Unsupervised learning

Unsupervised learning is a framework in machine learning where, in contrast to supervised learning, algorithms learn patterns exclusively from unlabeled data. Other frameworks in the spectrum of supervisions include weak- or semi-supervision, where a small portion of the data is tagged, and self-supervision. Some researchers consider self-supervised learning a form of unsupervised learning.

Conceptually, unsupervised learning divides into the aspects of data, training, algorithm, and downstream applications. Typically, the dataset is harvested cheaply "in the wild", such as massive text corpus obtained by web crawling, with only minor filtering (such as Common Crawl). This compares favorably to supervised learning, where the dataset (such as the ImageNet1000) is typically constructed manually, which is much more expensive.

There are algorithms designed specifically for unsupervised learning, such as clustering algorithms like k-means, dimensionality reduction techniques like principal component analysis (PCA), Boltzmann machine learning, and autoencoders. After the rise of deep learning, most large-scale unsupervised learning has been done by training general-purpose neural network architectures by gradient descent, adapted to performing unsupervised learning by designing an appropriate training procedure.

Sometimes a trained model can be used as-is, but more often they are modified for downstream applications. For example, the generative pretraining method trains a model to generate a textual dataset, before finetuning it for other applications, such as text classification. As another example, autoencoders are trained to produce good features, which can then be used as a module for other models, such as in a latent diffusion model.

Tasks

thumb|left|300px|Tendency for a task to employ supervised vs. unsupervised methods. Task names straddling circle boundaries is intentional. It shows that the classical division of imaginative tasks (left) employing unsupervised methods is blurred in today's learning schemes.Tasks are often categorized as discriminative (recognition) or generative (imagination). Often but not always, discriminative tasks use supervised methods and generative tasks use unsupervised (see Venn diagram); however, the separation is very hazy. For example, object recognition favors supervised learning but unsupervised learning can also cluster objects into groups. Furthermore, as progress marches onward, some tasks employ both methods, and some tasks swing from one to another. For example, image recognition started off as heavily supervised, but became hybrid by employing unsupervised pre-training, and then moved towards supervision again with the advent of dropout, ReLU, and adaptive learning rates.

A typical generative task is as follows. At each step, a datapoint is sampled from the dataset, and part of the data is removed, and the model must infer the removed part. This is particularly clear for the denoising autoencoders and BERT.

Neural network architectures

Training

During the learning phase, an unsupervised network tries to mimic the data it is given and uses the error in its mimicked output to correct itself (i.e. correct its weights and biases). Sometimes the error is expressed as a low probability that the erroneous output occurs, or it might be expressed as an unstable high energy state in the network.

In contrast to supervised methods' dominant use of backpropagation, unsupervised learning also employs other methods including: Hopfield learning rule, Boltzmann learning rule, Contrastive Divergence, Wake Sleep, Variational Inference, Maximum Likelihood, Maximum A Posteriori, Gibbs Sampling, and backpropagating reconstruction errors or hidden state reparameterizations. See the table below for more details.

Energy

An energy function is a macroscopic measure of a network's activation state. In Boltzmann machines, it plays the role of the Cost function. This analogy with physics is inspired by Ludwig Boltzmann's analysis of a gas' macroscopic energy from the microscopic probabilities of particle motion <math>p \propto e^{-E/kT}</math>, where k is the Boltzmann constant and T is temperature. In the RBM network the relation is <math> p = e^{-E} / Z </math>, the stochastic binary neuron outputs a probability that its state is 0 or 1. The data input is normally not considered a layer, but in the Helmholtz machine generation mode, the data layer receives input from the middle layer and has separate weights for this purpose, so it is considered a layer. Hence this network has 3 layers.

Comparison of networks

{| class="wikitable"

! !! Hopfield !! Boltzmann !! RBM !! Stacked RBM || Helmholtz !! Autoencoder !! VAE

| Usage & notables || CAM, traveling salesman problem || CAM. The freedom of connections makes this network difficult to analyze. || pattern recognition. used in MNIST digits and speech. || recognition & imagination. trained with unsupervised pre-training and/or supervised fine tuning. || imagination, mimicry ||  language: creative writing, translation. vision: enhancing blurry images || generate realistic data

| Neuron || deterministic binary state. Activation = { 0 (or -1) if x is negative, 1 otherwise } || stochastic binary Hopfield neuron || ← same. (extended to real-valued in mid 2000s) || ← same || ← same ||  language: LSTM. vision: local receptive fields. usually real valued relu activation. || middle layer neurons encode means & variances for Gaussians. In run mode (inference), the output of the middle layer are sampled values from the Gaussians.

| Connections || 1-layer with symmetric weights. No self-connections. || 2-layers. 1-hidden & 1-visible. symmetric weights. || ← same. no lateral connections within a layer. || top layer is undirected, symmetric. other layers are 2-way, asymmetric. || 3-layers: asymmetric weights. 2 networks combined into 1. ||  3-layers. The input is considered a layer even though it has no inbound weights. recurrent layers for NLP. feedforward convolutions for vision. input & output have the same neuron counts. || 3-layers: input, encoder, distribution sampler decoder. the sampler is not considered a layer

| Inference & energy || Energy is given by Gibbs probability measure :<math>E = -\frac12\sum_{i,j}{w_{ij}{s_i}{s_j+\sum_i{\theta_i}{s_i}</math> || ← same || ← same ||  || minimize KL divergence || inference is only feed-forward. previous UL networks ran forwards AND backwards || minimize error = reconstruction error - KLD

| Training || Δwij = si*sj, for +1/-1 neuron || Δwij = e*(pij - p'ij). This is derived from minimizing KLD. e = learning rate, p' = predicted and p = actual distribution.

|| Δwij = e*( < vi hj >data - < vi hj >equilibrium ). This is a form of contrastive divergence w/ Gibbs Sampling. "<>" are expectations. || ← similar. train 1-layer at a time. approximate equilibrium state with a 3-segment pass. no back propagation. || wake-sleep 2 phase training ||  back propagate the reconstruction error || reparameterize hidden state for backprop

| Strength || resembles physical systems so it inherits their equations || ← same. hidden neurons act as internal representatation of the external world || faster more practical training scheme than Boltzmann machines || trains quickly. gives hierarchical layer of features || mildly anatomical. analyzable w/ information theory & statistical mechanics ||  ||

| Weakness ||  || hard to train due to lateral connections ||  equilibrium requires too many iterations || integer & real-valued neurons are more complicated. ||  ||  ||

Hebbian Learning, ART, SOM

The classical example of unsupervised learning in the study of neural networks is Donald Hebb's principle, that is, neurons that fire together wire together.