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5.8 Shapley Values | Interpretable Machine Learning
The Shapley value of a feature value is not the difference of the predicted value after removing the feature from the model training. The interpretation of the Shapley value is: Given the current set of feature values, the contribution of a feature value to the difference between the actual prediction and the mean prediction is the estimated Shapley value.

The Shapley value is the wrong explanation method if you seek sparse explanations (explanations that contain few features). Explanations created with the Shapley value method always use all the features. Humans prefer selective explanations, such as those produced by LIME. LIME might be the better choice for explanations lay-persons have to deal with. Another solution is SHAP introduced by Lundberg and Lee (2016)41, which is based on the Shapley value, but can also provide explanations with few features.
computers  programming  machinelearning  maths  gametheory  statistics 
9 days ago by pozorvlak
Structured disentangled representations
How to interpret the various terms in the ELBO objective function, and how to generalise it to variational autoencoders (VAEs) with several latent variables.
computers  programming  maths  statistics  machinelearning  ai  deeplearning 
19 days ago by pozorvlak
Don’t waste your time on statistics - Towards Data Science
So if you’re dealing with uncertainty (e.g. “Will this machine learning system work on tomorrow’s data?”) and the options aren’t each alike in dignity (e.g. “We probably shouldn’t launch it unless it works.”) then you’ve come to the right place: statistics is for you. Zoom through its main ideas here. Everyone else, flee now before you end up crunching a bunch of numbers meticulously… and uselessly. Analytics is a better option for you.
maths  statistics  datascience 
25 days ago by pozorvlak
The Behavioral Approach to Open and Interconnected Systems
Studying control theory via relations rather than functions, because real systems have feedback loops rather than strict inputs and outputs.
maths  physics  engineering  controltheory 
5 weeks ago by pozorvlak
Common probability misunderstanding: half heads?
As n -> infinity, the probability of getting exactly n/2 heads tends to zero.
maths  statistics  probability 
7 weeks ago by pozorvlak
Golden strings & rabbit constant
Golden strings are analogous to Fibonacci numbers, except one uses concatenation rather than addition. Start with s1 = "1" and s2 = "10". Then define sn = sn-1
7 weeks ago by pozorvlak
Floating point error is the least of my worries
Modeling error is usually several orders of magnitude greater than floating point error. People who nonchalantly model the real world and then sneer at floating point as just an approximation strain at gnats and swallow camels.

maths  modelling  computers  programming  floatingpoint 
8 weeks ago by pozorvlak
SafeCurves: Introduction
Secure implementations of the standard curves are theoretically possible but very hard.

Most of these attacks would have been ruled out by better choices of curves that allow simple implementations to be secure implementations. This is the primary motivation for SafeCurves. The SafeCurves criteria are designed to ensure ECC security, not just ECDLP security.
security  infosec  crypto  maths  computers 
8 weeks ago by pozorvlak
Curve Ed448 and Karatsuba multiplication
The elliptic curve Ed448 is nicknamed "Goldilocks" for reasons explained here. It uses an algorithm requiring three multiplications where you'd expect four.
crypto  maths  algorithms  computers  security  infosec 
8 weeks ago by pozorvlak
What leads to success at math contests? | Power Overwhelming
"What leads to success at math contests?"

Highly generalisable advice, related somewhat to…
maths  learning  olympiads 
9 weeks ago by pozorvlak
Why Do We Pay Pure Mathematicians? – Math with Bad Drawings
"Like most researchers in her subfield [she] considers any number larger than 5 to be monstrously big."
maths  comics 
9 weeks ago by pozorvlak
Napkin | Power Overwhelming
Huge amounts of maths explained as if on the back of a napkin.
9 weeks ago by pozorvlak
Against the “Research vs. Olympiads” Mantra | Power Overwhelming
But we need this kind of problem-solving skill and talent too much for it to all be spent on computing R(6,6).
maths  olympiads  research  jobs 
9 weeks ago by pozorvlak
foxes are totally trustworthy — naamahdarling: thetasteoffire: ...
Just as the phrase “what the entire fuck” implies the existence of fractional fucks, the phrase “what the absolute fuck” implies the existence of both positive and negative fucks (or else there would be no need for an absolute value operation). Taken together with the phrase “what the actual fuck” (which implies the existence of imaginary fucks), we may thus conclude that fuckery is isomorphic with the complex field.
maths  funny 
9 weeks ago by pozorvlak
Following an idea to its logical conclusion
Following an idea to its logical conclusion might be extrapolating a model beyond its valid range.
models  maths  measurement  geometry  physics 
10 weeks ago by pozorvlak
Going Critical — Melting Asphalt
What I learned from the simulation above is that there are ideas and cultural practices that can take root and spread in a city that simply can't spread out in the countryside. (Mathematically can't.) These are the very same ideas and the very same kinds of people. It's not that rural folks are e.g. "small-minded"; when exposed to one of these ideas, they're exactly as likely to adopt it as someone in the city. Rather, it's that the idea itself can't go viral in the countryside because there are...
networking  socialnetworks  publichealth  vaccines  maths  dataviz  science  badscience  academia 
may 2019 by pozorvlak
The Subtle Art of the Mathematical Conjecture | Quanta Magazine
Mathematical conjectures as mountain summits, by @RHDijkgraaf:

For more ways in which moun…
maths  research  climbing 
may 2019 by pozorvlak
realhats v3.0
realhats is a package for LATEX that makes the \hat command put real hats on symbols.
tex  maths  funny  unicode 
april 2019 by pozorvlak
Good–Turing frequency estimation - Wikipedia
Good–Turing frequency estimation is a statistical technique for estimating the probability of encountering an object of a hitherto unseen species, given a set of past observations of objects from different species. In drawing balls from an urn, the 'objects' would be balls and the 'species' would be the distinct colors of the balls (finite but unknown in number). After drawing R red {\displaystyle R_{\text{red}}} R_\text{red} red balls, R black {\displaystyle R_{\text{black}}} R_\text{black} black balls and R green {\displaystyle R_{\text{green}}} R_\text{green} green balls, we would ask what is the probability of drawing a red ball, a black ball, a green ball or one of a previously unseen color.
maths  statistics  algorithms 
april 2019 by pozorvlak
Mean, variance, skewness & kurtosis computed with a fold
The sample statistics mean, variance, skewness, and kurtosis can be calculated in one pass through the data. We show how to do this with a fold operation.
maths  programming  statistics  algorithms  haskell  probability 
april 2019 by pozorvlak
Runge-Kutta implemented as a fold in Haskell
An ordinary differential equation solver like the famous Runge Kutta method is naturally expressed as a fold in functional programming.
computers  programming  maths  algorithms  haskell 
april 2019 by pozorvlak
Two types of viewpoint | David R. MacIver
A thamagar viewpoint can’t see the wood for the trees. A relip one can’t see the leaves for the tree. When you work in your area of expertise, your viewpoint is thamagar. When you explain it to someone unfamiliar with it, you try to give them a relip view.

The way you look at the ingroup is usually thamagar, and the way you look at the outgroup is usually relip. Combinatorics is thamagar, category theory is relip. Writing a poem requires you to be thamagar, teaching someone requires you to be relip.
teaching  maths  learning 
march 2019 by pozorvlak
The woman who invented abstract algebra | Cosmos
In Noether’s time, the scientific establishment worked hard to keep women out. A genius of Noether’s calibre, with Einstein’s backing, could maybe be included. Even today, in mathematics or physics, we can observe an asymmetry in the treatment of women and men in academia.

And as Emmy Noether taught us, whenever a symmetry is broken, that means something is being lost.
maths  antisemitism  sexism  physics  nazism  womeninstem  women 
march 2019 by pozorvlak
Going beyond the Golden Ratio. | Extreme Learning
The three "most irrational" (hardest to approximate with rationals) numbers are

- phi = (1 + sqrt(5))/2, the Golden Ratio
- 1 + sqrt(2)
- (9 + sqrt(221))/10
maths  dataviz 
march 2019 by pozorvlak
The Math That Unifies the Laws of Physics
In my 50s, too old to become a real expert, I have finally fallen in love with algebraic geometry. As the name suggests, this is the&;
maths  physics  quantum 
march 2019 by pozorvlak
Unscrambling the Hidden Secrets of Superpermutations | Quanta Magazine
A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What
maths  sf  superpermutations  computers  algorithms  4chan 
february 2019 by pozorvlak
[1806.07366] Neural Ordinary Differential Equations
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.
maths  deeplearning  machinelearning  computers  programming  ai 
january 2019 by pozorvlak
The FedEx Problem | Hacker News
How did FedEx choose their hub airport? How do they do flight scheduling? Some war stories from an early-hire operational researcher.
aircraft  shippingcontainers  optimization  startups  business  maths 
january 2019 by pozorvlak
Unprovability comes to machine learning
Ben-David and colleagues then prove that the ability to carry out a weak form of monotone compression is related to the size of certain infinite sets. The set that the authors ultimately use in their work is the unit interval, which is the set of real numbers between 0 and 1. Their results imply that the finite subsets of the unit interval have monotone-compression schemes, and therefore are learnable in EMX, if and only if the continuum hypothesis is true, which is known to be unprovable.
machinelearning  maths  logic 
january 2019 by pozorvlak
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