How would you visualize a multivariate Gaussian in high dimension (>3D)?
$begingroup$
Obviously, I can't do:
Plot3D[PDF[
MultinormalDistribution[{0, 0,
0}, {{1, 0, 0}, {0, 1, 0} {0, 0, 1}}], {x, y}], {x, -20,
20}, {y, -20, 20}]
How would you suggest me to effectively plot this multivariate probability density function?
plotting visualization
$endgroup$
add a comment |
$begingroup$
Obviously, I can't do:
Plot3D[PDF[
MultinormalDistribution[{0, 0,
0}, {{1, 0, 0}, {0, 1, 0} {0, 0, 1}}], {x, y}], {x, -20,
20}, {y, -20, 20}]
How would you suggest me to effectively plot this multivariate probability density function?
plotting visualization
$endgroup$
$begingroup$
What do you want out of the plot? Is it just informative, or would you plan to use it to actually determine some values of things?
$endgroup$
– MikeY
8 hours ago
$begingroup$
@MikeY, I have a 6D energy landscape I want to visualize.
$endgroup$
– 0x90
7 hours ago
add a comment |
$begingroup$
Obviously, I can't do:
Plot3D[PDF[
MultinormalDistribution[{0, 0,
0}, {{1, 0, 0}, {0, 1, 0} {0, 0, 1}}], {x, y}], {x, -20,
20}, {y, -20, 20}]
How would you suggest me to effectively plot this multivariate probability density function?
plotting visualization
$endgroup$
Obviously, I can't do:
Plot3D[PDF[
MultinormalDistribution[{0, 0,
0}, {{1, 0, 0}, {0, 1, 0} {0, 0, 1}}], {x, y}], {x, -20,
20}, {y, -20, 20}]
How would you suggest me to effectively plot this multivariate probability density function?
plotting visualization
plotting visualization
edited 7 hours ago
0x90
asked 12 hours ago
0x900x90
24719
24719
$begingroup$
What do you want out of the plot? Is it just informative, or would you plan to use it to actually determine some values of things?
$endgroup$
– MikeY
8 hours ago
$begingroup$
@MikeY, I have a 6D energy landscape I want to visualize.
$endgroup$
– 0x90
7 hours ago
add a comment |
$begingroup$
What do you want out of the plot? Is it just informative, or would you plan to use it to actually determine some values of things?
$endgroup$
– MikeY
8 hours ago
$begingroup$
@MikeY, I have a 6D energy landscape I want to visualize.
$endgroup$
– 0x90
7 hours ago
$begingroup$
What do you want out of the plot? Is it just informative, or would you plan to use it to actually determine some values of things?
$endgroup$
– MikeY
8 hours ago
$begingroup$
What do you want out of the plot? Is it just informative, or would you plan to use it to actually determine some values of things?
$endgroup$
– MikeY
8 hours ago
$begingroup$
@MikeY, I have a 6D energy landscape I want to visualize.
$endgroup$
– 0x90
7 hours ago
$begingroup$
@MikeY, I have a 6D energy landscape I want to visualize.
$endgroup$
– 0x90
7 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Full M-dimensional probability distributions are hard to display. However, the conditional distributions at the planes through the origin, showing the densities as cross-cut through the full distribution, can be plotted as contour plots. The conditional distribution of a multinomial Gaussian distribution is also a Gaussian distribution, and therefore the contours are ellipses.
Here are the conditional distributions for some 4-dimensional distributions (w0,w1,w2,w3).
I have used the ConditionalMultinormalDistribution function from Chris.
$endgroup$
add a comment |
$begingroup$
I am not sure what are the answers you are looking for. One way is to utilize color as a fourth dimension; another is to make multiple 3D plots over some grid for the variables non-visualized in those 3D plots.
Here is an example:
Clear[myPDF]
myPDF[x_, y_, z_] :=
Evaluate[PDF[
MultinormalDistribution[{-1, 1, 1}, {{1, 1/2, 0}, {1/2, 1, 0}, {0, 0, 1}}], {x, y, z}]];
myPDF[x, y, z]
(* E^(1/2 (-(1 + x) ((4 (1 + x))/3 -
2/3 (-1 + y)) - (-(2/3) (1 + x) + 4/3 (-1 + y)) (-1 + y) - (-1 +
z)^2))/(Sqrt[6] [Pi]^(3/2)) *)
Multicolumn[
Table[Plot3D[myPDF[x, y, z], {x, -3, 3}, {y, -6, 6},
MeshFunctions -> {#3 &}, MeshShading -> {None, Red, None, Yellow},
PlotRange -> {All, All, {0, 0.08}}, PlotPoints -> 25,
PlotLabel -> Row[{"z=", z}]], {z, -6, 6, 1}], 3]
$endgroup$
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Full M-dimensional probability distributions are hard to display. However, the conditional distributions at the planes through the origin, showing the densities as cross-cut through the full distribution, can be plotted as contour plots. The conditional distribution of a multinomial Gaussian distribution is also a Gaussian distribution, and therefore the contours are ellipses.
Here are the conditional distributions for some 4-dimensional distributions (w0,w1,w2,w3).
I have used the ConditionalMultinormalDistribution function from Chris.
$endgroup$
add a comment |
$begingroup$
Full M-dimensional probability distributions are hard to display. However, the conditional distributions at the planes through the origin, showing the densities as cross-cut through the full distribution, can be plotted as contour plots. The conditional distribution of a multinomial Gaussian distribution is also a Gaussian distribution, and therefore the contours are ellipses.
Here are the conditional distributions for some 4-dimensional distributions (w0,w1,w2,w3).
I have used the ConditionalMultinormalDistribution function from Chris.
$endgroup$
add a comment |
$begingroup$
Full M-dimensional probability distributions are hard to display. However, the conditional distributions at the planes through the origin, showing the densities as cross-cut through the full distribution, can be plotted as contour plots. The conditional distribution of a multinomial Gaussian distribution is also a Gaussian distribution, and therefore the contours are ellipses.
Here are the conditional distributions for some 4-dimensional distributions (w0,w1,w2,w3).
I have used the ConditionalMultinormalDistribution function from Chris.
$endgroup$
Full M-dimensional probability distributions are hard to display. However, the conditional distributions at the planes through the origin, showing the densities as cross-cut through the full distribution, can be plotted as contour plots. The conditional distribution of a multinomial Gaussian distribution is also a Gaussian distribution, and therefore the contours are ellipses.
Here are the conditional distributions for some 4-dimensional distributions (w0,w1,w2,w3).
I have used the ConditionalMultinormalDistribution function from Chris.
answered 11 hours ago
Romke BontekoeRomke Bontekoe
1,326818
1,326818
add a comment |
add a comment |
$begingroup$
I am not sure what are the answers you are looking for. One way is to utilize color as a fourth dimension; another is to make multiple 3D plots over some grid for the variables non-visualized in those 3D plots.
Here is an example:
Clear[myPDF]
myPDF[x_, y_, z_] :=
Evaluate[PDF[
MultinormalDistribution[{-1, 1, 1}, {{1, 1/2, 0}, {1/2, 1, 0}, {0, 0, 1}}], {x, y, z}]];
myPDF[x, y, z]
(* E^(1/2 (-(1 + x) ((4 (1 + x))/3 -
2/3 (-1 + y)) - (-(2/3) (1 + x) + 4/3 (-1 + y)) (-1 + y) - (-1 +
z)^2))/(Sqrt[6] [Pi]^(3/2)) *)
Multicolumn[
Table[Plot3D[myPDF[x, y, z], {x, -3, 3}, {y, -6, 6},
MeshFunctions -> {#3 &}, MeshShading -> {None, Red, None, Yellow},
PlotRange -> {All, All, {0, 0.08}}, PlotPoints -> 25,
PlotLabel -> Row[{"z=", z}]], {z, -6, 6, 1}], 3]
$endgroup$
add a comment |
$begingroup$
I am not sure what are the answers you are looking for. One way is to utilize color as a fourth dimension; another is to make multiple 3D plots over some grid for the variables non-visualized in those 3D plots.
Here is an example:
Clear[myPDF]
myPDF[x_, y_, z_] :=
Evaluate[PDF[
MultinormalDistribution[{-1, 1, 1}, {{1, 1/2, 0}, {1/2, 1, 0}, {0, 0, 1}}], {x, y, z}]];
myPDF[x, y, z]
(* E^(1/2 (-(1 + x) ((4 (1 + x))/3 -
2/3 (-1 + y)) - (-(2/3) (1 + x) + 4/3 (-1 + y)) (-1 + y) - (-1 +
z)^2))/(Sqrt[6] [Pi]^(3/2)) *)
Multicolumn[
Table[Plot3D[myPDF[x, y, z], {x, -3, 3}, {y, -6, 6},
MeshFunctions -> {#3 &}, MeshShading -> {None, Red, None, Yellow},
PlotRange -> {All, All, {0, 0.08}}, PlotPoints -> 25,
PlotLabel -> Row[{"z=", z}]], {z, -6, 6, 1}], 3]
$endgroup$
add a comment |
$begingroup$
I am not sure what are the answers you are looking for. One way is to utilize color as a fourth dimension; another is to make multiple 3D plots over some grid for the variables non-visualized in those 3D plots.
Here is an example:
Clear[myPDF]
myPDF[x_, y_, z_] :=
Evaluate[PDF[
MultinormalDistribution[{-1, 1, 1}, {{1, 1/2, 0}, {1/2, 1, 0}, {0, 0, 1}}], {x, y, z}]];
myPDF[x, y, z]
(* E^(1/2 (-(1 + x) ((4 (1 + x))/3 -
2/3 (-1 + y)) - (-(2/3) (1 + x) + 4/3 (-1 + y)) (-1 + y) - (-1 +
z)^2))/(Sqrt[6] [Pi]^(3/2)) *)
Multicolumn[
Table[Plot3D[myPDF[x, y, z], {x, -3, 3}, {y, -6, 6},
MeshFunctions -> {#3 &}, MeshShading -> {None, Red, None, Yellow},
PlotRange -> {All, All, {0, 0.08}}, PlotPoints -> 25,
PlotLabel -> Row[{"z=", z}]], {z, -6, 6, 1}], 3]
$endgroup$
I am not sure what are the answers you are looking for. One way is to utilize color as a fourth dimension; another is to make multiple 3D plots over some grid for the variables non-visualized in those 3D plots.
Here is an example:
Clear[myPDF]
myPDF[x_, y_, z_] :=
Evaluate[PDF[
MultinormalDistribution[{-1, 1, 1}, {{1, 1/2, 0}, {1/2, 1, 0}, {0, 0, 1}}], {x, y, z}]];
myPDF[x, y, z]
(* E^(1/2 (-(1 + x) ((4 (1 + x))/3 -
2/3 (-1 + y)) - (-(2/3) (1 + x) + 4/3 (-1 + y)) (-1 + y) - (-1 +
z)^2))/(Sqrt[6] [Pi]^(3/2)) *)
Multicolumn[
Table[Plot3D[myPDF[x, y, z], {x, -3, 3}, {y, -6, 6},
MeshFunctions -> {#3 &}, MeshShading -> {None, Red, None, Yellow},
PlotRange -> {All, All, {0, 0.08}}, PlotPoints -> 25,
PlotLabel -> Row[{"z=", z}]], {z, -6, 6, 1}], 3]
answered 11 hours ago
Anton AntonovAnton Antonov
23.5k167114
23.5k167114
add a comment |
add a comment |
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$begingroup$
What do you want out of the plot? Is it just informative, or would you plan to use it to actually determine some values of things?
$endgroup$
– MikeY
8 hours ago
$begingroup$
@MikeY, I have a 6D energy landscape I want to visualize.
$endgroup$
– 0x90
7 hours ago