37 reputation
4
bio website cs.umd.edu/~jasonfil
location College Park, Maryland
age 26
visits member for 2 years, 7 months
seen Nov 28 at 21:41

CS Researcher / PhD student.


Nov
1
accepted Computation of a limit where De l'Hospital's rule yields no results
Nov
1
comment Computation of a limit where De l'Hospital's rule yields no results
Well, that was embarassing. Any ideas on why one of two fractions would work instead of either?
Nov
1
asked Computation of a limit where De l'Hospital's rule yields no results
May
10
comment On the semantics of the gamma distribution
That's the essence of the work that I (and my colleagues) have been carrying out. More or less, we've ported a Prolog - based activity recognition system to a probabilistic logic programming framework which, unlike a Prolog-based system, acknowledges probabilities in its input. The paper describing this system is under review for publication by the TPLP journal but I'm able to refer people to the technical report version here: arxiv.org/abs/1204.1851. I'm looking into ways to refine the probability generation described in section 8 of that paper because it is done rather crudely.
May
10
comment On the semantics of the gamma distribution
I don't mind at all. The goal is to develop an activity recognition system under uncertainty. Recognize high level events of interest given a series of short term events. These short term events are captured by cameras. In the dataset I'm using, there's no information about the noise that these cameras have to face; I'd like to make a realistic assumption about the noise, and one such assumption is that the short term events are captured with a degree of certainty, represented by a so-called detection probability. The lower the probability, the higher the noise, and vice - versa.
May
10
awarded  Supporter
May
10
comment On the semantics of the gamma distribution
I am not aware of any other way in which I could draw random numbers from a distribution, and naturally constrain them in the interval between 0 and 1 to make sure that these random numbers are probabilities. The reason for which I'm using a gamma distribution and not a gaussian or an exponential one is that, to the best of my knowledge, gamma noise is the noise produced by sensors, cameras, etc and what I'm trying to do is emulate this noise.
May
10
comment On the semantics of the gamma distribution
Actually, the more I think about it, the more my question seems self-answerable from the semantics of the mean and the mode themselves: Since I will need to sample a bunch of random numbers from every single PDF, it is the mean, and not the mode, that I want to revolve around from.
May
10
comment On the semantics of the gamma distribution
If you will notice, the constraining of the CDF as well as the hardcoding of either the mean or the mode to 0.1, 0.2 and so on give me a system of 2 equations, which I can then solve to obtain both k and θ.
May
10
comment On the semantics of the gamma distribution
Absolutely. I'd like to model noise in the form of probabilities. I'd like to represent different levels of noise, some more severe (probabilities close to 0), some less (probabilities close to 1). What I've been doing is constrain the CDF as pre-mentioned (so that I don't compromise the distribution's shape) and set the mode to 0.1, 0.2, 0.3 and 0.4. These choices will give me low probabilities; when it's time to obtain higher probabilities, I "mirror" the distribution at 0.5 by sampling the 1-complement of these values. My question is:do I set the mode or mean to those hardcoded values?
May
10
accepted On the semantics of the gamma distribution
May
10
comment On the semantics of the gamma distribution
Thanks, I got it. Here's another relevant question: I have been using the distribution's CDF (link to exact characterization: en.wikipedia.org/wiki/Gamma_Distribution) to make sure that my parameters k and θ are such that 98% of the distribution's mass is between 0 and 1. Moreover, I want to vary either the mean or the mode so that the distribution tends to produce values closer to 0 or to 1. Given this short discussion, would you prefer to constrain the mode so that it is close to 0 (or 1) or the mean to be close to 0 or 1? Mathematically, θ*(κ-1) =0.1 or θ*k = 0.1;
May
10
asked On the semantics of the gamma distribution
May
8
awarded  Scholar
May
8
accepted Question on y axis of Gamma probability distribution
May
8
awarded  Student
May
8
asked Question on y axis of Gamma probability distribution
May
8
awarded  Autobiographer