Spaces:
Runtime error
Runtime error
File size: 2,347 Bytes
1fcb538 9131bec 1fcb538 931207e ba93ad8 61a9e50 617fdc7 1f08540 4c6f386 cc7b71f 96f9a87 9131bec 96f9a87 432ab81 96f9a87 617fdc7 96f9a87 9131bec bea8b09 96f9a87 9131bec 16e4f76 9131bec |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 |
import streamlit as st
import numpy as np
import matplotlib.pyplot as plt
st.title('Fitting simple models with JAX')
st.header('A quadratric regression example')
st.markdown('*\"Parametrised models are simply functions that depend on inputs and trainable parameters. There is no fundamental difference between the two, except that trainable parameters are shared across training samples whereas the input varies from sample to sample.\"* [(Yann LeCun, Deep learning course)](https://atcold.github.io/pytorch-Deep-Learning/en/week02/02-1/#Parametrised-models)')
st.latex(r'''h(\boldsymbol x, \boldsymbol w)= \sum_{k=1}^{K}\boldsymbol w_{k} \phi_{k}(\boldsymbol x)''')
# Sidebar inputs
number_of_observations = st.sidebar.slider('Number of observations', min_value=50, max_value=150, value=100)
noise_standard_deviation = st.sidebar.slider('Standard deviation of the noise', min_value = 0.0, max_value=2.0, value=1.0)
cost_function = st.sidebar.radio('What cost function you want to use for the fitting?', options=('RMSE-Loss', 'Huber-Loss'))
np.random.seed(2)
X = np.column_stack((np.ones(number_of_observations),
np.random.random(number_of_observations)))
w = np.array([3.0, -20.0, 32.0]) # coefficients
X = np.column_stack((X, X[:,1] ** 2)) # add x**2 column
additional_noise = 8 * np.random.binomial(1, 0.03, size = number_of_observations)
y = np.dot(X, w) + noise_standard_deviation * np.random.randn(number_of_observations) \
+ additional_noise
fig, ax = plt.subplots(dpi=320)
ax.set_xlim((0,1))
ax.set_ylim((-5,26))
ax.scatter(X[:,1], y, c='#e76254' ,edgecolors='firebrick')
st.pyplot(fig)
# Fitting by the respective cost_function
if cost_function == 'RMSE-Loss':
st.write('You selected the RMSE loss function.')
st.latex(r'''\ell(X, y, w)=\frac{1}{m}||Xw - y||_{2}^2''')
st.latex(r'''\ell(X, y, w)=\frac{1}{m}\big(\sqrt{(Xw - y)\cdot(Xw - y)}\big)^2''')
st.latex(r'''\ell(X, y, w)= \frac{1}{m}\sum_1^m (\hat{y}_i - y_i)^2''')
else:
st.write("You selected the Huber loss function.")
st.latex(r'''
\ell_{H} =
\begin{cases}
(y^{(i)}-\hat{y}^{(i)})^2 & \text{for }\quad |y^{(i)}-\hat{y}^{(i)}|\leq \delta \\
2\delta|y^{(i)}-\hat{y}^{(i)}| - \delta^2 & \text{otherwise}
\end{cases}''')
st.write(X[:5, :]) |