Category: Theory

Posted on

18. Representations: Classes, Trajectories, Transitions

Vocabulary

In a semantic net, a diagram of relations between objects, essential notions can be defined as follows:

  • Combinators: linking objects together
  • Reification: actions implying results
  • Localization: a frame where objects and actions happen
  • Story sequence: a series of actions happening linearly in time

Classification

In natural language, knowledge is generally organized from general categories to basic objects and finally specific objects.

Transition

Another element of language is recording change in the evolution of objects during the unfolding of stories.

Trajectory

Language also tracks movement in the description of actions.

An agent makes an object move from a source to a destination using a instrument. A co-agent may be involved, the action might be aimed towards a beneficiary, and the motion may be helped by a conveyance, etc. In English, preposition tend to be used to define the role of each part in the action, enabled recording of interactions.

Language corpuses, such as the Wall Street Journal Corpus, are generally composed of 25% of transition or trajectory.

Story sequences

Agents’ action determine transitions in the semantic net, which result in trajectories.

Story libraries

Each type of story implies a number of characteristics that correspond to the situation. Example: events can be disasters or parties, they have a time and place, involved people, casualties, money, places…

Posted on

17. Learning: Boosting

“Wisdom of a weighted crowd of experts”

Classifiers

Classifiers are tests that produce binary choices about samples. They are considered strong classifiers if their error rate is close to 0,  weak classifiers if their error rate is close to 0.5.

By using multiple classifiers with different weights, data samples can be sorted or grouped according to different characteristics.

Decision tree stumps

Aside from classifiers, a decision tree can be used to sort positive and negative samples in a 2-dimension space. By adding weights to different tests, some samples can be emphasized over the others. The total sum of weights must always be constrained to 1 to ensure a proper distribution of samples.

Dividing the space

By minimizing the error rate of the tests from the weights, the algorithm can cut the space to sort positive and negative examples.

No over fitting

Boosting algorithms seems not to be over fitting, as the decision tree stumps tends to be very tightly close to outlying samples, only excluding them from the space.

Posted on

16. Learning: Support Vector Machines

Decision boundaries

Separating positive and negative example with a straight line that is as far as possible from both positive and negative examples, a median that maximizes the space between positive and negative examples.

Constraints are applied to build a support vector (u) and define a constant b that allow to sort positive examples from negative ones. The width of a “street” between the positive and negative values is maximized.

Going through the algebra, the resulting equation show that the optimization depends only on the dot product of pair of samples.

The decision rule that defines if a sample is positive or negative only depends on the dot product of the sample vector and the unknown vector.

No local maximum

Such support vector algorithm can be proven to be evolving in a convex space, meaning that it will never be blocked at a local maximum.

Non linearity

The algorithm cannot find a median between data which cannot be linearly separable. A transformation can however be applied to the space to reorganize the samples so that they can be linearly separable. Certain transformations can however create an over fitting model that becomes useless by only sorting the example data.

Posted on

15. Learning: Near Misses, Felicity Conditions

One-shot learning

Learning in human-like way, in one shot: learning something definite from each example.

The evolving model

Comparing an initial model example, a seed, with a near miss or another example, the evolving model understands an important characteristic for each new near miss or example compared.

The evolving model develops a set of heuristics to describe the seed, specializing with near misses (reducing the potential matches) or generalizing with examples (broadening the potential matches) the characteristics of the seed.

  • Require link heuristic: specialization
  • Forbid link heuristic: specialization
  • Extend set heuristic: generalization
  • Drop link heuristic: generalization
  • Climb tree heuristic: generalization

Felicity conditions

The teacher and learner must know about each other to achieve the best learning. The learner must talk to himself to understand what he is doing.

How to package ideas better

To better communicate ideas to others in order to achieve better results, the following 5 characteristics makes communication more effective.

  • Symbol: ease to remember the idea
  • Slogan: focus the idea
  • Surprise: catch the attention
  • Salient: one thing to stand out
  • Story: helps transmission to people
Posted on

14. Learning: Sparse Spaces, Phonology

Visual recognition to sound production

Words can be classified in tables representing the 14 features of each sound, notably if they are “voiced” or not. With such a matrix of sounds, a “speaking machine” can be built to produce words and sentences.

Example: a machine pronouncing plurals

The machine processes from recognition through different characteristics of words (verbs, nouns, plurals…) and constraints (pronunciation of plural) to produce sounds. The machine’s input comes from visual recognition and its output is sounds to mimic a voice to produce the right sound, “z“, “s” or “e-z“.

  1. The vision apparatus recognizes objects
  2. The information flows to the meaning register, labeling the objects, as well as through characteristics register to define if they are plural or not
  3. The information from the meaning register also flows through the characteristics register to define if they are nouns or verbs, and to a buffer which stores the beginning of the word letters while waiting to know if a “z” or “s” or “e-z” plural sound needs to be added.
  4. The buffer letters moves to be processed by the pronunciation apparatus, waiting to be processed by the plural constraint.
  5. The word is send to the plural constraint processor.
  6. If the word is plural and the last letter is voiced, the constraint adds a “z” sound, if not voiced an “s” sound is added. If the word is not plural, nothing is added, ending the word’s pronunciation.

Such machine is called a propagator as connections are reversible: by hearing a plural word, the machine can figure where are many of the objects to be seen by the visual apparatus.

Building phonological algorithm

  1. Collect + and – examples
  2. Pick and seed positive
  3. Generalize by churning useless information where + and – examples are not differentiated
  4. Quit when cover a negative example, or go back to step 3 and generalize more

Sparse space

The plural machine works because in a high dimensional sparse space, a hyperplane can easily separate two sets of examples, as phonemes constitutes a 14-dimension space.

Generalizing to problem solving with AI

  1. Define the problem
  2. Devise a representation suiting the problem
  3. Determine an approach / method
  4. Pick a mechanism or devise an algorithm
  5. Experiment

Troubles ensues when people focus on a specific mechanism rather the problem at hand.

The right representation does the following:

  • it makes the problem explicit
  • it exposes constraint
  • it generates localness to solve the problem: the answer can be pinpointed rather than gathered from various sources, areas, places, etc.