| … | … | @@ -120,19 +120,21 @@ must correspond to the words in a sentences, and the word-order must |
| 120 | 120 | be preserved. |
| 121 | 121 | |
| 122 | 122 | ## Markov logic and Bayesian blankets |
| 123 | | Theorem proving (and generally, constraint-satisfaction) are known hard |
| 124 | | problems, and so, defacto this is what this project is aiming at. All |
| 125 | | the pitfalls apply, including combinatoric explosion, algorithmic |
| 126 | | heuristics, etc. On top of all of this, a very explicit aim is that |
| 127 | | each of the jigsaw pieces and connectors are weighted, so that certain |
| 128 | | kinds of assemblies are preferred over others. Were it not for this |
| 129 | | weighting, one might consider using existing constraint satisfaction |
| 123 | [Theorem proving](https://en.wikipedia.org/wiki/Automated_theorem_proving) |
| 124 | (and generally, |
| 125 | [constraint satisfaction](https://en.wikipedia.org/wiki/Constraint_satisfaction)) |
| 126 | are known hard problems, and so, defacto this is what this project is |
| 127 | aiming at. All the pitfalls apply, including combinatoric explosion, |
| 128 | algorithmic heuristics, etc. On top of all of this, a very explicit aim |
| 129 | is that each of the jigsaw pieces and connectors are weighted, so that |
| 130 | certain kinds of assemblies are preferred over others. Were it not for |
| 131 | this weighting, one might consider using existing constraint satisfaction |
| 130 | 132 | solvers. For example, Answer-Set Programming (ASP) is a particularly |
| 131 | 133 | convenient way of specifying discrete, crisp-logic constraints. More |
| 132 | | generally, one might even consider SAT solvers, or even Satisfiability |
| 133 | | Modules Theories (SMT) solvers. Once on throws in weightings, none |
| 134 | | of the existing SMT solvers appear to be adequate for the job. Thus, |
| 135 | | this project. |
| 134 | generally, one might even consider SAT solvers, or maybe even |
| 135 | [Satisfiability Modules Theories (SMT)](https://en.wikipedia.org/wiki/Satisfiability_modulo_theories) |
| 136 | solvers. Once on throws in weightings, none of the existing SMT solvers |
| 137 | appear to be adequate for the job. Thus, this project. |
| 136 | 138 | |
| 137 | 139 | The goal of saying "weighting" is to avoid saying "probability". In |
| 138 | 140 | reality (based on long experience) the weights do resemble |
| … | … | @@ -142,7 +144,7 @@ theoretical arguments that the correct weighting is the Boltzmann |
| 142 | 144 | distribution, and thus, the assembled jigsaw pieces form a Markov |
| 143 | 145 | blanket. Insofar as the jigsaw pieces can encode logic, the resulting |
| 144 | 146 | blankets can be taken to be Markov Logic blankets. Again, the formation, |
| 145 | | discovery and data-mining of such blankets is a know-hard problem, |
| 147 | discovery and data-mining of such blankets is a known-hard problem, |
| 146 | 148 | filled to the brim with combinatoric explosions, and eminently lacking |
| 147 | 149 | in general tractable algorithms. C'est la vie. |
| 148 | 150 | |
| … | … | @@ -152,14 +154,16 @@ network be directed and acyclic. Thus, again, MLN solvers and Bayesian |
| 152 | 154 | network solvers (belief networks, decision networks) are insufficient to |
| 153 | 155 | tackle the problem at hand. Although the jigsaw connectors can have a |
| 154 | 156 | polarity (and thus connections can be directed), there is no presumed |
| 155 | | constraint that the resulting graph is acyclic. |
| 157 | constraint that the resulting graph is acyclic or directed (or planar, |
| 158 | or has any other long-range properties that aren't encoded in the connector |
| 159 | scheme.) |
| 156 | 160 | |
| 157 | 161 | # Strategic Development Plan |
| 158 | 162 | The above provides an very abstract description of the project, and |
| 159 | 163 | emphasizes just how daunting it is. The abstract goals are not |
| 160 | 164 | achievable in a handful of programmer-years; it is potentially |
| 161 | 165 | some dozens if not hundreds of scientist-years of research effort. |
| 162 | | Thus, a narrower, righter focus is needed. |
| 166 | Thus, a narrower, tighter focus is needed. |
| 163 | 167 | |
| 164 | 168 | ## Characterizing learning systems |
| 165 | 169 | This project is motivated by a need to characterize and evaluate |