in the training set.
A Framework for Scene Recognition Using Convolutional Neural Network as Featu...Tahmid Abtahi
This document presents a framework for scene recognition using convolutional neural networks (CNNs) as feature extractors and machine learning kernels as classifiers. The framework uses a VGG dataset containing 678 images across 3 categories (highway, open country, streets). CNNs perform feature extraction via convolution and max pooling operations to reduce dimensionality by 10x. The extracted features are then classified using perceptrons and support vector machines (SVMs) in a parallel implementation. Results show SVMs achieve higher accuracy than perceptrons and accuracy increases with more training data. Future work involves task-level parallelism, increasing data size and categories, and comparing CNN features to PCA.
Everything You Wanted to Know About Optimizationindico data
Presented by Madison May, co-founder and machine learning architect at indico, at the Boston ML meetup.
Overview:
In recent years the use of adaptive momentum methods like Adam and RMSProp has become popular in reducing the sensitivity of machine learning models to optimization hyperparameters and increasing the rate of convergence for complex models. However, past research has shown when properly tuned, using simple SGD + momentum produces better generalization properties and better validation losses at the later stages of training. In a wave of papers submitted in early 2018, researchers have suggested justifications for this unexpected behavior and proposed practical solutions to the problem. This talk will first provide a primer on optimization for machine learning, then summarize the results of these papers and propose practical approaches to applying these findings.
Random forest is an ensemble machine learning algorithm that combines multiple decision trees to improve predictive accuracy. It works by constructing many decision trees during training and outputting the class that is the mode of the classes of the individual trees. Random forest can be used for both classification and regression problems and provides high accuracy even with large datasets.
Deep learning involves core components like parameters, layers, activation functions, loss functions, and optimization methods. Loss functions measure how incorrect a model's predictions are and include types like squared error loss and cross-entropy loss. Squared error loss assesses the quality of a predictor or estimator by measuring the mean squared error. Hyperparameters like the learning rate, regularization, momentum, sparsity, and optimization method also impact deep learning models. The learning rate affects how much model parameters are adjusted with each iteration, and optimization methods like gradient descent, RMSprop, and Adam are used to update parameters to minimize the loss function.
The document discusses linear programming models and optimization techniques. It covers sensitivity analysis and duality analysis to determine parameter values where a linear programming solution remains valid. It also discusses solving linear programming problems with integer constraints and using network models to solve transportation problems. The document then provides an example of using the simplex method and sensitivity analysis to solve a linear programming problem to maximize profit based on production capacity constraints.
Paper review: Learned Optimizers that Scale and Generalize.Wuhyun Rico Shin
The paper proposes a novel hierarchical RNN architecture for a learned optimizer that aims to address scalability and generalization issues. The architecture uses a hierarchical structure of parameter, tensor, and global RNNs to enable coordination of updates across parameters with low memory and computation costs. It also incorporates features inspired by hand-designed optimizers like computing gradients at attended locations and dynamic input scaling to provide the learned optimizer with useful information. The optimizer is meta-trained on diverse small problems and can generalize to optimizing new problem types, though it struggles on very large models. Ablation studies show the importance of the paper's design choices for the learned optimizer's performance.
Similar to Methods of Optimization in Machine Learning (20)
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1. Presented By: Aayush Srivastava
& Divyank Saxena
Methods of
Optimization in
Machine Learning
2. Lack of etiquette and manners is a huge turn off.
KnolX Etiquettes
Punctuality
Join the session 5 minutes prior to
the session start time. We start on
time and conclude on time!
Feedback
Make sure to submit a constructive
feedback for all sessions as it is
very helpful for the presenter.
Silent Mode
Keep your mobile devices in silent
mode, feel free to move out of
session in case you need to attend
an urgent call.
Avoid Disturbance
Avoid unwanted chit chat during
the session.
3. Our Agenda
01 What is Optimization in
Machine Learning
02 What is Gradient Descent
03
What is Minibatch Stochastic
Gradient
04
What is Adam optimization
05
Demo
05
06
What is Stochastic Gradient
Descent
4. .
What is Optimization in ML
● Optimization in Machine Learning is a technique used to find the best set of parameters for a given
model to minimize a loss function and improve its performance. It is an essential step in the training
process of a machine learning model.
● The goal of optimization is to find the best weights and biases for the model, so that it can make
accurate predictions.
● Optimization is used in machine learning because models typically have many parameters, and finding
the best values for those parameters can be a challenging task.
● With optimization techniques, the model can automatically search for the best parameters, rather than
relying on manual tuning by the user.
5. .
What is Cost Function
● A cost function is a function which measures the error between predictions and their actual values
across the whole dataset.
● Minimizing the cost function helps the learning algorithm find the optimal set of parameters, such as
weights and biases, that produce the best predictions.
● Cost function is a measure of how wrong the model is in estimating the relationship between X(input)
and Y(output) Parameter
- m is the number of samples
- Sum from i to m,
- The actual calculation is just the hypothesis value for h(x)
minus the actual value of y. Then you square whatever you get.
6. .
What is Cost Function
● Let’s run through the calculation for best_fit_1.
1.The hypothesis is 0.50. This is the h_the ha(x(i)) part
what we think is the correct value.
2.The actual value for the sample data is 1.00.
So we are left with (0.50 — 1.00)^2 , which is 0.25.
3.Let’s add this result to an array called results and do the same for all three points
4.Results = [0.25, 2.25, 4.00]
5.Finally, we add them all up and multiply by ⅙ .We get the cost for best_fit1 = 1.083
7. .
What is Cost Function
● COST: best_fit_1: 1.083
best_fit_2: 0.083
best_fit_3: 0.25
● A low costs represents a smaller difference.
8. .
What is Loss Function
● A loss function, also known objective function, is a mathematical measure of how well a model is able
to make predictions that match the true values.
● A loss function measures the error between a single prediction and the corresponding actual value.
● Loss and cost functions are methods of measuring the error in machine learning predictions. Loss
functions measure the error per observation, whilst cost functions measure the error over all
observations.
Types:
1.Mean Squared Error (MSE): This loss function measures the average squared difference between the
predicted values and the true values.
2.Mean Absolute Error (MAE): This loss function measures the average absolute difference between the
predicted values and the true values.
9. ● Gradient, in plain terms means slope or slant of a surface. So gradient descent literally means
descending a slope to reach the lowest point on that surface
● Gradient descent enables a model to learn the gradient or direction that the model should take in
order to reduce errors (differences between actual y and predicted y).
● This algorithm that tries to find a minimum of a function iteratively
What is Gradient Descent
10. .
What is Learning Rate
● Learning Rate:
The learning rate is a hyperparameter in machine learning that determines the step size at which the
optimization algorithm updates the model's parameters. It is used to control the speed at which the
model learns.
11. .
Limitation of Gradient Descent
● Some limitations and drawbacks that can affect its performance and efficiency.
● Local Minima: Gradient Descent can get stuck in a local minimum, which may not be the global
minimum, and therefore, the optimization will not produce the best result.
● Vanishing gradient: When training deep neural networks, the gradients can become very small,
leading to the vanishing gradient problem, which can slow down or prevent convergence.
12. ● Stochastic Gradient Descent (SGD) is a variant of Gradient Descent optimization algorithm, that is
used to update the parameters of a model in a more efficient and faster way.
● “Stochastic” in plain terms means “random”
● In SGD, at each step, the algorithm calculates the gradient for one observation picked at random,
instead of calculating the gradient for the entire dataset..
● So, let’s have a dataset that contains 1000 rows, and when we apply SGD it will update the model
parameters 1000 times in one complete cycle of a dataset instead of one time as in Gradient Descent.
What is Stochastic Gradient Descent
13. ● In the left diagram of the above picture, we have SGD (where 1 per step time) we take a Gradient
Descent step for each example and on the right diagram is GD(1 step per entire training set).
● This represents a significant performance improvement, when the dataset contains millions of
observations.
What is Stochastic Gradient Descent
14. Advantages of Stochastic Gradient Descent
● It is easier to fit into memory due to a single training sample being processed by the network
● For larger datasets it can converge faster as it causes updates to the parameters more frequently
● Due to frequent updates the steps taken towards the minima of the loss function have oscillations
which can help getting out of local minimums of the loss function
What is Stochastic Gradient Descent
15. ● So far we encountered two extremes in the approach to gradient-based learning:
● First Gradient Descent uses the full dataset to compute gradients and to update parameters, one
pass at a time. And Conversely, Stochastic Gradient Descent processes one training example at a
time to make progress. Either of them has its own drawbacks.
● Gradient descent is not particularly data efficient whenever data is very similar. Stochastic gradient
descent is not particularly computationally efficient since CPUs and GPUs cannot exploit the full
power of vectorization.
● This suggests that there might be something in between, and in fact, that is what we have been using
so far in the examples we discussed.
What is Minibatch Stochastic Gradient
16. ● Mini Batch Gradient Descent is considered to be the cross-over between GD and SGD. In this
approach instead of iterating through the entire dataset or one observation, we split the dataset into
small subsets (batches) and compute the gradients for each batch.
● Steps involved in Mini-batch stochastic gradient:
1. Pick a mini-batch
2. Feed it to Neural Network
3. Calculate the mean gradient of the mini-batch
4. Use the mean gradient we calculated in step 3 to update the weights
5. Repeat steps 1–4 for the mini-batches we created
What is Minibatch Stochastic Gradient
17. ● Minibatch stochastic gradient descent is able to trade-off convergence speed and computation
efficiency. A minibatch size of 10 is more efficient than stochastic gradient descent; a minibatch size
of 100 even outperforms GD in terms of runtime.
What is Minibatch Stochastic Gradient
18. Advantages of Mini-Batch Gradient Descent:
● Reduces variance of the parameter update and hence lead to stable convergence
● Speeds the learning
● Helpful to estimate the approximate location of the actual minimum
Disadvantages of Mini Batch Gradient Descent:
● Loss is computed for each mini batch and hence total loss needs to be accumulated across all mini
batches
Advantages and Disadvantages
19. The Adam optimization algorithm is an extension to stochastic gradient descent that has recently
seen broader adoption for deep learning applications in computer vision and natural language
processing.
The method is really efficient when working with large problem involving a lot of data or parameters.
Adam is an adaptive learning rate method, which means, it computes individual learning rates for
different parameters. Its name is derived from adaptive moment estimation
What is Adam Optimizer
20. The method computes individual adaptive learning rates for different parameters from estimates of
first and second moments of the gradients.
Adam optimizer involves a combination of two gradient descent methodologies:
1. Momentum:
This algorithm is used to accelerate the gradient descent algorithm by taking into consideration
the ‘exponentially weighted average’ of the gradients. Using averages makes the algorithm
converge towards the minima in a faster pace.
2. Root Mean Square Propagation (RMSP):
It maintains per-parameter learning rates that are adapted based on the average of recent
magnitudes of the gradients for the weight (e.g. how quickly it is changing). This means the
algorithm does well on online and non-stationary problems (e.g. noisy).
How Adam Optimizer Work
21. List of attractive benefits of using Adam, as follows:
● Straightforward to implement.
● Computationally efficient.
● Less memory requirements.
● Well suited for problems that are large in terms of data and/or parameters.
● Appropriate for problems with very noisy/or sparse gradients.
● Hyper-parameters have intuitive interpretation and typically require little tuning.
Benefits of Adam Optimizer