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Results for geometry
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7
votes
1
answer
825
views
Information geometry tutorial
I would like to know more about the topic of information geometry, but i don't want to delve deeply into it. …
12
votes
2
answers
4k
views
Algebraic Geometry for Statistics
I have heard about uses of Algebraic Geometry in Statistics and Machine Learning. I wanted to try to learn a bit about this topics. … I don't know nearly anything about Algebraic Geometry, but I have background in math, and I know about basic group theory, rings fields and some commutative algebra. …
4
votes
0
answers
161
views
Ay (2017) vs Amari (2016) for information geometry
I am interested in learning information geometry in detail with a focus on applications, and am currently considering two main texts: Amari (2016)'s "Information Geometry and Its Applications" and Ay et … al. (2017)'s "Information Geometry". …
7
votes
0
answers
291
views
Reference Request: Information Geometry for Ridge Regression
Question: I am eager to read empirical type papers where these information geometry techniques are used to compare ridge regressors on real data.
Does anyone know of any such papers? … Note: A question has already been asked about the usefulness of informational geometry.
Using information geometry to define distances and volumes…useful? …
- 1,783
4
votes
2
answers
352
views
Connection between LASSO regression and Taxicab Geometry
The following is written on the Wikipedia entry of Taxicab Geometry:
The [taxicab] geometry has been used in regression analysis since the 18th century, and is often referred to as LASSO. …
- 143
24
votes
3
answers
12k
views
Does differential geometry have anything to do with statistics?
I am doing master in statistics and I am advised to learn differential geometry. … Does anyone happen to know applications for differential geometry in statistics? …
- 1,304
9
votes
1
answer
3k
views
What is the most beginner-friendly book for information geometry?
The book:
Amari and Nagaoka, Methods of Information Geometry,
is often mentioned as a reference for information geometry. … Murray, Differential Geometry and Statistics. …
- 6,479
1
vote
0
answers
139
views
How to learn information geometry from a statistical background [closed]
I have started learning information geometry from the book Differential geometry and Statistics by M.K.murray and J.W. Rice.But I am facing huge difficulties in understanding mathematics behind it. …
3
votes
0
answers
58
views
Examples of Problems in Statistics Accessible only Using Information Geometry
I am just curious if there are some examples of problems in statistics that is indeed accessible using information geometry while proofs completely avoiding geometry is unknown. … In other words, problems solved by considering the statistical model $\mathcal{P}$ in the problem as a statistical manifold and then using results in differential geometry while proofs not really using …
- 639
4
votes
1
answer
377
views
Regression coefficient on a triangle using geometry
My question is: how to compute $\beta_1$ based on geometry? If we draw the graph, we could see that we are doing a right-top triangle within the unit square $[0,1] \times [0,1]$. …
- 143
11
votes
1
answer
488
views
Clarification in information geometry
This question is concerned with the paper Differential Geometry of Curved Exponential Families-Curvatures and Information Loss by Amari.
The text goes as follows. …
- 1,181
0
votes
1
answer
71
views
Question about Geometry of statistical model
I am reading "Methods of information geometry by Shun-ichi Amari"
and I got the following doubt
Let $X$ be a finite set and $P(X)=\{p:X\to\mathbb{R}/p(x)>0 \forall x\in X,\int p(x)dx=1\}$
which in turn …
- 133
5
votes
3
answers
649
views
References for use of symplectic geometry in statistics?
I have heard that many problems in Mathematical Statistics can be stated and solved in terms of Symplectic Geometry. …
- 153
1
vote
3
answers
329
views
Algorithm for generating a Poisson process on a complicated 2d geometry
Given a $\lambda$ parameter for a county, I need to simulate a Poisson realization of events on that county geometry. … However if I have an irregular geometry, then the algorithm will generate points outside of the boundaries of a county. …
- 1,582
4
votes
0
answers
80
views
Intuition/meaning of information geometry distances and geodesics?
In information geometry, we consider a manifold of probability distributions, together with the Fisher Information metric (given by the Fisher Information matrix). …
- 1,405