31–40 of 56 posts
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1. https://www.youtube.com/watch?v=iN_BDcKhtWk
2. https://en.wikipedia.org/wiki/Time_loop
3. https://en.wikipedia.org/wiki/List_of_films_featuring_time_l...
"The bullshit here is the implicit claim of an author that German language is needed. Maybe it is for advanced applications (like Goethe's poetry), but it is certainly not needed to describe basic ideas."
(proceeds to explain the same basic concepts 10x more verbose than in any math textbook on the subject)
Math/statistics nomenclature is certainly not perfect (think of it as a general utilities library that has been in active development for 200+ years), but it is widely used for a reason: once you learn the language it becomes second nature (very much the same as knowing all the details of the standard library API in your language of choice) allowing to communicate arbitrarily complex abstract ideas with speed and precision.
The intuition is, you set up a graph where the vertices are names, and the edges are based on name similarity. Two names are neighbors if e.g. their edit distance is within some limit. You start at a random name, then at the neighbors, flip a biased coin with the ratio of the P(x) of your current name and the neighbor, if heads you move to the neighbor.
I'm sure this is wrong in many and subtle ways, but when I read an article like this I expect some intuition like this to be imparted.
Earlier quoted context omitted.
Could you explain further please? I agree with what you're saying but I don't' understand how it applies to what I said so there's definitely something I could learn here. Edit: Thanks.
Sure. As I see MCMC it’s basically a mathematical trick that lets you sample from probability distributions even if you only know the relative probability of different samples. It’s based on the observation that some Markov processes have a stationary distribution that is identical to a distribution you may want to sample from. But you need to carefully construct the Markov process for that observation to hold, and t…
Earlier quoted context omitted.
But a random walk is precisely a stochastic process for which the _next state_ depends only on the _current state_. In terms of graphs (where _random walk_ comes from), the next node is decided by randomly selecting a neighbor of the current node.
That's not true for random walks in general I don't think. A random walk is a process derived from taking random steps in some mathematical space. It can include jumps and it can include memory. Take a "path-avoiding" random walk. At time t the distribution of the next step depends on whether or not I have at some point hit any of the adjacent nodes in the current path. That's not the current state, that's memory.
Given a graph, a random walk is a sequence of vertices [v1, v2, ..., vk] such that each v{i+1} is selected uniformly at random from the neighbors of vi.
In weighted graphs, the next vertex is chosen with probability proportional to edge weights.
Earlier quoted context omitted.
But a random walk is precisely a stochastic process for which the _next state_ depends only on the _current state_. In terms of graphs (where _random walk_ comes from), the next node is decided by randomly selecting a neighbor of the current node.
That's not true for random walks in general I don't think. A random walk is a process derived from taking random steps in some mathematical space. It can include jumps and it can include memory. Take a "path-avoiding" random walk. At time t the distribution of the next step depends on whether or not I have at some point hit any of the adjacent nodes in the current path. That's not the current state, that's memory.
Earlier quoted context omitted.
That's not true for random walks in general I don't think. A random walk is a process derived from taking random steps in some mathematical space. It can include jumps and it can include memory. Take a "path-avoiding" random walk. At time t the distribution of the next step depends on whether or not I have at some point hit any of the adjacent nodes in the current path. That's not the current state, that's memory.
A random walk on a graph is a stochastic process that starts at a vertex and, at each step, moves to a randomly chosen neighboring vertex. Formally: Given a graph, a random walk is a sequence of vertices [v1, v2, ..., vk] such that each v{i+1} is selected uniformly at random from the neighbors of vi. In weighted graphs, the next vertex is chosen with probability proportional to edge weights.
Hmm. I'm not an expert, but some of this seems definitely not to be accurate. Some of the "Bullshit" turns out perhaps to be quite important. Take the statement: > Markov Chain is essentially a fancy name for a random walk on a graph Is that really true? I definitely don't think so. To my understanding, a Markov process is a stochastic process that has the additional (aka "Markov") property that it is "memoryless". T…
I won’t pretend to know the technical details (as the other replies do) but I want to make a point for the “pedagogical” effect here, which I agree with the author. The way I interpret the article, it’s not supposed to be a deep, theoretical treatise on the subject; more of an introductory, “intuitive” take on it. This works for those who need to either learn the concept to begin with, or refresh their memories if th…
Earlier quoted context omitted.
I won’t pretend to know the technical details (as the other replies do) but I want to make a point for the “pedagogical” effect here, which I agree with the author. The way I interpret the article, it’s not supposed to be a deep, theoretical treatise on the subject; more of an introductory, “intuitive” take on it. This works for those who need to either learn the concept to begin with, or refresh their memories if th…
I see, where you're coming from, but in that particular case, the "intuitive" explanation (walk on a graph) is far less intuitive for me than the proper explanation, that a Markov process is memoryless. That said, I used MCMC in the past to do physics simulation, where the Markov property also applies to the underlying physical process. So maybe it's just me.
Hmm. I'm not an expert, but some of this seems definitely not to be accurate. Some of the "Bullshit" turns out perhaps to be quite important. Take the statement: > Markov Chain is essentially a fancy name for a random walk on a graph Is that really true? I definitely don't think so. To my understanding, a Markov process is a stochastic process that has the additional (aka "Markov") property that it is "memoryless". T…
As in, the state you track is no longer the probability that you have ended at a given node at time T, but instead includes a new vector of the probability you have visited the node at any time in the past (which can be obtained from PDF of location from previous time step + stochastic "diffusion").
So, we're randomly walking over a graph, but the graph is not the same as the graph used in MCMC. The MCMC graph is the state with random transitions that must model what you want to observe. That separation does not violate the statement that "it's just a random walk" it just severely complicates it I suppose.