Another con might be that it's random. Similar to how gen-ai is random, it seems like Monte Carlo Integration might give slightly different results every time.
adam2451
I wonder if the randomness is fixed by doing the integration over and over again until it converges to a stable value.
jerrymby
I want to have a deeper understanding of the disadvantages of "slow to converge". Is there an estimate of the convergence rate for different functions? I'm thinking about the sampling theory we learned earlier in the class, less samples can create aliased estimates. Maybe the "frequency" of the function is an indicator of the speed of convergence?
zepluc
I think Monte Carlo Intrgration relies on the law of large numbers, where the sample mean converges to the expected value as the number of samples increases. It might generate images with visible noise due to litimted number of samples. However, as the number of samples increases, the results of these random samples will stabilize. Therefore, I don't think random is a big disadvantage for this.
saif-m17
Similar to a few of the other questions, I'm curious about how big a limitation noise can be on monte carlo integration as a method. How often is the error introduced visible? I know it was mentioned in the lecture that we try to create an unbiased method to take advantage of the fact that these estimates should be correct "on average," but I'm curious if there are any specific cases where the impact of noise is more apparent.
danielhsu021202
In Data 102, we learned some techniques to reduce the variance and thus reduce the noise in Monte Carlo based algorithms, and I think it can be applied here too. These include importance sampling, which samples more frequently from "important regions". Another is stratified sampling, which divides the integration domain into subregions and samples these subregions separately to reduce variance.
yangbright-2001
I remember CS188 discussed Monte Carlo Tree search in games, it also adopts the idea of random, e.g., it enables the "machine" to randomly pay hundreds of chess games randomly
llejj
Are there ways to determine the variance of the underlying function that we are sampling from (to help determine the convergence rate)?
Another con might be that it's random. Similar to how gen-ai is random, it seems like Monte Carlo Integration might give slightly different results every time.
I wonder if the randomness is fixed by doing the integration over and over again until it converges to a stable value.
I want to have a deeper understanding of the disadvantages of "slow to converge". Is there an estimate of the convergence rate for different functions? I'm thinking about the sampling theory we learned earlier in the class, less samples can create aliased estimates. Maybe the "frequency" of the function is an indicator of the speed of convergence?
I think Monte Carlo Intrgration relies on the law of large numbers, where the sample mean converges to the expected value as the number of samples increases. It might generate images with visible noise due to litimted number of samples. However, as the number of samples increases, the results of these random samples will stabilize. Therefore, I don't think random is a big disadvantage for this.
Similar to a few of the other questions, I'm curious about how big a limitation noise can be on monte carlo integration as a method. How often is the error introduced visible? I know it was mentioned in the lecture that we try to create an unbiased method to take advantage of the fact that these estimates should be correct "on average," but I'm curious if there are any specific cases where the impact of noise is more apparent.
In Data 102, we learned some techniques to reduce the variance and thus reduce the noise in Monte Carlo based algorithms, and I think it can be applied here too. These include importance sampling, which samples more frequently from "important regions". Another is stratified sampling, which divides the integration domain into subregions and samples these subregions separately to reduce variance.
I remember CS188 discussed Monte Carlo Tree search in games, it also adopts the idea of random, e.g., it enables the "machine" to randomly pay hundreds of chess games randomly
Are there ways to determine the variance of the underlying function that we are sampling from (to help determine the convergence rate)?