Really interesting to see how long ideas take to go mainstream. From my recollection, Oleg and Chung-chieh Shan did this first back in 2009 as a library in OCaml [1,2].
Uncertain
91–100 of 101 posts
Re: Uncertain<T>
#92Earlier quoted context omitted.
https://github.com/klipto/uncertainty
10 years since commit and no attached documents besides a tiny readme. Pass.
Sometimes things can just be "done", and the paper is pretty good documentation if the implementation is faithful to what is described there.
Re: Uncertain<T>
#93Once one understands that a variable (in a programming context) can hold a specification for a variable (in a mathematical context), one opens up incredible doors that are at the foundation of modern AI. When you see y = m * x + b, your recollections of math class may note that you can easily solve for "m" or find a regression for "m" and "b" given various data points. But from a programming perspective, if these are…
This comment seems to conflate variables, functions, and linear systems. I don't think these are worth conflating.
If you store a specification for a probability distribution and give that specification a name, it can behave like a function in that it can be sampled for a scalar output. It can behave like a variable in that you can assign it to a new variable name, play with it as you would anything else in a programming language. And a linear system, perhaps overdetermined, is but one of many ways that the specification can be defined under the hood.
The fact that one can play with complicated nested probability distributions that unify these concepts, as one would play with dolls in a dollhouse, is the point!
Re: Uncertain<T>
#94Earlier quoted context omitted.
While it does sound like GP missed a distinction, I don't see how (-2.35, 2.35) would be sensible. The extremes can happen (or else they wouldn't be part of the input intervals) and the code has to sensibly deal with that event in order to be correct.
Interval arithmetic isn't useful because it only tells you the extreme values, but not how likely these values are. So you have to interpret them as uniform random. Operations like multiplications change the shape of these distributions, so then uniform random isn't applicable any more. Therefore interval arithmetic basically has an undefined underlying distribution that can change easily without being tracked.
> Operations like multiplications change the shape of these distributions, so then uniform random isn't applicable any more.
Doesn't addition as well? Like if you roll d6+d6, the output range is 2-12, but it's not nearly the same as if you rolled d11+1.
Re: Uncertain<T>
#95Back when I was studying physics, we frequently had to do calculations with error propagation. I tried to implement something very similar in C++ and in Python, but never finished it. I also thought it would be neat if a spreadsheet program could understand uncertainties, and also units, so you could enter 1m +- 10cm and it would propagate the errors correctly. If you laid out the data with one column for the values and one for the errors, I had a couple of OpenOffice macros that would perform the calculations.
Another place where I think this would be neat would be in CAD. Imagine if you are trying to create a model of an existing workpiece or of a room, and your measurements don't exactly add up. It's really frustrating and you have to go back and measure again, and you usually end up idealizing the model and putting in rounder numbers to make it fit, but it is less true to reality. It would be cool if you could put in uncertainties for all lengths and angles, and it would run a solver to minimize the total error.
Re: Uncertain<T>
#96Earlier quoted context omitted.
Interval arithmetic isn't useful because it only tells you the extreme values, but not how likely these values are. So you have to interpret them as uniform random. Operations like multiplications change the shape of these distributions, so then uniform random isn't applicable any more. Therefore interval arithmetic basically has an undefined underlying distribution that can change easily without being tracked.
> Operations like multiplications change the shape of these distributions, so then uniform random isn't applicable any more. Doesn't addition as well? Like if you roll d6+d6, the output range is 2-12, but it's not nearly the same as if you rolled d11+1.
Yes that's true! I used multiplication because that was my original example.
Re: Uncertain<T>
#97Once one understands that a variable (in a programming context) can hold a specification for a variable (in a mathematical context), one opens up incredible doors that are at the foundation of modern AI. When you see y = m * x + b, your recollections of math class may note that you can easily solve for "m" or find a regression for "m" and "b" given various data points. But from a programming perspective, if these are…
This sounds super interesting, but as someone who knows little about ML or math in general, could you give an ELI5?
I have a bunch of points. I want to fit a curve to them. I could write a function that takes a bunch of parameters as floats that specify the curve, and an x coordinate as a float, and have it output the most likely y value as a float.
If I have a library, though, that lets me add and multiply not just floats but entire computation subgraphs with the same exact + and * operators, though, I can have the library reverse that function automatically, and say: “optimize the parameters to minimize the difference between the curve and the data points.”
LLMs and other ML systems, to paint with a very broad stroke, solve that problem with billions of parameters in a million-dimensional space. Developing intuition for those high dimensions is hard! But the code is simple because once you’ve done the math for the forward pass, you can go straight from chalkboard to Python code, and the libraries largely assist with reversing and building a GPU-accelerated training process automatically!
Re: Uncertain<T>
#98Earlier quoted context omitted.
Yeah it's probably field specific and I guess Gaussian-based uncertainty would be more about statistical sampling rather than tolerances. I've noticed that if arithmetic is being done on it it's almost certainly Gaussian. I just mean whenever I see uncertainty like this, I don't know what is meant!
In Mechanical Engineering, tolerances ensure that when you put parts together, they will fit as long as the tolerances were respected. It's not statistical. If the machinist makes a part that's not within the +/- bounds, they throw it away and start again. If you tried to fit multiple parts, all with only statistical respect for tolerances, you would run into trouble almost 100% of the time with just a few pieces.
Yeah understood. In electronics: Resistor values are Gaussian but they test and bucket the resistors so that they can be treated as tolerances for similar reasons.
Re: Uncertain<T>
#99Earlier quoted context omitted.
> Operations like multiplications change the shape of these distributions, so then uniform random isn't applicable any more. Doesn't addition as well? Like if you roll d6+d6, the output range is 2-12, but it's not nearly the same as if you rolled d11+1.
Yes that's true! I used multiplication because that was my original example.
Okay, thanks :-). I was just trying to make sure I was understanding what I was reading.
Re: Uncertain<T>
#100Earlier quoted context omitted.
The article says, > Under the hood, Uncertain models GPS uncertainty using a Rayleigh distribution. And the Rayleigh distribution is clearly not just an interval with a uniformly random distribution in between. Normal interval arithmetic isn't useful because that uniform random distribution isn't at all a good model for the real world. Take for example that Boost library you linked. Ask it to compute (-2,2)*(-2,2). I…
While it does sound like GP missed a distinction, I don't see how (-2.35, 2.35) would be sensible. The extremes can happen (or else they wouldn't be part of the input intervals) and the code has to sensibly deal with that event in order to be correct.
-2 and 2 were not the extremes to begin with.