Since joint entropy is commonly used to quantify the average information of random variables, in order to compare the amount of information, can we directly compare the joint entropy of multivariate normal distributions with different dimensions? (e.g., one MVN with 2x2 covariance matrix while another MVN with 4x4 covariance matrix)
2026-03-26 07:58:35.1774511915
Compare differential entropy of multivariate Gaussian with different dimensions
494 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in INFORMATION-THEORY
- KL divergence between two multivariate Bernoulli distribution
- convexity of mutual information-like function
- Maximizing a mutual information w.r.t. (i.i.d.) variation of the channel.
- Probability of a block error of the (N, K) Hamming code used for a binary symmetric channel.
- Kac Lemma for Ergodic Stationary Process
- Encryption with $|K| = |P| = |C| = 1$ is perfectly secure?
- How to maximise the difference between entropy and expected length of an Huffman code?
- Number of codes with max codeword length over an alphabet
- Aggregating information and bayesian information
- Compactness of the Gaussian random variable distribution as a statistical manifold?
Related Questions in ENTROPY
- Relation between Shanon entropy via relation of probabilities
- How to maximise the difference between entropy and expected length of an Huffman code?
- Appoximation of Multiplicity
- Two questions about limits (in an exercise about the axiomatic definition of entropy)
- Computing entropy from joint probability table
- Joint differential entropy of sum of random variables: $h(X,X+Y)=h(X,Y)$?
- What is the least prime which has 32 1-bits?
- Eggs, buildings and entropy
- Markov chains, entropy and mutual information
- Entropy and Maximum Mutual Information
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
No, because there is no operational interpretation of differential entropy in the first place (and thus no common ground on which one could reasonably make a comparison). Cf. the Cross Validated question on differential entropy.
If you have two pairs of multivariate Gaussians, one for each dimension, then you may interpret differences of KL divergence as how much faster Neyman–Pearson hypothesis testing distinguishes one pair relative to the other, à la Stein's lemma.