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Lecture

Splines and Machine Learning

Description

This lecture by the instructor covers the concept of supervised learning as an ill-posed problem and how constraints are imposed on the solution through regularization. The talk introduces a new representer theorem that characterizes the solution of functional optimization problems, leading to classical algorithms like kernel-based techniques and smoothing splines. The lecture explores the integration of sparse adaptive splines into neural architectures, resulting in high-dimensional adaptive linear splines and deep neural networks with ReLU activations.

Official source

Ontological neighbourhood

Information engineering

Machine learning: Artificial neural networks

Related concepts (32)

Deep learning

Deep learning is part of a broader family of machine learning methods, which is based on artificial neural networks with representation learning. The adjective "deep" in deep learning refers to the use of multiple layers in the network. Methods used can be either supervised, semi-supervised or unsupervised.

Convolutional neural network

Convolutional neural network (CNN) is a regularized type of feed-forward neural network that learns feature engineering by itself via filters (or kernel) optimization. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by using regularized weights over fewer connections. For example, for each neuron in the fully-connected layer 10,000 weights would be required for processing an image sized 100 × 100 pixels.

Feedforward neural network

A feedforward neural network (FNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. Its flow is uni-directional, meaning that the information in the model flows in only one direction—forward—from the input nodes, through the hidden nodes (if any) and to the output nodes, without any cycles or loops, in contrast to recurrent neural networks, which have a bi-directional flow.

Rectifier (neural networks)

In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the positive part of its argument: where x is the input to a neuron. This is also known as a ramp function and is analogous to half-wave rectification in electrical engineering. This activation function was introduced by Kunihiko Fukushima in 1969 in the context of visual feature extraction in hierarchical neural networks.

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

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Deep Splines: Unifying Framework for Deep Neural Networks

Introduces a functional framework for deep neural networks with adaptive piecewise-linear splines, focusing on biomedical image reconstruction and the challenges of deep splines.

Supervised Learning Overview

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Neural Networks: Training and Activation

Explores neural networks, activation functions, backpropagation, and PyTorch implementation.

Introduction to Machine Learning: Supervised Learning

Introduces supervised learning, covering classification, regression, model optimization, overfitting, and kernel methods.

Feedforward Neural Networks: Activation Functions and Backpropagation