Decision network - artificial-intelligence

Do you know what is this, and How they represent decisions (using probabilities) in Decision Theory
Are they similar to decision trees?

Yes, they share similar concepts, and both mainly contains: decision nodes & chance nodes.
Except in a network, you don't necessarily start from one node but it could start with a combination of different nodes, and instead of every node taking a single input in tree, in a network, a decision/chance could be based on multiple inputs.
e.g. in a single node in a network : Weather=Sunny + Holiday=True => go for a hike=True.
so you dont need to split it into multiple nodes as in trees.
In general, their differences are similar as to trees and graphs in a traditional sense. You should be able to work out a decision network easily if you are familiar with decision trees.
Hope this is helpful.

Related

Multiple Keys for exact and approximate lookups in C

I am trying to develop a network resource manager component in C which keeps track of various network elements over TCP/UDP sockets. For this, I use three values :
Hardware Location Number
Service Group Number
Node Number
The rule is that no two elements on a network may have the same set of these three numbers. Thus, each location's identity will be unique on the network. This information needs to be saved in the program (non-persistently) in a way so that given any of the parameters (could be just a single number, or a combination of any two, or all three) the program returns the eligible candidates by performing a quick search.
The addition and deletion should also be efficient, but given that there will be few insertions or deletions after the initial transient phase if they are a bit slower than search, it should be OK. Using trees is one option, but the answer of 'Which one to use?' still eludes me (Not that I know of many, but I look forward to learning newer ones if they serve my purpose).
To do this, I could have three different trees maintained separately with similar nodes pointing to a same structure in memory, but I feel that is inefficient and not compact. I am looking for a unified data set which can handle these variations like multiple keys.
Or I could have a single AVL tree with multiple keys (if that is allowed).
The number of elements in the network is dynamic, so using a 3D array is out of option.
A friend also suggested hashing, but I am not too sure.
Please help.
Hashing seems like a silly choice for this. Perhaps the most significant reason is that you seem interested in approximate lookups. Hashing your values will likely mean iterating through the entire collection to find a group of nodes that have a common prefix, or a similar prefix.
PATRICIA is commonly used in routing tables, and makes itself quite amenable to searching for items that have similar keys. Note that I have found much misleading information about PATRICIA tries, which I've written about here. I found this resource to be particularly helpful.
Similarly to an AVL tree, you'll need to combine the three keys to form one (without hashing, preferably).
unsigned int key[3] = { hardware_location_number, service_group_number, node_number };
/* ^------- Use something like this as your key */

Does a Decision Network / Decision Forest take into account relationships between inputs

I have experience dealing with Neural Networks, specifically ones of the Back-Propagating nature, and I know that of the inputs passed to the trainer, dependencies between inputs are part of the resulting models knowledge when a hidden layer is introduced.
Is the same true for decision networks?
I have found that information around these algorithms (ID3) etc somewhat hard to find. I have been able to find the actual algorithms, but information such as expected/optimal dataset formats and other overviews are rare.
Thanks.
Decision Trees are actually very easy to provide data to because all they need is a table of data, and which column out of that data what feature (or column) you want to predict on. That data can be discrete or continuous for any feature. Now there are several flavors of decision trees with different support for continuous and discrete values. And they work differently so understanding how each one works can be challenging.
Different decision tree algorithms with comparison of complexity or performance
Depending on the type of algorithm you are interested in it can be hard to find information without reading the actual papers if you want to try and implement it. I've implemented the CART algorithm, and the only option for that was to find the original 200 page book about it. Most of other treatments only discuss ideas like splitting with enough detail, but fail to discuss any other aspect at more than a high level.
As for if they take into account the dependencies between things. I believe it only assumes dependence between each input feature and the prediction feature. If the input was independent from the prediction feature you couldn't use it as a split criteria. But, between other input features I believe they must be independent of each other. I'd have to check the book to ensure that was true or not, but off the top of my head I think that's true.

How should I store a sparse decision tree(move list) in a database?

I have been thinking of making an AI for a board game for a long time, and recently I've started to gather resources and algorithms. The game is non-random, and most of the time, there < 3 moves for a player, sometimes, there are >20 moves. I would like to store critical moves, or ambiguous moves so that the AI learns from its mistakes and will not make a same mistake the next time. Moves that surely win or lose need not be stored. So I actually have a sparse decision tree for the beginning of games.
I would like to know how I should store this decision tree in a database? The database does not need to be SQL, and I do not know which database is suitable for this particular problem.
EDIT: Please do not tell me to parse the decision tree into memory, just imagine the game as complicated as chess.
As you will be traversing the tree, neo4j seems like a good solution to me. SQL is no good choice because of the many joins you would need for queries. As i understand the question, you are asking for a way to store some graph in a database, and neo4j is a database explicitely for graphs. For the sparseness, you can attach arrays of primitives or Strings to the edges of your graph to encode sequences of moves, using PropertyContainers (am i right that by sparseness and skipping of nodes you mean your tree-edges are sequences of moves rather than single moves?).
Firstly what you are trying to do sounds like a case based reasoning(CBR) problem see: http://en.wikipedia.org/wiki/Case-based_reasoning#Prominent_CBR_systems . CBR will have a database of decisions, your system would in theory pick the best outcomes available.
Therefore I would suggest using neo4j which is a nosql graph database. http://neo4j.org/
So to represent your game each position is a node in the graph, and each node should contain potential moves from said position. You can track scoring metrics which are learnt as games progress so that the AI is more informed.
I would use a document database (NOSQL) like RavenDB because you can store any data structure in the database.
Documents aren't flat like in a normal SQL database and that allows you to store hierarchical data like trees directly:
{
decision: 'Go forward',
childs: [
{ decision: 'Go backwards' },
{
decision: 'Stay there',
childs: [
{ decision: 'Go backwards' }
]
}
]
}
Here you can see an example JSON tree which can be stored in RavenDB.
RavenDB also has a built-in feature to query hierarchical data:
http://ravendb.net/faq/hierarchies
Please look at the documentation to get more information how RavenDB works.
Resources:
What type of NoSQL database is best suited to store hierarchical data?
You can use memory mapped file as storage.
First, create "compiler". This compiler will parse text file and convert it into compact binary representation. Main application will map this binary optimized file into memory. This will solve your problem with memory size limitation
Start with a simple database table design.
Decisions:
CurrentState BINARY(57) | NewState BINARY(57) | Score INT
CurrentState and NewState are a serialized version of the game state. Score is a weight given to the NewState (positive scores are good moves, negative scores are bad moves) your AI can update these scores appropriately.
Renju, uses a 15x15 board, each location can be either black, white or empty so you need Ceiling( (2bits * 15*15) / 8 ) bytes to serialize the board. In SQL that would be a BINARY(57) in T-SQL
Your AI would select the current moves it has stored like...
SELECT NewState FROM Decisions WHERE CurrentState = #SerializedState ORDER BY Score DESC
You'll get a list of all the stored next moves from the current game state in order of best score to least score.
Your table structure would have a Composite Unique Index (primary key) on (CurrentState, NewState) to facilitate searching and avoid duplicates.
This isn't the best/most optimal solution, but because of your lack of DB knowledge I beleive it would be the easiest to implement and give you a good start.
If I compare with chess engines, those play from memory, maybe apart from opening libraries. Chess is too complicated to store a decinding decision tree. Chess engines play by assigning heuristic evaluations to potential and transient future positions (not moves). Future positions are found by some kind of limited depth search, may be cached for some time in memory, but often are plainly recalculated each turn as the search space is just too big to store in a way faster to look up than recalculating is possible.
Do you know Chinook — the AI that solves checkers? It does this by compiling a database of every possible endgame. While this is not exactly what you are doing, you might learn from it.
I can't clearly conceive neither the data structures you handle in your tree nor their complexity.
But here are some thoughts which may interest you :
Map your decision tree into sparse matrix, a tree is a graph after all
Devise a storage/retrieval strategy taking advantage of sparse matrix properties.
I would approach this with the traditional way an opening book is handled in chess engines:
Generate all possible moves
For each move:
Make that move
Look the resulting position up in your database
Undo the move
Make the move that had the highest score in your database
Looking up a move
Chess engines usually compute a hash function of the current game state via Zobrist hashing, which is a simple way to construct a good hash function for gamestates.
The big advantage of this approach is that it takes care of transpositions, that is, if the same state can be reached via alternate paths, you don't need to worry about those alternate paths, only about the game states themselves.
How chess engines do this
Most chess engines use static opening books that are compiled from recorded games and hence use a simple binary file that maps these hashes to a score; e.g.
struct book_entry {
uint64_t hash
uint32_t score
}
The entries are then sorted by hash, and thanks to operating system caching, a simple binary search through the file will find the needed entries very quickly.
Updating the scores
However, if you want the engine to learn continously, you will need a more complicated data structure; at this point it is usually not worth doing yourself, and you should use an available library. I would probably use LevelDB, but anything that lets you store key-value pairs is fine (Redis, SQLite, GDBM, etc.)
Learning the scores
How exactly you update the scores depends on your game. In games with a lot of data available, a simple approach such as just storing the percentage of games won after the move that resulted in the position works; if you have less data, you can store the result of a game tree search from the position in question as score. Machine learning techniques such as Q learning are also a possibility, although I do not know of a program that actually does this in practice.
I'm assuming your question is asking about how to convert a decision tree into a serial format that can be written to a location and later used to reconstruct the tree.
Try using a pre-order traversal of the tree, using a toString() function (or its equivalent) to convert the data stored at each node of the decision tree to a textual descriptor. By pre-order traversal, I mean implementing an algorithm that first performs the toString() operation on the node, and writes the output to a database or file, and then recursively performs the same operation on its child nodes, in a specified order. Because you are dealing with a sparse tree, your toString() operation should also include information about the existence or non-existence of subtrees.
Reconstructing the tree is simple - the first stored value is the root node, the second is the root member of the left subtree, and so on. The serial data stored for each node should provide information as to which subtree the next inputted node should belong to.

How to turn Prim's algorithm into Kruskal's algorithm?

I've implemented Prim's algorithm in C (www.bubblellicious.es/prim.tar.gz) but I was just wondering how to transform this into Kruskal's algorithm.
It seems they're quite similar, but I can't imagine how can I modify my old code into that new one. It'd be delicious if you give some advices or something. I know that's easy, but I'm still a n00b in C programming ...
Why not just write Kruskal's from scratch and see how they compare in your own solutions? Best way to learn.
To convert you need a forest (i.e. a set of trees where initially each node is a tree) as your temporary output structure rather than a single tree. Then on each step, rather than finding the cheapest vertex that adds a currently unconnected node to your tree, you find the cheapest edge in the graph and, if it creates a new tree (i.e. connects two previously unconnected nodes) add that tree to the forest and remove the source trees. Otherwise discard the edge.
A proper implementation of Kruskal is more memory intensive but less time intensive than a proper Prim implementation.
But the differences between the two are quite large. Probably all you can keep between are some helper functions and some data structures. Not a conversion, more a rewrite using more high level building blocks.
Why dont you consider switching to C++ and using the boost graph library
(http://www.boost.org/)?
It contains very well implementations for both algorithms. Type-safe and highly performant.
See kruskal_minimum_spanning_tree and prim_minimum_spanning_tree

Are nested intervals a viable solution to nested set (modified pre-order traversal) RDBMS performance degredation?

Among the known limitations of Joe Celko's nested sets (modified pre-order traversal) is marked degredation in performance as the tree grows to a large size.
Vadim Tropashko proposed nested intervals, and provides examples and theory explanation in this paper: http://arxiv.org/html/cs.DB/0401014
Is this a viable solution, are there any viable examples (in any language) abstracted away from the native DB layer?
While I've seen examples for nested sets, I haven't seen much for nested intervals, although in theory it shouldn't be difficult to convert from one to the other. Instead of doing pre-order traversal to label the nodes, do a breadth-first recursion. The trick is to work out the most efficient way of labelling n children of a node. Since the node between a/b and c/d is (a+c)/(b+d), an ill-conditioned insert (for instance, inserting the children left to right), runs the risk of creating the same exponential growth in the index values as, for instance, using a full materialized path. It is not difficult to counteract this effect - create the new indexes one at a time, inserting each at the location that produces the lowest resulting denominator.
As far as performance degradation goes, much depends on the operations you intend to do. There are still some operations that will require a complete relabeling of the entire tree - the nested set or nested interval methods both work best for structures that seldom change. If you are doing a lot of structure changes to the hierarchy, the 'standard' parent-child table structure may be easier to work with. remember too that some operations (such as number of descendants) are far easier with the integer labeling of nested sets than the interval methods.
I have written a gem that abstracts away all the computations of nested intervals to be used with Rails's ActiveRecord https://github.com/clyfe/acts_as_nested_interval/ used in production on several systems.

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