Lecture

Optimization in Machine Learning: Gradient Descent

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture introduces optimization in machine learning, focusing on gradient descent. It covers the analytical solution for linear regression, the lack of analytical solutions for logistic regression, and the use of specialized optimizers. The concept of convexity, stochastic gradient descent, and early stopping are explained. Practical considerations such as choosing a good learning rate and preprocessing data are discussed. The lecture also delves into solving the XOR problem without feature engineering using logistic regression and neural networks.

Official source

Ontological neighbourhood

Information engineering

Machine learning: Artificial neural networks

Statistics

Data analysis: Regression analysis

Related concepts (32)

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Backpropagation

As a machine-learning algorithm, backpropagation performs a backward pass to adjust the model's parameters, aiming to minimize the mean squared error (MSE). In a single-layered network, backpropagation uses the following steps: Traverse through the network from the input to the output by computing the hidden layers' output and the output layer. (the feedforward step) In the output layer, calculate the derivative of the cost function with respect to the input and the hidden layers.

Gradient descent

In mathematics, gradient descent (also often called steepest descent) is a iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent.

Stochastic gradient descent

Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calculated from the entire data set) by an estimate thereof (calculated from a randomly selected subset of the data).

Logistic regression

In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination).

Related lectures (64)

Neural Networks: Multilayer Perceptrons

Covers Multilayer Perceptrons, artificial neurons, activation functions, matrix notation, flexibility, regularization, regression, and classification tasks.

Linear and Logistic Regression

Introduces linear and logistic regression, covering parametric models, multi-output prediction, non-linearity, gradient descent, and classification applications.

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.

Neural Networks: Multilayer Learning

Covers the fundamentals of multilayer neural networks and deep learning, including back-propagation and network architectures like LeNet, AlexNet, and VGG-16.

Regression Trees and Ensemble Methods in Machine Learning