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ObjectOfObjects's profile
Object Of Objects
Object Of Objects
Object Of Objects
@ObjectOfObjects

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Object Of Objects

@ObjectOfObjects

IMO, THIS.

Joined September 2014

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    Object Of Objects‏ @ObjectOfObjects Jan 24
    • Report Tweet

    What's the fastest way to sample a random walk on a directed graph conditional on the start and end points?

    12:11 AM - 24 Jan 2020
    • 2 Likes
    • ZowLambda Cause Of Problem
    3 replies 0 retweets 2 likes
      1. New conversation
      2. egbert b. gebstadter‏ @npmedium Jan 24
        • Report Tweet
        Replying to @ObjectOfObjects

        If acyclic, go depth first from source and remove all edges that don't eventually lead to sink then walk randomly uniform over the edges sounds optimal? O(V + E) or something

        1 reply 0 retweets 0 likes
      3. Object Of Objects‏ @ObjectOfObjects Jan 24
        • Report Tweet
        Replying to @npmedium

        I actually need it to work for acyclic graphs. Also, this won't produce the correct distribution because it doesn't penalize entering nodes that had a lot of dead end out-edges.

        1 reply 0 retweets 1 like
      4. 5 more replies
      1. New conversation
      2. GeniesLoki‏ @GeniesLoki Jan 24
        • Report Tweet
        Replying to @ObjectOfObjects

        I haven't checked details but I think following works: Precompute P(ever reaches desired end given uniform walk) using linear algebra Beginning at start, walk sampling each node with weight proportional to the precomputed probability.

        1 reply 0 retweets 0 likes
      3. GeniesLoki‏ @GeniesLoki Jan 24
        • Report Tweet
        Replying to @GeniesLoki @ObjectOfObjects

        This should work. Certainly it gives you a random walk of the right type, and it produces the right answer for sure if all nodes have the same number of out edges (it's a Boltzmann sampler then) but like I say haven't checked details.

        2 replies 0 retweets 0 likes
      4. 4 more replies
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      2. Amateur Slacker‏ @noop_noob Jan 24
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        Replying to @ObjectOfObjects

        Assumption: this is an acyclic graph, and you want each path to have equal probability of occurring. Do a topological sort of the graph. Then, using this sorted order, use dynamic programming to label each node with the number of paths from that node to the destination node.

        1 reply 0 retweets 0 likes
      3. Amateur Slacker‏ @noop_noob Jan 24
        • Report Tweet
        Replying to @noop_noob @ObjectOfObjects

        Finally, sample a path, choosing each node in the path randomly one-by-one. At each step, look at all the possible next nodes, and make the probability of choosing a certain next node proportional to the number on its label.

        0 replies 0 retweets 0 likes
      4. End of conversation

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