# Technology

Inatas uses technology based on decision theoretic generalizations of Bayesian Networks. Our technology is the result of research into machine learning and artificial intelligence using statistical methods. It is the current cutting edge of statistical analysis and offers enormous benefits for users. On this page you will find:

- An overview of Bayesian networks
- An explanation of how such technology can be extended to provide for automated decision making
- An explanation of Inatas' compatibility with other applications
- An explanation of some of Inatas' most important technical advantages
- A comparison chart of the features provided by Inatas and its direct competitors

The explanation of Inatas' advantages is, of necessity, quite technical. However it is worth examining - particularly the discussion about the use of meta-models. If you have questions, please feel free to contact us.

## Bayesian Networks

Bayesian Networks are the latest generation technology from the fields of artificial intelligence and machine learning. They have featured in MIT's Technology Review list of emerging technologies that will change the world.

In essence, Bayesian Networks pull apart joint probability distributions through their conditional independencies by means of the chain rule of probability, rendering calculations that are intractable with a naive use of the joint distribution computable. This means that Bayesian Networks, alone among complex stochastic modeling technologies, are able to work directly with probability distributions without simplifying assumptions. This has significant advantages:

- Improved predictive accuracy.
- Increased information, including:
- Aposteriori probability distributions for all variables of interest (rather than simply classifications regarding values such variables are most likely to take).
- Principled Confidence Intervals/Error Bars for these aposteriori probability estimates.
**Inatas Only**

Further, the network structure which encodes the found conditional independencies has a number of extremely useful properties, including:

- Providing an easily understandable graphic model of how the variables relate to one another (see here).

This permits intuitive checks on the results provided by the network, as well as assisting in the use of the network in explaining decisions and predictions made to both expert and lay audiences. - Providing information regarding what subset of the system is required to obtain complete knowledge of the influences on the variables that we are interested in. This permits advanced redundancy examination of the variables involved, and can provide substantial cost benefits when data acquisition is expensive.

## Automated Decision Making

Bayesian Networks can be generalized to provide decision theoretic capabilities. This is done by specifying:

- The utility to you of the system being modeled being in particular states.
- The variables that are under your control. These represent the decisions you are to make.
- The variables that, if they are not currently known, will be known at the time a given decision is made.

So generalized, the network can produce decision policies, informing you of the optimal settings for the variables under your control given the knowledge you have of the system being modeled at the time of the decision.

## Compatibilities

Inatas products are able to import and export to any ODBC data source. Such data sources include all major relational databases.

It is also possible to import data from text files and export results to LaTex pdf scripts.

## Inatas Technical Advantages

### Structural Learning **Inatas Only**

When learning the network structure, by default Inatas products search over the 'Markov Equivalence Classes' of possible structures. Basic structural learning involves examining the relative merit of competing network topologies, and maximizing this fitness using a variety of heuristic methods. However, different topologies can encode the same conditional independencies, and the number of topologies encoding a particular set of conditional independencies may vary by many orders of magnitude. Searching graph topologies by heuristic methods therefore effectively assigns a prior on the set of conditional independencies that the final network will represent, making those represented by many topologies much more likely to be selected even if they perform relatively poorly. To avoid this unwanted bias, we search equivalence classes of topologies. This is a large improvement, which has been made possible by recent developments in the underlying mathematics. As well as producing more accurate models, it permits the use of learning algorithms with optimality guarantees. Inatas is currently the only commercial company providing these advanced techniques - though you can choose to search basic topologies as well, if you wish.

### Inference **Inatas Only**

When performing inference on a network or meta-model Inatas provides the option of utilizing second order probabilities to obtained principled estimates of the density of the probability density function located within a specified vicinity of the maximum aposteriori probability estimates. The principle step in this procedure is the differentiation of the probability functions involved in the calculations of aposteriori probabilities. The result of this is that we are able to provide principled error bars around the aposteriori probability estimates outputted by the model. This allows users to judge the confidence you should have in particular outputs, which is important even in the best models, since new cases may lie on the fringe of the model's knowledge.

### Meta Models **Inatas Only**

Models can - and should - be thought of as hypotheses regarding the relationships that hold between the variables of the system being modeled. Results, such as predictions of the values certain variables will take or the decision policies that will maximize expected utility, are predicated on the model being either a correct representation of the system or at least sufficiently close to the correct representation that it provides useful information regarding how the system functions.

However, models - like hypotheses - are themselves more or less probable given observations of the system they model. It is therefore possible to use a collection of models,
weighting each by their aposteriori likelihood, to obtain more robust predictions and decision policies: We no longer obtain results *given* a hypothesis, but results
that take into account the hypotheses that undergird them!

It is such a collection of models which we term a meta-model, and Inatas' use of meta-models is one of its most significant technological advantages. We cannot, of course, include all possible networks in a meta-model. However, since, with any reasonably sized data set to learn from, the most probable networks dominate the aposteriori probability distribution, we can often obtain results based on upward of 99% of the weighted hypotheses.

We believe that Inatas provides the only commercially available Bayesian Network based stochastic modeling technology that includes meta-models, and we are certain that we provide the only commercially available technology that permits the utilization of meta-models for automated decision making.

### Speed

Inatas' software was programmed in highly optimized, very low level C++. The result is an extremely efficient application: We estimate that Inatas System Modeler can process more information in four hours than a pure R implementation could in a year.

The importance of this goes far beyond convenience: It is necessary to process massive amounts of information to perform high quality structural learning procedures. Inatas is, perhaps uniquely, able to provide this.

## Competitor Comparison

The following is correct to the best of our knowledge. Please contact us with any corrections.

Company | GUI | Learn Parameters | Learn Structure | Searches Equivalence Classes | Meta Models | Utility | Meta Models Utility | Confidence Intervals | Export/Import to Relational Databases | API | 64 bit |
---|---|---|---|---|---|---|---|---|---|---|---|

Inatas | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes | For automation | Yes |

Agena | Yes | Yes | No | No | No | No | No | No | No | Yes | No |

Bayesia Ltd | Yes | Yes | Yes | No | No | Yes | No | No | No | No | No |

Bayes Server | Yes | Yes | No | No | No | No | No | No | No | Yes | No |

Bayes Ware | Yes | Yes | Yes | No | No | No | No | No | No | No | No |

DeriveIt LLC | No | Yes | Yes | No | No | No | No | No | No | No | No |

Hugin | Yes | Yes | Conditional Independency Testing | No | No | Yes | No | No | No | Yes | Yes |

HyperGraph Software | Yes | Yes | Yes | No | No | No | No | No | No | No | No |

Lumina | Yes | No | No | No | No | Yes | No | No | Yes | Yes | Yes |

Noetic Systems | Yes | No | No | No | No | No | No | No | No | Yes | No |

Norsys | Yes | Yes | Yes | No | No | No | No | No | No | Yes | No |

Structured Data | No | No | Yes | No | No | No | No | No | No | Yes | No |