What is to be learned?

Relative frequency
Co-occurrence statistics: joint, conditional probabilities
`hat A(D) = text{argmax}_A\ p(A|D)`
(A: analysis, D: data)
Categories and categorization (classification)
Sequence classification (labeling)
Clustering
Dimensionality reduction
Segmentation
How to perform a task

Language models

n-gram models
Predict the next unit (usually word) in a sequence from the previous n-1 units; assign a probability to a sequence of units. A bigram model:
`P(w_1, w_2, w_3, ..., w_n) ~~ P(w_1|S_0) * P(w_2|w_1) * ... * P(w_n|w_(n-1)) * P(S_f|w_n)`
Language model: assigns a probability to a sequence of words (or other units) in a particular language.

Classifiers and clustering

Given some input (values for a set of features), assign it to one of a finite set of classes (perhaps with a probability).
Naive Bayes classifiers: probability of a particular class given a vector of features is a function of the probability of the class, the probability of the features, and the probability of the features given the class.
`p(c|f_1, f_2, ..., f_n) = (p(f_1, f_2, ..., f_n|c) p(c)) / (p(f_1, f_2, ..., f_n))`
Decision list classifiers: a sequence of tests is applied to an input; when a test succeeds, a class is returned; otherwise other tests in the last are applied in sequence.
Support vector machines: construct hyperplanes that maximally separate classes in high-dimensional feature space
Clustering (usually unsupervised, unlike classifiers)

Inferring hidden states and events

Hidden Markov models and sequence classification
- A sequence of observed units is viewed as resulting from a sequence of hidden causal states
- Two problems
  - Given an HMM, find the best set of labels
  - Learn the parameters of an HMM, given some data
Noisy channel models
- An observed event is viewed as a noisy version of a hidden event; separate the process into two factors (using Bayes' theorem)
- `hat H = text{argmax}_H\ p(O|H)\ p(H)`
Log-linear models
- The probability of the hidden event (given the observed event) is viewed as a function of a log-linear combination of weighted values for a set of feature functions of the hidden and observed events
- `hat H = text{argmax}_H\ text{exp} [sum_m^M lambda_m h_m(H,O)]`

Variations on knowledge-based models

Probabilistic grammars: combine linguistic and statistical methods.

S → NP VP PU               [.80]
NP → JJ NN                 [.20]
NP → JJ NNS                [.15]
NP → NP PP                 [.30]
VP → VBD NP                [.35]
PP → IN NP                 [.85]

NN → news [.001] | effect [.0005]
NNS → markets  [.0002]
JJ → economic [.001] | little [.01] | financial [.001]
VBD → had  [.10]
IN → on  [.18]
PU → .

Learning dependency parsing: learn scores for different parsing actions using graph created so far and a stack of unfinished nodes as features

Vector-space models

A word can be described in terms of a very large set of features, such as its co-occurrence statistics with other words or a reduced set of such features.
These features define a representational space for words in which they can be compared for similarity, etc.

Reinforcement learning

The task is defined in terms of a (usually) finite set of states and actions.
At any given time, the system selects an action, based on its current state and its long-term memory for the consequences of previous actions.
On the basis of the action selected (and the state), the system receives a reinforcement from the environment; it updates is long-term memory accordingly.