Hi James! Thank you so much for sharing this video. It is beneficial to my research. I'm wondering would you mind to also talk about the Practical Filter?
Thank you very much for this video! But how we obtain w_i given that target distribution is unknown or we can't easily sample from it? Are we using sensor measurementsfor this , to estimage w_i? And then, using w_i and proposal distribution we can approximate target distribution ? Probably, it follows from 3:00 of a video.
Hey! Thanks for your question. So at 3:00, we are writing the definition of what w is (always true), and since we know the form of the target and proposal distribution (these specific forms come from what we are trying to compute in state estimation), we find that w is simply proportional to p(y_t|x_t) which is our measurement model. And great news! We have the measurement model. Hence, we can find our target distribution given our proposal distribution using the measurement model. Does that clear things up?
@@jameshan8 Thank you so much, but still not clear if we can or need sample from target distribution? Because it is really confusing that we use g(x_i) without mentioning that we try to estimate it.
@@ocamlmail Sorry I'm not completely understanding your question, and I want to answer it correctly, so may you please try re-wording your question? g(x) is a deterministic function: when we consider something like y = g(x) + n, g(x) is exact and 'n' is the noise. So, we don't sample from g(x). We use the sensor model equation 'y=g(x)+n' to compute p(y|x), which is what we use as the importance weight.
@@jameshan8 Sorry for delay. I don't understand how we compute w_i. From it's equation w_i = g(x_i)/f(x_i). We don't know g(x). Moreover, I thought that it is target distribution function which we "approximate" with f(x), where we know f(x) and how to sample from f(x), namely f(x_i). Next, given our sensors, we can measure something and calculate w_i. So it looks like we caluclate w_i = (some sensor measure)/f(x_i), both RHS are perfectly known. Then we use this w_i to calc. target distribution, so it looks like g(x_i) ~ (some sensor measure). I still confuse how we calculate w_i. Put it simply, given video and your comments: 1) w_i is proportioanal to some measurement model (is it measurments from sensors, btw?). 2) given w_i we can calculate target distr. by g(x_i) = w_i*f(x_i); Is this correct? If so, I just confused how we obtained formula for 1) because we derive it via target distribution so it seems a little bit recursive to me. It is not that we have some independant from g(x) way of determining w_i, source of measurment. What relations between g(x) and measurement model?
the problem with this explanation is that it's a mindless set of whats, eg: do this then do that then do this etc. What would be really useful is every so often discussing the need for that step, why (not what) it's there etc. atm this video just sounds like someone reading out of a book with fancy diagrams.
Great when slowed down to 0.75 :D
Thank you for teaching me this!
Thank you
Hi James! Thank you so much for sharing this video. It is beneficial to my research. I'm wondering would you mind to also talk about the Practical Filter?
Hi Frank! You're welcome! Unfortunately I'm not familiar with the Practical Filter, so I'm unable to help you... Good luck with your research!
Thank you very much for this video!
But how we obtain w_i given that target distribution is unknown or we can't easily sample from it? Are we using sensor measurementsfor this , to estimage w_i? And then, using w_i and proposal distribution we can approximate target distribution ?
Probably, it follows from 3:00 of a video.
Hey! Thanks for your question. So at 3:00, we are writing the definition of what w is (always true), and since we know the form of the target and proposal distribution (these specific forms come from what we are trying to compute in state estimation), we find that w is simply proportional to p(y_t|x_t) which is our measurement model. And great news! We have the measurement model. Hence, we can find our target distribution given our proposal distribution using the measurement model. Does that clear things up?
@@jameshan8 Thank you so much, but still not clear if we can or need sample from target distribution? Because it is really confusing that we use g(x_i) without mentioning that we try to estimate it.
@@ocamlmail Sorry I'm not completely understanding your question, and I want to answer it correctly, so may you please try re-wording your question? g(x) is a deterministic function: when we consider something like y = g(x) + n, g(x) is exact and 'n' is the noise. So, we don't sample from g(x). We use the sensor model equation 'y=g(x)+n' to compute p(y|x), which is what we use as the importance weight.
@@jameshan8 Sorry for delay. I don't understand how we compute w_i. From it's equation w_i = g(x_i)/f(x_i). We don't know g(x). Moreover, I thought that it is target distribution function which we "approximate" with f(x), where we know f(x) and how to sample from f(x), namely f(x_i). Next, given our sensors, we can measure something and calculate w_i. So it looks like we caluclate w_i = (some sensor measure)/f(x_i), both RHS are perfectly known. Then we use this w_i to calc. target distribution, so it looks like g(x_i) ~ (some sensor measure). I still confuse how we calculate w_i.
Put it simply, given video and your comments:
1) w_i is proportioanal to some measurement model (is it measurments from sensors, btw?).
2) given w_i we can calculate target distr. by g(x_i) = w_i*f(x_i);
Is this correct? If so, I just confused how we obtained formula for 1) because we derive it via target distribution so it seems a little bit recursive to me. It is not that we have some independant from g(x) way of determining w_i, source of measurment. What relations between g(x) and measurement model?
the problem with this explanation is that it's a mindless set of whats, eg: do this then do that then do this etc. What would be really useful is every so often discussing the need for that step, why (not what) it's there etc. atm this video just sounds like someone reading out of a book with fancy diagrams.
Thanks for the feedback! I will keep that in mind for the future
video is awesome, but the music in the background is totally unnecessary ://