Command line completion (CLC) an illustration of learning and - PowerPoint PPT Presentation

Command line completion (CLC) an illustration of learning and decision making using the imprecise Dirichlet model Erik Quaeghebeur – p. 1/15

Classical CLC in action login: erik Password: Last login: Tue Feb 17 08:24:47 on tty1 command-prompt$ _ – p. 2/15

Classical CLC in action login: erik Password: Last login: Tue Feb 17 08:24:47 on tty1 command-prompt$ log<TAB> logger login logname logout command-prompt$ log_ – p. 2/15

Classical CLC in action login: erik Password: Last login: Tue Feb 17 08:24:47 on tty1 command-prompt$ log<TAB> logger login logname logout command-prompt$ logn<TAB> command-prompt$ logname <ENTER> erik command-prompt$ _ – p. 2/15

Classical CLC in action login: erik Password: Last login: Tue Feb 17 08:24:47 on tty1 command-prompt$ log<TAB> logger login logname logout command-prompt$ logn<TAB> command-prompt$ logname <ENTER> erik command-prompt$ ls<ENTER> mail/ logic.dvi logic.tex command-prompt$ _ – p. 2/15

Classical CLC in action login: erik Password: Last login: Tue Feb 17 08:24:47 on tty1 command-prompt$ log<TAB> logger login logname logout command-prompt$ logn<TAB> command-prompt$ logname <ENTER> erik command-prompt$ ls<ENTER> mail/ logic.dvi logic.tex command-prompt$ dvips log_ – p. 2/15

Classical CLC in action login: erik Password: Last login: Tue Feb 17 08:24:47 on tty1 command-prompt$ log<TAB> logger login logname logout command-prompt$ logn<TAB> command-prompt$ logname <ENTER> erik command-prompt$ ls<ENTER> mail/ logic.dvi logic.tex command-prompt$ dvips log<TAB> logic.dvi logic.tex command-prompt$ dvips logic.d<TAB> command-prompt$ dvips logic.dvi _ – p. 2/15

Properties of classical CLC Two completion action types: list the possible completions, or return the unique completion. – p. 3/15

Properties of classical CLC Two completion action types: list the possible completions, or return the unique completion. Rule-based: allows for context dependency, and requires a categorized database of commands. – p. 3/15

Properties of classical CLC Two completion action types: list the possible completions, or return the unique completion. Rule-based: allows for context dependency, and requires a categorized database of commands. User independent: reliable, but does not take command history into account. – p. 3/15

Complementing classical CLC We want to take the command-history into account: Whenever there are multiple completions possible. – p. 4/15

Complementing classical CLC We want to take the command-history into account: Whenever there are multiple completions possible. By building and updating a model for the user’s behavior. – p. 4/15

Complementing classical CLC We want to take the command-history into account: Whenever there are multiple completions possible. By building and updating a model for the user’s behavior. To add completion action types, such as returning the ‘best guess’ completion on the command line, listing a set of ‘best guesses’, listing all possible completions, but ordered. – p. 4/15

The set of possible completions Two illustrative completions: command-prompt$ ha<TAB> halt hash command-prompt$ pin<TAB> pine ping pinky – p. 5/15

The set of possible completions Two illustrative completions: command-prompt$ ha<TAB> halt hash ⇒ Ω ha = { halt , hash } ∋ ω ha command-prompt$ pin<TAB> pine ping pinky ⇒ Ω pin = { pine , ping , pinky } ∋ ω pin – p. 5/15

b b b b The user as a multinomial process Model of the user’s behavior: A priori, there is a fixed probability t command for every command. – p. 6/15

b b b b The user as a multinomial process Model of the user’s behavior: A priori, there is a fixed probability t command for every command. After typing part of a command, the remaining possible completions are chosen with the corresponding conditional probabilities. – p. 6/15

b b b b The user as a multinomial process Model of the user’s behavior: A priori, there is a fixed probability t command for every command. After typing part of a command, the remaining possible completions are chosen with the corresponding conditional probabilities. Graphical representation of a user: ( t halt , t hash ) = ( 1 4 , 3 4 ) halt hash b ∆ ha – p. 6/15

The user as a multinomial process Model of the user’s behavior: A priori, there is a fixed probability t command for every command. After typing part of a command, the remaining possible completions are chosen with the corresponding conditional probabilities. Graphical representation of a user: pinky ( t pine , t ping , t pinky ) b = ∆ pin ( 1 3 , 1 3 , 1 3 ) b pine ping b b – p. 6/15

b b b b b b b b The user as a Markov process Model of the user’s behavior: A priori, there is a fixed probability t command|previous for every command and every previously typed command. – p. 7/15

b b b b b b b b The user as a Markov process Model of the user’s behavior: A priori, there is a fixed probability t command|previous for every command and every previously typed command. After typing part of a command, the remaining possible completions are chosen with the corresponding conditional probabilities for the previous command. – p. 7/15

The user as a Markov process Model of the user’s behavior: A priori, there is a fixed probability t command|previous for every command and every previously typed command. After typing part of a command, the remaining possible completions are chosen with the corresponding conditional probabilities for the previous command. Graphical representation of a user: ∆ pin|halt ∆ pin|hash b b b b b b b b – p. 7/15

Knowledge about the user’s behavior Three models: An exact model: t command is known for all commands. – p. 8/15

Knowledge about the user’s behavior Three models: An exact model: t command is known for all commands. A precise Dirichlet model (PDM): the uncertainty about the exact model is determined by a Dirichlet distribution. Di( � ϑ | h,� t ) halt hash – p. 8/15

Knowledge about the user’s behavior Three models: An exact model: t command is known for all commands. A precise Dirichlet model (PDM): the uncertainty about the exact model is determined by a Dirichlet distribution. Di( � ϑ | h,� t ) halt hash r t = P Di ( � � ϑ | h,� t ) ∆ ha X ( � ϑ )Di( � t )d � P Di ( X | h,� ϑ | h,� � t ) = ϑ – p. 8/15

Knowledge about the user’s behavior Three models: An exact model: t command is known for all commands. An imprecise Dirichlet model (IDM): the uncertainty is determined by a set of Dirichlet distributions. halt hash – p. 8/15

Knowledge about the user’s behavior Three models: An exact model: t command is known for all commands. An imprecise Dirichlet model (IDM): the uncertainty is determined by a set of Dirichlet distributions. T halt hash | | t = P ( � � t = P ( � � ϑ | h, T ) ϑ | h, T ) t ∈ T P Di ( X | h,� P Di ( X | h, T ) = inf � t ) t ∈ T P Di ( X | h,� P Di ( X | h, T ) = sup � t ) – p. 8/15

Observations, Sufficient statistics, and . . . Observations: (a sequence of) executed commands for the multinomial model, or (a sequence of) consecutively executed commands for the Markov model. – p. 9/15

Observations, Sufficient statistics, and . . . Observations: (a sequence of) executed commands for the multinomial model, or (a sequence of) consecutively executed commands for the Markov model. Keep what’s relevant for the model: sufficient statistic , the number of occurrences of the commands � n , or the number of occurrences of a transition between commands N . – p. 9/15

. . . Likelihood functions Likelihood function : likelihood of an exact model given the observations, n ( � a multinomial distribution L � ϑ ) , or a Whittle distribution L N (Θ) , proportional to the n ( � product of the L � ϑ ) for each of the previous commands. – p. 10/15

Learning using a PDM/IDM Updating a Dirichlet distribution using Bayes’ rule: � n ( � ϑ | h,� n ) = Di( t ) L � ϑ ) f ( � ϑ | h,� t,� n | h,� P ( L � t ) � t n = h� t + � n ϑ | h n = h + n,� = Di( h + n ) . – p. 11/15

Learning using a PDM/IDM Updating a Dirichlet distribution using Bayes’ rule: � n ( � ϑ | h,� n ) = Di( t ) L � ϑ ) f ( � ϑ | h,� t,� n | h,� P ( L � t ) � t n = h� t + � n ϑ | h n = h + n,� = Di( h + n ) . Graphically: prior posterior observed halt hash – p. 11/15

Learning using a PDM/IDM Updating a PDM is updating the underlying distribution: � n P ( X | h,� P ( X | h n ,� t ) − → t n ) . – p. 11/15

Learning using a PDM/IDM Updating a PDM is updating the underlying distribution: � n P ( X | h,� P ( X | h n ,� t ) − → t n ) . Graphically: pinky b � t n observed r r pine ping b b � t – p. 11/15

Learning using a PDM/IDM Updating an IDM comes down to updating the corresponding (set of) PDM’s: P ( X | h n , T n ) = t n = h� t + � n inf { P ( X | h n ,� t n ) | h n = h + n,� h + n ,� t ∈ T } . – p. 11/15