Plotting Stochastic gradient Descent

Question

I need to plot this surface. It turns out it was plotted in Matlab. I don’t have access to Matlab so I did the whole thing in python and got the x, y and z for the surface.

This is how it looks:

Is there any chance that this could be made with tikZ?

These are the coordinates:

learning rate: 
[0.0,
 0.0,
 0.0,
 0.0,
 0.005,
 0.005,
 0.005,
 0.005,
 0.01,
 0.01,
 0.01,
 0.01,
 0.015,
 0.015,
 0.015,
 0.015]

rmse:

[2.7689,
 2.7687,
 2.7688,
 2.7688,
 0.9809,
 0.9417,
 0.9268,
 0.9231,
 0.9486,
 0.9243,
 0.9306,
 0.9316,
 0.9406,
 0.934,
 0.9381,
 0.9419]

number of epochs:


[10, 20, 30, 40, 10, 20, 30, 40, 10, 20, 30, 40, 10, 20, 30, 40]

Algorithm:

Implementation of the algorithm:

def SGD(data):
    '''Learn the vectors p_u and q_i with SGD.
       data is a dataset containing all ratings + some useful info (e.g. number
       of items/users).
    '''

    n_factors = 10  # number of factors
    alpha = .01  # learning rate
    n_epochs = 10  # number of iteration of the SGD procedure

    # Randomly initialize the user and item factors.
    p = np.random.normal(0, .1, (data.n_users, n_factors))
    q = np.random.normal(0, .1, (data.n_items, n_factors))

    # Optimization procedure
    for _ in range(n_epochs):
        for u, i, r_ui in data.all_ratings():
            err = r_ui - np.dot(p[u], q[i])
            # Update vectors p_u and q_i
            p[u] += alpha * err * q[i]
            q[i] += alpha * err * p[u]


def estimate(u, i):
    '''Estimate rating of user u for item i.'''
    return np.dot(p[u], q[i])

mwe

\ documentclass{article}

\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}

\pgfplotsset{compat=1.3}

\begin{document}
\thispagestyle{empty}

\begin{tikzpicture}
    \begin{axis}
    \addplot3[patch,patch refines=3,shader=faceted interp,patch type=biquadratic] 
        table[z expr=x^2-y^2]
    {
        x y
        -2 -2
        2 -2
        2 2
        -2 2
        0 -2
        2 0
        0 2
        -2 0
        0 0
    };
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 1

I'm having trouble with your function. It seems, as I understand it, to rely on a dataset and user ratings that I don't have. I'm looking for a multivariable function such as f(x,y)= x^2*y^2. Using this f(x,y), I have a proof of concept for your problem. xcoords = [10, 20, 30, 40] is one of your vectors, say p, and ycoords = [0,1,2,3] is the other vector q. Set the axis of tikzpicture to use your values (10,40,0,3) to get the following code.

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepackage{sagetex}
\pgfplotsset{compat=1.15} 
\begin{document}
\begin{sagesilent}
xcoords = [10, 20, 30, 40]
ycoords = [0,1,2,3]

output = ""
output += r"\begin{tikzpicture}[scale=1.0]"
output += r"\begin{axis}[xmin=%d, xmax=%d, ymin=%d, ymax=%d]"%(10,40,0,3)
output += r"\addplot3[surf,mesh/rows=%d] coordinates {"%(4)
# 4 is the number of y values
for y in ycoords:
    for x in xcoords:
        output += r"(%f, %f, %f) "%(x,y,x^2*y^2)

output += r"};"
output += r"\end{axis}"
output += r"\end{tikzpicture}"
\end{sagesilent}
\sagestr{output}
\end{document}

Here is the output running in Cocalc:

You can adapt this example to your specific data and your f(x,y). Remember that SAGE is not part of LaTeX; the best way to use the sagetex package is through a free Cocalc account.